ANTIPROTON DEUTERON INTERACTIONS FROM 1.60
TO 2.90 Ger

Thesis for the Degree of Ph. D‘
”MICHIGAN STATE UNIVERSITY ‘
PAUL STANLEY EASTMAN
1972

 

    
 

Michigan 3 u? ,2
L‘Jivcrsiry ( '

5..
EM: 1'.

ABSTRACT
ANTIPROTON DEUTERON INTERACTIONS
FROM l.60 TO 2.90 GeV/c
By
Paul Stanley Eastman

In a bubble chamber experiment, the cross sections for zero- and
two- through eight-prong topologies, along with the reaction cross sec-

tions within the two through six prong topologies for antiproton mo-

menta from 1.60 to 2.90 GeV/c have been determined. Resonance production

cross sections in antiproton-neutron multipion annihilations for multi-
plicities of three through six pions and their angular and momentum
distributions are presented with comparisons of the predictions of a
multiperipheral model and a statistical model. Particular emphasis has
been given to investigating the isospin-one structure at center-of-mass
energy of 2350 MeV derived from the total cross section measurements

of antiproton-proton and antiproton deuteron interactions. The momen-
tum to momentum dependence of the cross sections shows a possible en-
hancement in the w production channels from the four and six pion anni-
hilations, however further data at lower energies is necessary to con-

firm this enhancement.

 

ANTIPROTON DEUTERON INTERACTIONS
FROM l.60 TO 2.90 GeV/c
By
Paul Stanley Eastman

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Physics

1972

 

,— r (it
C7" 1% Wm.

ACKNOWLEDGMENTS

I wish to express my appreciation to Professor Gerald A. Smith

for his help and guidance throughout the preparation of this thesis.

I would especially like to thank Professor Robert J. Sprafka for
his confidence, his advice, his friendship, and his beer.

I wish also to thank Professor Z. Ming Ma and Dr. Benedict Y. Oh
for help and advice throughout the analysis of this experiment and for
the many helpful suggestions which have been given to me; and to thank
Dr. Donald L. Parker for preceding me and smoothing the obstacles of
analysis.

I also wish to acknowledge the programming efforts of Mr.
Sherwood K. Haynes II who many times has helped me to find the obvious.

I am grateful to our scanning and measuring staff for all their
efforts; and also to the Michigan State University Computing Center
staff without whose special help this thesis would still be many
months from completion.

Last but not least, I would like to thank my wife, Sheila, for
putting up with my research for the last three years.

This research was supported in part by the National Science

Foundation.

ii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS ..................... ii
LIST OF TABLES ..................... v
LIST OF FIGURES ..................... vii
Chapter
l. INTRODUCTION ................... l
2. EXPERIMENTAL PROCEDURES ............. 5
3. TOPOLOGICAL CROSS SECTIONS
3.1 Experimental Methods ............ To
3.2 Cross Sections ............... ll
3.3 Conclusions ................. ll
4. REACTION CROSS SECTIONS
4.1 Experimental Methods ............ l4
4.2 Two Prong Cross Sections .......... 17
4.3 Three and Four Prong Cross Sections ..... 20
4.4 Five and Six Prong Cross Sections ...... 30
4.5 Conclusions . .' ............... 33
5. RESONANCE PRODUCTION IN THE MULTIPION
ANNIHILATIONS
5.l Experimental Methods ............ 38
5.2 Three Pion Final States ........... 41
5.3 Four Pion Final States ........... 41
5.4 Five Pion Final States ........... 46

Chapter Page

5.5 Six Pion Final States ........... 46
5.6 Conclusions ................ 59
6. UPPER LI MT ON THE DECAY w-+ 2n ........ 64
7. ANGULAR AND MOMENTUM DISTRIBUTIONS ....... 69
8. MODELS FOR NUCLEON-ANTINUCLEON
ANNIHILATIONS ................. l20
9'. SUMMARY AND CONCLUSIONS ............ l28
LIST OF REFERENCES .................. 130

iv

Table

10.

ll.

LIST OF TABLES

Topological Event Statistics . . . . . .......

Topological Cross Sections in mb ..........

Reaction Cross Sections (mb) in the Two Prong

Topology Corrected for One Prong Losses ......

Reaction Cross Sections (mb) in the Three

and Four Prong Topologies . . ...........

Reaction Cross Sections (mb) in the Five

and Six Prong Topologies ..............

Reaction Cross Sections (mb) for Multipion

Fits with Spectator Cuts ..............

Resonance production cross sections for the

n+2n' channel ...................

Resonance production cross sections in mb

for the n+2u'w channel ..............

Resonance production cross sections in mb

for the 2n+3n- channel ...............

Resonance production cross sections in mb
for the Zn

Legendre polynomial coefficients

ll.l Legendre Polynomial Coefficients from

the three pion final state ..........

ll.2 Legendre Polynomial Coefficients from

the four pion final state . . ........

ll.3 Legendre Polynomial Coefficients from

the five pion final state ..........

ll.4 Legendre Polynomial Coefficients from

the six pion final state . . . ........

3n'n° channel ..............

Page

12

l9

27

34

4O

43

48

53

58

79

8]

82

Table
12.

Asymmetry and Col1imation parameters

12.1 Parameters for n+ from the

final state ................

12.2 Parameters for

final state ................

12.3 Parameters for

final state ................

12.4 Parameters for

final state ................

12.5 Parameters for

final state ................

12.6 Parameters for
final state .

12.7 Parameters for

final state ................

12.8 Parameters for

final state ................

n- from

n+ from

n' from

1r° from

it" from

«T from

the

the

the

the

the

the

three pion

three pion

four pion

four pion

four pion

five pion

five pion

six pion

12.9 Parameters for n“ from the six pion

final state ................

12.10 Parameters for w° from the six pion

final state

vi

Page

94
95
96
97
98
99
100
101
102

103

Figure

LIST OF FIGURES

Topological cross sections in mb ..........

Spectator momentum distributions in the multipion
annihilations. The solid curves are the predic-
tion of the deuteron wave function assuming an
impulse model

2.1 Distribution for pd +~pn +2n' .........
Distribution for pd +-n2n*2n .........
Distribution for pd +-pw n+2n n° ........
Distribution for pd +-p2n: 3n" .........
Distribution for pd +~n3n: 3n‘ .........
2.6 Distribution for pd +p21r+ 3n" n° ........

NNNN
01th

Distributions from the _analysis of events fitting
the hypothesis pd ->-pnp1r+ n

3.1 Missing mass distribution of events classi-
fied as belonging to pd +pnp1r+ n Shaded
events also fit the hypothesis of multipion

annihilation ..................

3.2 Angular distribution of the outgoing anti-
proton from events classified as belonging
to pd + pnpn+ n' . Shaded events also fit

the hypothesis of multipion annihilation. . . .

3.3 Neutral particle mass _distribution for
events fitting pd‘+ ppn +n'X°. Shaded
events are those classified as belonging to

the hypothesis pd + pnpn+ n‘ ..........

3.4 Confidence level distribution of events
classified as belonging to pd +-pnpn+w .
Shaded events also fit the hypothesis of

multipion annihilation ............

Missing mass squared and confidence level distri-
butions for events_fitting the multipion annihi-
lation hypothesisw + pn n'n'n°

4.1 Missing mass squared distribution for

events between 1.60 and 2.00 GeV/c ......

vii

Page
13

16

16
16

16

23

23

23

23

26

Figure

10.
11.

12.

4.2
4.3
4.4

Confidence level distribution for events

between 1.60 and 2.00 GeV/c ...........
Missing mass squared distribution for

events between 2.15 and 2.90 GeV/c .......
Confidence level distribution fOr events

between 2.15 and 2.90 GeV/c ...........

Reaction cross sections for single and double

pion production without annihilation in the three

and four prong topologies. Other experiments

shown are: (l) 1.96 GeV/c, ref. 19; (2) 2.8 GeV/c,
ref. 20, 21; (3) 5.55 GeV/c, ref. 22; (4) 1.0 -

1.6 GeV/c, ref. 44 ..................

Reaction cross sections for annihilation channels
in the three and four prong topologies. 5p data
is from ref. 11 ...................

Missing mass squared and confidencelevel distri-
butions for events fitting the multipion annihi-

lation hypothesis 5d +-pn

7.1
7.2
7.3
7.4

11+ 11" 11' 11" 11°

Missing mass squared distribution for events
between 1.60 and 2.00 GeV/c ...........
Confidence level distribution for events

between 1.60 and 2.00 GeV/c ...........
Missing mass squared distribution for events
between 2.15 and 2.90 GeV/c . . .........
Confidence level distribution fOr events

between 2.15 and 2.90 GeV/c ....... . . . .

Reaction cross sections for annihilation channels
in the five and six prong topologies. pp data is
from ref. 11 ................... ‘. .

Resonance production cross sections for the
1*2n- channel ........ . ...........

Invariant mass distributions for the 1121' channel . .

Resonance production cross sections for the
n*21'n° channel ...................

Invariant mass distribution for the n+2n'n°
channel . . . . ...................

viii

Page

26
26
26

28

29

32
32
32
32

36

42
45

47

50

Figure
13.

14.

15.

‘16.

17.

18.

19.

20.

21.

22.

Resonance production cross sections for the
2n+3n' channel. Open points are fipI=l +-p°p°fl°

from reference 4 ...................

Invariant mass distributions for the 2n+3n'

channel .......................

Resonance production cross sections for the

2n+3n'n° channel ...................

Invariant mass distributions for the 2n+3n'n°

channel .......................

Resolution ideogram of the error frpm invariant

mass combinations between 0.7 GeV c and 0.8 GeV/c2

with the mass fixed at 0.75 GeV/c
17.1 Ideogram for events fitting pd + pn+2n' for

the momentum range 1.60 to 2.00 GeV/c .....

17.2 Ideogram for events fitting pd +1p21+31‘

in the momentum range 1.60 to 2.00 GeV/c . . . .

17.3 Ideogram for events fitting pdi+ pn+2n'

in the momentum range 2.15 to 2.90 GeV/c . . . .

17.4 Ideogram for events fitting pd +ip21 31'

in the momentum range 2.15 to 2.90 GeV/c . . . .

Angular distributions for the three pion final
state. The solid curves are fits to the

Legendre polynomials .................

Angular distributions for the four pion final
state. The solid curves are fits to the‘

Legendre polynomials .................

Angular distributions for the five pion final
state. The solid curves are fits to the

Legendre polynomials .................

Angular distributions for the six pion final
state. The solid curves are fits to the

Legendre polynomials .................

Legendre polynomial coefficients

22.1 Legendre polynomial coefficients for 1*

from the four pion final state .........

ix

Page

52

55

57-

61

67

67

67

67

71

73

75

77

Figure Page

22.2 Legendre polynomial coefficients for 1‘

from the four pion final state . . . . ..... 85
22.3 Legendre polynomial coefficients for 1°

from the four pion final state ......... 86
22.4 Legendre polynomial coefficients for 1+

from the five pion final state ......... 87
22.5 Legendre-polynomiaI coefficients for 1'

from the five pion final state ......... 88
22.6 Legendre polynomial coefficients for 1+

from the six pion final state ......... 89
22.7 Legendre polynomial coefficients for 1'

from the six pion final state ......... 90
22.8 Legendre polynomial coefficients for 1°

from the six pion final state ......... 91

23. Asymmetry and collimation parameters

23.1 Parameters for 1+ from the three pion final

state ..................... 94
23.2 Parameters for 1* from the three pion

final state .................. 95
23.3 Parameters for 1+ from the four pion

final state .................. 96
23.4 Parameters for 1' from the four pion

final state .................. 97
23.5 Parameters for 1° from the four pion

final state .................. 98
23.6 Parameters for 1+ from the five pion

final state .................. 99
23.7 Parameters for 1' from the five pion

final state .................. 100
23.8 Parameters for 1+ from the six pion

final state .................. 101
23.9 Parameters for 1' from the six pion

final state .................. 102
23.10 Parameters for 1° from the six pion

final state .................. 103

24. Center-of-mass longitudinal and transverse momentum
distributions. The solid curves are fits to
statistical model predictions

24.1 Longitudinal momentum distributions from
three pion final states between 1.60 and
2.00 GeV/c . . ................. 106

Figure Page

24.2 Transverse momentum distributibns from
- three pion final states between 1.60 and
2.00 GeV/c ................. 107
24.3 Longitudinal momentum distributions from
four pion final states between 1.60 and
2.00 GeV/c ................. 108
24.4 Transverse momentum distribtuions from
four pion final states between 1.60
and 2.00 GeV/c ............... 109
24.5 Longitudinal momentum distributions from
four pion final states between 2.15 and
2.90 GeV/c ................. 110
24.6 Transverse momentum distributions from
four pion final states between 2.15 and
2.90 GeV/c ................. 111
24.7 Longitudinal momentum distributions from‘
five pion final states between 1.60 and
2.00 GeV/c ................. 112
24.8 Transverse momentum distributions from
five pion final states between 1.60 and
2.00 GeV/c ................. 113
24.9 Longitudinal momentum distributions from
five pion final states between 2.15 and
2.90 GeV/c ................. 114
24.10 Transverse momentum distributions from
five pion final states between 2.15 and
2.90 GeV/c ................ 115
24.11 Longitudinal momentum distributions from
six pion final states between 1.60 and
2.00 GeV/c ................. 116
24.12 Transverse momentum distributions from
six pion final states between 1.60 and
2.00 GeV/c ................ 117
24.13 Longitudina1 momentum distributions from
six pion final states between 2.15 and
2.90 GeV/c ................ 118
24.14 Transverse momentum distributions from
six pion final states between 2.15 and

2.90 GeV/c ................ 119
25. Regge diagrams with nucleon exchange used in the
CLA model
25.1 Three pion final state ........... 122
25.2 Four pion final state ........... 122
25.3 Five pion final state ........... 122
25.4 Six pion final state ............ 122

xi

Figure Page

26. Comparison of the multipion annihilations
with the multiperiphera1 and statistical models.
Solid (dashed) curves are predictions of the
multiperipheral (statistical) model ........ 125

xii

CHAPTER 1
INTRODUCTION

Antiproton-deuteron interactions are interesting as a means fbr
studying antiproton-neutron interactions. There is no available source
of free neutrons for use as a target; however the deuteron with its low
binding energy of 2.2 MeV provides a source of almost free neutrons
which may be used as a target. When the range of interaction and the
wavelength of the incident particle are short compared with the separa-
tion of the individual nuclei within the nucleus, the incident particle
can interact with a single nucleon. Thus, in deuterium the beam parti-
cle can interact with one of the nucleons leaving the "spectator"
nucleon with the same momentum it had before the interaction. This is
called the ”impulse model" and is the basic assumption in using deute-
rons as a source of neutron targets.

In a high statistics counter experiment in 1967, Abrams et.a1.1
measured the total cross section for antiprotons on hydrogen and
deuterium and found structure in both total cross sections. This
structure in itself is not unique since structure has been found in
the total cross sections for 1's and K's in both hydrogen and
deuteriumz. One possible interpretation for the structure is that
some final state is rising sharply from its threshold value causing an
inflection in the total cross section. An example of this is seen in

both K'p and K'd interactions where there is a rapid increase of the

1

total cross section starting at the threshold for the production of the
K*(890). Another possible interpretation for such structure is the for-
mation of a direct channel resonance such as occurs in the 1+p interac-
tions wherein the total cross section peaks strongly as the total cen-
ter-of-mass energy passes through the region of the A++(1235) resonance.
The antiproton-neutron system is an eigenstate of isospin with
an eigenvalue of one, I=1, while the antiproton-proton system is a
superposition of two such eigenstates with eigenvalues I=1 and I=0.
Thus by combining the total cross sections for antiprotons on protons
and deuterons, the experimenters of reference 1 were able to determine
the isospin component cross sections of antiproton-nucleon interactions.
By fitting the I=1 total cross sections to a smooth polynomial back-
ground, they found two "bumps" which, assuming Breit-Nigner descrip-
tions, were referred to as the 1:(2190, 85) and the 1:(2350, 140),
where the subscript is the isospin and (E0, r) are the center-of-mass
energies and fu11 center-of-mass widths in MeV. The corresponding in-
cident momentum and height for these structures are 1.32 GeV/c and
5.5 mb for the 11(2190) and 1.77 GeV/c and 3.2 mb for the 11(2350).
Several experiments have been performed to attempt to determine the

3, tried to explain the

origin of these structures. One such study
11(2190) as a threshold effect from single pion production without
annihilation and concluded that an excitation curve sufficient to ex-
plain the structure was inconsistent with the data. A formation ex-
periment4 has reported an enhancement in the pp1 cross section at

2190 MeV with a width 20 MeV 5 r 5 80 MeV which the experimenters

3

associate with the 11(2190). Similarly, missing mass experiments in
W'p gave evidence for narrow boson resonances with I=1 or 2 at energies
of 2195 MeV, the T meson(width less than 13 MeV), and 2375 MeV, the U
meson (width of about 30 MeV); however the reported widths are much
narrower than those reported in the pp and 5d total cross sections.

In this thesis, a comprehensive study of inelastic antiproton-
deuteron interactions between 1.60 GeV/c and 2.90 GeV/c is presented.
Emphasis has been placed on the topological, reaction, and resonance
production cross sections with particular regard to searching for the
origins of the I=1 structures in the total cross section using the
antiproton-neutron annihilations. An earlier study in the 1.60 GeV/c
to 2.00 GeV/c momentum region as well as a pp exposure in the same
energy range has led to a published report8 of an I=1 enhancement in
the K*Khw final state centered at 2360 i 25 MeV but with a width,

P < 60 MeV. Both the mass and the width of this enhancement agree
with those of the U meson, however, the narrow width is inconsistent
with that observed for the «((2350).

A study of the angular and momentum dependence of the multipion
annihilations is also presented. The angular dependence is analyzed
in terms of both Legendre polynomials and collimation and asymmetry
parameters. Furthermore, the collimation and asymmetry parameters are
discussed in relation to the general features of a multiperipheral
multi-Regge pole model. The center-of-mass longitudinal momentum dis-
tributions and transverse momentum distributions of the individual
pion charge states are compared with predictions of a statistical

model, with quite good agreement. In addition, the general features

4

of the multipion annihilations are discussed in terms of both a multi-

peripheral model and a statistical model.

CHAPTER 2

EXPERIMENTAL PROCEDURES

The data used in this thesis was obtained from two separate ex-
posures of deuterium to antiproton beams from the Zero Gradient Syn-
chroton at the Argonne National Laboratory. The exposures, taken in
the 30-inch MURA bubble chamber, consisted of (1) 130,000 stereo triads
at incident momenta 1.60, 1.75, 1.85 and 2.00 GeV/c (total center-of-
mass energies of 2289, 2342, 2378 and 2430 MeV) and (2) 126,000 stereo
triads at 2.15, 2.30, 2.45, 2.60 and 2.90 GeV/c (total center-of—mass
energies of 2483, 2534, 2586: 2636, and 2736 MeV.).

The 1.60 - 2.00 GeV/c film was scanned fOr all 2-8 prong events
(events with 2-8 charged tracks leaving the interaction vertex) and
for all events with neutral vee decays (decays where an unseen neutral
particle decays into two charged particles which leave tracks in the
bubble chamber) and one-sixth of the film was rescanned. A list was
made of all events on which the two scans disagreed as to the existence
of an event or its event type and these events were looked at again to
resolve the differences. From the overlap of the two independent scans,
it was possible to determine the efficiency (the number of events found
on a single scan divided by the calculated total number of events in
the fiducial volume) for each topology at each momentum. Typical single

scan efficiencies for this film were 92% for events without neutral vee

5

6

decays and are listed in Table 1.
The combined antiproton-proton, antiproton-neutron, and anti-
proton-deuteron elastic cross sections are a large fraction of the to-

9’10 and are dominated by inter-

tal antiproton-deuteron cross section
actiOns with very low momentum transfer from the antiproton beam to

the target. The principle characteristic of these events is that the
elastically scattered antiprotons in the low momentum transfer region
cannot be distinguished from the antiprotons which do not interact.
Thus for this and other reasons one prong events were not looked at in
this experiment since the scanning losses would be too great and there
would be little justification for the amount of effort expended.

The 2.15 - 2.90 GeV/c film was scanned for events with neutral
vee decays and in two independent scans was simultaneously scanned and
measured for 3- and 4-prong events, 5- and 6-prong events. In addi-
tion, an interaction count was made on 0-, 7-, and 8-prong events on
a limited sample of the film at selected momenta. One-third of this
film was second scanned for 3- and 4-prong, and 5- and 6-prong events
and typical scan efficiencies found were 87% and 83% respectively.
Since a similar investigation of the antiproton-proton system was being
conducted in the same momentum range in two separate bubble chamber
exposures, only one-sixth of the 2.15 - 2.90 GeV/c film was scanned
for 4-prong and 6-prong events. The results of the study of the anti-
proton-proton system are described elsewhere.10

Approximately 80% of the 1.60 - 2.00 GeV/c film was scanned and

measured at Lawrence Berkeley Laboratory. The remainder of this ex—

posure and the 2.15 - 2.90 GeV/c exposure was measured using image

Table l.

Topological Event Statistics

 

 

Measuring and Scanning Statistics
NUmber of

Number of

 

PL Event type events found Scanning events used
(GeV/c) on complete efficiency in the final
first scan (%) physics analysis
1.60 2-prongs 32680 90.9 26724
3-prongs 9158 92.9 7831
4-prongs 20271 92.9 16949
5-prongs 4411 97.6 2885
6-prongs 5290 97.6 3611 p
1.75 2-prongs 19720 93.3 16348
3-prongs 5850 90.3 5091
4-prongs 11793 90.3 10107
5-prongs 2713 96.0 1846
6-prongs 3258 96.0 2353
1.85 2-prongs 20281 93.8 17259
3-prongs 6003 94.2 5240
4-prongs 12405 94.2 10751
S-prongs 2952 95.7 1946
6-prongs 3534 95.7 2547
2.00 2-prongs 11246 92.8 9363
3-prongs 5252 92.3 4663
4-prongs 11851 92.3 9844
5-prongs 2518 96.1 1835
6-prongs 2842 96.1 2378
2.15 3-prongs 3466 83.1 3087
4-prongs 5030 82.2 4243
5-prongs 1824 83.7 1504
6-prongs 389 79.1 328
2.30 3-prongs 3527 78.0 3309
4-prongs 1599 84.5 1729
5-prongs 1948 83.4 1612
6-prongs 450 83.4 374
2.45 3-prongs 3360 77.8 2992
4-prongs 1528 83.9 1451
5-prongs 1841 83.4 1550
6-prongs 449 83.4 370
2.60 3-prongs 4099 77.5 3886
4-prongs 1457 86.1 1354
5-prongs 2428 83.4 ' 2056
6-prongs 510 83.4 417
2.90 3-prongs 3417 77.6 3110
4-prongs 1384 86.2 1312
5-prongs 1959 83.2 1682
6-prongs 496 85.0 424

 

Conflict Scanning Statistics

 

 

 

Event type PL ggggegvgzts ggggegvgzts ggggegvgzts
(GeV/c) found on found on found on
first scan second scan both scans
3- and 4-prongs 1.60 1389 1259 1170
1.75 1337 1322 1194
1.85 1111 1161 1094
2.00 1070 1060 978
2.15 976 1048 900
2.30 1041 1143 937
2.45 1186 1252 1094
2.60 1003 995 921
2.90 920 963 864
5- and 6-prongs 1.60 468 410 376
1.75 441 441 403
1.85 404 391 357
2.00 392 369 339
2.15 1214 1355 1102
2.90 1362 1472 1240

9

plane digitizers at Michigan State University. The measured events
were processed through the three-dimensional geometric reconstruction
program, TVGP11, and the kinematic fitting program, SQUAN12 using the
Michigan State University CDC 3600. Events which failed reconstruc-
tion on the first attempt were remeasured resulting in an overall
passing rate (percentage of scanned events for which one or more of
the attempted hypotheses was successfully fitted) of between 90% and
95%. In order to reduce bias in the final sample, the acceptance
criteria for fits of measured events was made deliberately loose
(i.e., successful fits correspond to confidence levels greater than
10'5.) This procedure resulted in many events successfully fitting

more than one hypotheses.

CHAPTER 3

TOPOLOGICAL CROSS SECTIONS

3.1 Experimental Methods

 

The antiproton-deuteron cross section in the 1.60 - 2.90 GeV/c
momentum range is sufficiently large that several interactions occur
in each frame. The calculation of o/N, the cross section per event,
was based on a track count and an attenuation factor determined from

the mean interaction length

 

2= 2 (1)
otpAo

where at is the total antiproton-deuteron cross section from reference
1, p is the density of liquid deuterium, and A0 is Avagodro's number.
The total number of tracks at each momentum, Ntks’ was determined by
counting the number of tracks entering the fiducial volume (the volume
of the bubble chamber common to all three views) on every 50th frame.
The cross section per event was then calculated from

”t

 

_.q_=
N

-A/2 (2)

where the effective length of the bubble chamber, A, was determined
from the limits of the interaction vertex positions of events and the

paths of tracks in the chamber.

10

11

3.2 Cross Sections

Table 2 and Figure 1 show the topological cross sections which
were obtained from multiplying o/N at each momentum by the number of
events of a given topology found in the scanning and corrected by the
efficiency for that scan. To determine whether or not any of the
w:(2350) was present in the data, both the three and the five prong
cross sections were individually subtracted from the total I=1 cross
section. The remaining I=1 cross section was then fitted to a six

parameter function.

 

[4 am ] 1N
o = 2 1 + a 2 2
1 i=0 E 5[p* [(55.1%] +1] (3)

where p* is the p c.m. momentum, E the fin total c.m. energy and N a
normalization factor which is adjusted to give a value of 3.2 mb for

'k
the 11(2350) in the total I=1 cross section.

3.3 Conclusions

The fits showed that the three prong events could account for
a6(E=EO) x 3.2 mb = 0.34 i 3.67 mb of the enhancement while the five
prong events showed a contribution of a5(E=Eo) x 3.2 mb = -0.80t3.03 mb
where E0 = 2350 MeV. Obviously, these results neither support nor rule
out any association of these channels with the n:(2350). For an accu-
rate determination of the contribution to the enhancement cross section,
this method of fitting a subtracted background requires many closely
spaced points with small relative errors neither condition being met

by the present data.

l2

._ ooeocmmmc mo mcoeuoom «coco peace
use soc; eomuomm mmoco um>cmmeo we» we 25m we» memuuccunam an coemcpao cc: co.uoom mmocu mecca meo umucsmumm as» «

 

chmm came came came mecca _
ecccceccmm
- - - - - e18. 362 cheap chm? . ccm

mo.onom.m wo.ompm.m oo.ou¢¢.~ mo.omm¢.~ mo.owmm.~ mo.omm¢.~ no.oumm.~ mo.owmm.~ wo.c«wm.m mucm>m Amumu
. 66> vu>comeo

 

ma.chmm. . - N.chma. - - ccc.hmmc. ~mc.accc. ccc.hmmm. Nec.hamm. mecca c
Nc.chmm. - ~.chma. - - ccc.hcmc. mmc.hc~e. mmc.hcce. mec.hccm. mecca a
c.ch_a.c_ c.chcm.cc c.chca.m m.chcc.m c.ch_c.m cm.mhmm.m cm.chmm.m, cm.chmc.m .cm.mhm~.m mecca c
cc.chma.c cc.chmc.a cc.ccac.c. cc.chcm.a ce.chcc.c ce.ccac.a cc.cham.a ce.cacm.a ce.chma.a mecca m
N.che.m~ N.ahm.mm m.chm.~m N.cha.cm m.chm._m . c.ahm.cm c._ae.em P.Phc.mm _.ahe.am mecca c
ce.chcc.mc cc.chac.~c me.chec.mc mc.chc~.cc cm.chca.aa ac.chmc.m_ mc.chm~.cc Fm.chcc.aa cm.chca.ca mecca m
- . - - - - m._hc.Nm c.ahm.mm c.chc.~m a._hm.cm mecca N

c.cc ~.m - m.chc.m - - c.ehm_.m - - mc.am.m mecca c
cm.~ cc.~ mc.~ mm.N m..~ cc.~ mm.a ma._ cc.P zchmcmcacc

 

as ea meovuomm mmocu Fcupmopoaop .N mpncp

l3

 

 

 

604 O O-prongs
1* V 2-prongs
50_ i f i A 3- prongs
O 4-prongs
4 I 5-prongs
40‘ C O 6-prongs
‘ Q 0 §
30~ ‘7 ‘ii is {D
204
A A A A A
-D 10-
5 1/
b
10~ § § §
8" i 1* 1 1
6‘ 9
1 t . <1 <1
115 210 2] 310
PL (GeV/c)
213 2.4 215 216 2.'7 2T8
Ec.m. (GeV/c)
Figure l. Topological cross sections in mb

 

CHAPTER 4
REACTION CROSS SECTIONS

4.1 Experimental Methods

Since the fitting criteria were made deliberately loose (i.e.,
successful fits correspond to confidence levels greater than 10'5).
additional cuts, which will be explained later, were made on the con-
fidence levels and missing mass values. The individual reaction cross
sections were corrected for events lost through failure of the recons-
truction programs by normalizing to the topological cross sections,
using the total available sample after reconstruction. This procedure
eliminates any bias of the reconstruction programs toward any indivi-
dual topology and eliminates a second renormalization in topologies
where only a partial sample of the film was measured.

The momentum distribution of the spectator nucleon in the anni-
hilation channels showed a large excess of events in the high momen-
tum tail. This excess of events, which appears to come from throughout
the undistorted distribution, is attributed to secondary scattering of
the spectator nucleon by the pions13. This effect resulted in a
larger contribution to the cross sections from even prong events than
would be expected if the spectator momentum was that predicted by the

impulse model. Figure 2 shows the spectator momentum distributions

14

Figure 2.

15

Spectator momentum distributions in the multipion annihi-
lations. The solid curves are the prediction of the
deuteron wave function assuming an impulse model

Distribution for pd +~p1+21’

. Distribution for pd + n21+21'
Distribution for 5dr+ p1+21'1°
Distribution for 5d + p21+31‘
Distribution for pa + 131331-
Distribution for pd + p21+31'1°

NNNNNN
aim-puma

16

3:65 1838ch

 

 

 

 

 

 

cccm om. m? cm.” cwm cm, cm c -
c
189
3
A
a
U
a
I
Z
1°8~ o
m
M
3
c.~
68m
onmazv Acouauuoamva
cc... 8. 8. 8m ca 9.: 8 c
if p b h u b b o
.8
3
A
3
U
a
I
m
.9: w
M
3
.cc~
2
329: 133683..
23 8e 8.. can SN 8. 8 c
b m p m p p - O
3
a
18.5. m.
n
a
m
M
3
.8.
3..

 

3:3: T8383:

 

 

 

 

 

 

 

com ow. coo awn ovu oo_ on o
L L p b F > L) O
foca—
roao~
n.~
flit. coca
AU\>utv Acouauuoamva
com owe owe o~m ovu on. on c
m p b p b L) O
can
.ooc
.ooo
~.~
Aux>uzv Acouauuonmva
com one cow o~n o¢~ co. on o
L1 L1 b h h h b O
voo—
roou
p.~
.oom

 

3/A'H 03/930943

3/A'H 02/339343

3/A3H OZ/‘Quafil

17

for six different annihilation reactions within the three through six

14 1101‘-

prong topologies compared with the Moravcsik III wave function
malized to the same area under the curves. Figures 2.1 and 2.4 are
the nucleon spectator momentum distributions for the four constraint
fits pd-+ p1+21‘ and pd-+ p21+31'. Figures 2.2, 2.3, 2.5 and 2.6 show
the spectator distributions for the one constraint fits pd-+ n21+21’,
pa + mien-1°, 5d + n31+31', and 5d + p21+31-1° respectively. In the
fits with a 1°, the large distortion of the lower momentum data arises
from the odd (three and five) prong events. When the spectator is not
seen in the bubble chamber its momentum is set to zero with errors of
30 MeV, 30 MeV, and 40 MeV in the x, y and 2 directions. These errors
allow the fitted momentum of the spectator to be adjusted properly when
all other particles involved in the final reaction are directly ac-
counted for, however, when there is another unseen particle such as in
the case of the 1°, the errors in the momentum of the unseen particle
do not allow sufficient adjustment of the spectator momentum. Thus
the momentum of the spectator is held close to the initial assumption
in the optimized fit.

All errors in the reaction cross sections are statistical with_
a minimum of 3%. All the cross sections are observed cross sections
with no cuts on the momentum of the spectator nucleon and no correc-
tions for the shadowing of one nucleon by another as described by

15 16

Glauber and Franco and Glauber .

4.2 Two-Prong Cross Sections
Measurements of 76,000 two-prong events in the 1.60 GeV/c to

2.90 GeV/c momentum range have been completed with each event fitted

18
to the following hypotheses: 1

13d + 131113 (4a)
+ p11" .- (4b)
+ W1° (M
—> (II-lir- (4(1)
+ d5 (M
+ 361° (4f)
-> M11" (49)

and the corresponding zero-constraint "missing mass fits." One other
zero-constraint fit:

} id -> 61% (4h)
was also tried. Both reactions (4b) and (4e) were four constraint fits
and were accepted into the hypothesis if the confidence level exceeded
10'4. Antiproton-deuteron elastic scattering, reaction (4e), has been
previously publishedg. Reactions (4c) and (49) have extremely small
cross sections, on the order of one hundred ab, and the latter hydro-

10’17’18, thus no

gen like reaction can best be described elsewhere
attempt has been made to separate these reactions from the missing mass
channels. No events were found which fit hypothesis (4b) and an upper
limit is listed in Table 3. Most of the data reduction in the two-
prong topology has been done and is included with the permission of

Dr. Z. Ming Ma. The reaction cross sections from the two-prong events

corrected for losses in the one-prong events are shown in Table 3.

19

Table 3. Reaction Cross Sections (mb) in the Two Prong Topology
Corrected for One Prong Losses

 

 

MOM
1.60 1.75 1.85 2.00
REACTION
5d1+ pnB 29.3 s 1.7
-+ an 37.9 e 1.6 37.3 e 2.7 32.7 e 2.5 32.4 e 3.2
+ 581° 1.21 e 0.05 1.65 i 0.07 1.83 e 0.08 1.82 e 0.10
+ 181' 1.34 s 0.05 1.51 e 0.07 1.67 e 0.07 1.87 e 0.10

+ pn- < 2 ub < 3 ub < 3 ub < 5 ub

 

20
4.3 Three and Four Prong;Cross Sections
Measurements have been made of 24,000 3-prong and 49,000 4-prong
events in the 1.60 - 2.90 GeV/c film and 16,000 3-prong and 9,700
4-prong events in the 2.15 - 2.90 GeV/c film. Each measured event was

fitted to the following hypotheses:

5d + 9951' (5a)
+ 1111151?"° (5b)
+ ppiir'i' (5e)
+ 131113111“ (5d)
+ p1+1'1' (5e)
4 p11+n'1r'11° (51°)
+ pKfK'17 (59)

and the corresponding zero-constraint missing mass fits. The four-

prong events were also fitted to the hypotheses:

id -> din+n-1- (5h)
+ dpn 1' (51)
+ 051+1'1° (SJ)
+ "11+n+n'11' (5k)

and their corresponding missing mass fits.t

The three double pion production channels (5b) - (5d) rise
sharply from the AK threshold and therefore were only analyzed in the
2.15 - 2.90 GeV/c data. An ionization study (a comparison of the pre-’
dicted bubble density with that observed in the film) allowed the com-p
plete separation of (5b) and (5c) due to the presence of at least two
slow charged nucleons in the laboratory system. About one-half the

events classified as belonging to hypothesis (5d) had antiprotons with

21

a momentum greater than 1.2 GeV/c in the lab (relative ionization of
less than 1.5) and thus were ambiguous with the missing mass class
pd-+ pflffl-fl-MM even after the ionization analysis.

Figure 3.1 shows the missing mass distribution of the events
classified as belonging to hypothesis (5d) with the shaded events re—
presenting those events which were ambiguous between reaction (5d) and
pd-+ p1+1'1'MM. The confidence level distribution for events classi-
fied as belonging to (5d) is shown in Figure 3.4 with the shaded re-
gions representing the ambiguous events. Similarly, Figure 3.2 shows
the angular distribution of the outgoing antiproton from the events
belonging to reaction (5d). All three of these figures indicate that
those events which were ambiguous with the reaction pd-+ pnfn‘n'MM
(the shaded events) belong to hypothesis (5d). Thus, unless the ioni-
zation ruled out the nucleon hypothesis, the event was determined to
belong to (5d). This is further justified by Figure 3.3 where all
events from the three and four prong topologies that had at least one
of their fits corresponding to 5d-+ pp111'x° (where X° represents any
neutral particle or any combination of neutral particles) are plotted
with the shaded portions representing those events classified as be-
longing to hypothesis (5d).

Both reactions (5a) and (5e) were four-constraint hypotheses
and were accepted if their confidence levels for the fits were greater
than 10'3. Events fitting reaction (5f) were accepted if their confi-

-3

dance level was greater than 10 and the missing mass squared was

within 2.5 standard deviations of the nominal value of the 1° mass

Figure 3.

22

Distributions from the analysis of events fitting the
hypothesis pdi+ pnp1+1-

3.1

3.2

3.3.

3.4

Missing mass gistribption of events classified as
belonging to pd +-pnp1+1'. Shaded events also fit
the hypothesis of multipion annihilation.

Angular distribution of the outgoing antiproton from
events classified as belonging to pd + pnp1+1'.
Shaded events also fit the hypothesis of multipion
annihilation. ~

Neutral particle mass distribution for events
fitting pd + pp1+1'x°. Shaded events are those
classified as belonging to the hypothesis

Dd + pnfinI'n'

Confidence level_distripution of events classified
as belonging to pdi+ pnp1 1'. Shaded events also
fit the hypothesis of multipion annihilation.

213

pm>ap aoeovamcou

 

.E.u
-m ccc

o.o

 

~.m

m.ou

 

. op

. cm

1 on

10*

. om

 

T om

l0'/510343

'/sauaA3

ZO

a~c\>cmv mace

c._ N.a c“,

 

a~c\>cmv mac:
e._ m.c c._

   
 

 

 

w.o o.m

.¢op

.¢¢N

 

comm

m.c o.o

rop

.om

.om

.oe

.om

10K

 

ecm

23/195 10'/51ua43

ZD/ABO 10'/54ua43

24

squared and with an upper limit of mass squared of 0.3 GeV2.- Analysis
of these events showed a significant amount of contamination on the
high side of the 1° mass.

By requiring the confidence level to be greater than 10‘], the
contamination was significantly reduced. The missing mass squared
distributions for events fitting reaction (5f) are shown in Figure 4.1
for events in the 1.60 GeV/c to 2.00 GeV/c and Figure 4.3 for events in
the 2.15 GeV/c to 2.90 GeV/c incident momentum ranges. The confidence
level distributions for reaction (5f) for the 1.60 GeV/c to 2.00 GeV/c
and 2.15 GeV/c to 2.90 GeV/c incident momentum ranges are shown in
Figures 4.2 and 4.4 respectively. The shaded regions represent those

I confidence level cut. The total reaction

events excluded by the 10'
cross section was then calculated by fitting the remaining (i.e. un-
shaded) missing mass squared distributions to a Breit-Nigner_line shape
centered around the 1° mass squared value to obtain the true number of
events and then correcting this number for those events excluded by the
out by multiplying by 10/9.
' The hydrogen-like reaction (5k) also was contaminated on the

high side of the neutron mass. The analysis was treated similarly, but.
since the mass of the neutron is much greater than that of the pion it
was necessary to fit the missing mass squared spectrum to a Gaussian
rather than a Breit-Nigner.

f The four-constraint reaction (5g) was accepted if the confidence
level of the fit was greater than 10'3. However, an additional require-

ment that the ionization be consistent with the kaon interpretations

was imposed on the final sample. Table 4 and Figures 5 and 6 show the

Figure 4.

25

Missing mass squared and confidence level distributions
for events fitting the multipion annihilation hypothesis

[3d + p11+1r"11'1r°

4.1 Missing mass squared distribution for events between
1.60 and 2.00 GeV/c

4.2 Confidence level distribution for events between
1.60 and 2.00 GeV/c

4.3 Missing mass squared distribution for events between
2.15 and 2.90 GeV/c

4.4 Confidence level distribution for events between
2.15 and 2.90 GeV/c

 

2265

_o>o— oocovrmcou

cm_ m.c cmc cmc ~.c c.c

   
 

amp

cum

¢.¢

own
po>mp oucmv_meou

cmc ma

 

ZO'/510343

ZO'/510343

a~c\~>ccv acme:

 

 

 

 

 

 

 

c ~.c a.c cwc awe- Nee- m.cn
c
ice
tea
ic~_
re
a~c\~>c$ ~35...
mmc awe- Nye- c.m-

c
rec.
1m~m
icoe

_.. Team

Za/znas 10'/81u943

zalznas 10'/51uaA3

27'

 

 

 

 

ma.ncm.m~ ac.nma._~ ma.nem.m~ ma.cmm.m~ Pm.nmc.cm cm.nmc.m~ 5cm.h~c.m~ cm.hcc.mm ~m.aac.cm mace Newmmce
‘ e c c
-.hc~.a m~.ncc.a c~.hmm.a a~.nca.m m~.nmm.a cm.nmc.m am.h~c.ca mm.n_c.c. mm.hmc.ca mace wecmmce
:9. m
mm.h.c.ca mm.h~a.c. mm.nc_.~_ cm.ncm._a m~.nam.cc m_.ncm..a m_.nc~.~a c~.nmm.mc mc.nc~.ma 5cm
cc.hmma. cmc.hc_a. ccc.nmma. ccc.ncca. amc.ncma. mNc.nmm~. ccc.h_ca. cmc.n~c~. ch.hamm. -e-¥+ga+.
e_.nam. ea.nam. ca.nac.c ea.n_a._ ea.ncN._ ac.ham.a ac.nca.c mc.nam._ ac.hm_.~ -e-e+e+ee+
ma.nae.~ c~.nam.~ -.nmc.m c~.ham.m m_.nma.m ma.nmc.c ma.n.a.m ca.e~a.c ma.hcc.c .e-e-e+ea..
mcc.hmmm. .mc.hcmm. mmc.hmem. ch.nmcm. cmc.nacm. mcc.cmmc. _mc.nmam. cmc.namm. mec.haa_.a -e-e+ea+
a~.hac.m mec.nmcc.a Nac.nmac._, cea.naam.a «Na.nmaa. - - - - -e+emea+
mmc.ncmm. mcc.nmm_. mec.acma. amc.nacc. mmc.nmcc. - - - - -e-emaa+
aac.hmca. mcc.ncmm. mcc.n~ec. ch.namm. cc.cnmma. - - - - .e-emaa+
cm.hac.c c_.ncm.e m~.nem.c _~.ncm.e ca.n_~.e _a.hmm.c a_.nma.m _a.nca.m mc.hmc.m -eaaa.ce
zcmacema
cm.~ cc.~ me.~ cm.N mF.N cc.N cc._ ma._ cc._ 4
a
mmemopogop mecca csoa nee mace» 6;» cm Anev meowuomm mmoco coepocmm .e opnch

 

28

 

 

 

 

 

5‘ 0 Bd+ipp"' i
u pd+ ppn1+1' g i i
4_ 9 § 9;
$9 "
.- 2.1
3 9
5 § (5.55 GeV/c)
b 2_ § §
6 i i
'I—
Q i
C)
0 i P 1 1
1.0 2.0 3.0
PL (GeV/c)
1‘ 8 5d + ppp1'1°
3; 0 Dd +Tlppn-1r- §
2: i i 9
i A éi
{u} ‘
0 J, . . T
1.0 2.0 3.0
PL(GeV/c)
T 1 1 1 1
2.0 2.2 2.4 2.6 2.8

Ec.m. (GeV)

Figure 5. Reaction cross sections for single and double pion pro-

duction without annihilation in the three and f0ur prong

topologies. Other experiments shown are: (1) 1.96 GeV/c,
ref. 19; (2) 2.8 GeV/c, ref. 20,21; (3) 5.55 GeV/c, ref.

22; (4) 1.0-1.6 GeV/c, ref. 44.

29

7" - + -
i I pd + p11 21 11°
0 pp + 211+Zn'
i . pd + n21+21-
6"i . _ + _
q? 1‘ pd-+ p1 Zn
5“ a
4 —1

37

0 (mb)

 

 

 

._ . { Q
5- 4 ‘3 [Y
5
4 § ,
1 V
5 a

0 115 2r 1 r
. .0 PL (Gav/c) 2.5 3.0

213 214 2'.5 216 277 T

E (GeV)

c.m.

Figure 6. Reaction cross sections for annihilation channels in the
. three and four prong topologies. pp data is from ref. 11

3O
reaction cross sections for the combined 3-prong and 4-prong data. A
further study of reaction (59), as well as pd-+ pKIK'1+1'1‘ and similar
antiproton-proton reactions, appears elsewherea. Since the cross sec-
tions for reactions with a deuteron in the final state (hypotheses (5h),
(51) and (5j)) were extremely small, no attempt was.made to extract the

events fitting these hypotheses.

4.4 Five and Six Prong Cross Sections
Measurements of 8,500 5-prong and 11,000 6-prong events in the
1.60 - 2.00 GeV/c film and 8,400 5-prong and 1,900 6-prong events in the
2.15 - 2.90 GeV/c film have been completed. Each event was fitted to

the following final states:

Dd + pn+11+1r-1r-1r- (63)
+ p1r+11+11-11-11-11° (6b)
-> pK+K'1r+n'ir' (5C)

and the missing mass hypothesis pd-+ p1+1+1'1'1‘ . The six prong

events were also fitted to
pd-+ n1+1+1+1'1'1' (6d)
as well as the corresponding missing mass fit.

As in the three prong and four prong events, reaction (6a) was
accepted if the confidence level was greater than 10'3. Hypotheses (6b)
and (6d) showed contamination similar to that of hypotheses (59) and
(5k). Again by requiring that the confidence level be greater than 10‘1
the contamination was reduced significantly. The missing mass squared
distributions for events fitting reaction (6b) are shown in Figure 7.1
for events in the 1.60 GeV/c to 2.00 GeV/c and Figure 7.3 f0r events in

2.15 GeV/c to 2.90 GeV/c incident momentum ranges. *The confidence level

 

 

Figure 7.

31

Missing mass squared and confidence level distributions for
events fitting the multipion annihilation hypothesis
pd + p11+11+11'11'1i'11°

7.1 Missing mass squared distribution for events between
1.60 and 2.00 GeV/c

7.2 Confidence level distribution for events between
1.60 and 2.00 GeV/c

7.3 Missing mass squared distribution for events between
2.15 and 2.90 GeV/c

7.4 Confidence level distribution for events between 2.15
and 2.90 GeV/c ‘

32

o.p

,—

m.o

    
  

m.o

po>o_ oucoupccou

c._c

—w>0_. flue—Qt pup—0U

o.o
c

v.~

3c

e.o
_

 

owp

oep

omw

owe

com

ZO'I510343

ZO'/510343

m.o

~.c

 

 

A~0\~>mov Nmmm:

o.o
r

m.~
RNU\N>OGV Nmmfiz
owe

p.o-
_

p.ou

N.o-

~.oi

m.oi
Me

Too

Temp

Iomw

loom

 

m.oi

 

noem

1ow¢

Iowa

 

foom

ZD/ZA39 l0'/51U343

23/2A39 lO'/510943

33

distributions for reaction (6b) in the two momentum ranges are shown
in Figure 7.2 and Figure 7.4 respectively. The shaded events again
represent those events excluded by the 10'1 confidence level cut.
Fitting the remaining missing mass squared distributions of (6b) to a
Breit-Wigner line shape and (6d) to a Gaussian line shape was used to
obtain the true number of events in each hypothesis for use in calcula-
ting the total reaction cross sections. A correction factor of 10/9
was again used to compensate for the confidence level cut. The analy-
sis of (5c) was done in a similar manner as reaction (59), again re-
quiring a confidence level of greater than 10"3 and a film ionization
of the kaon pair consistent with that predicted by the fit. The re-
action cross sections for the combined 5-prong and 6-prong events are

shown in Table 5 and Figure 8.

4.5 Conclusions

 

The reaction cross sections from the two- through six-prong to-
pologies have been determined for incident momenta between 1.60 and
2.90 GeV/c. Whereas any structure in the total cross sections may be
more noticeable in the reaction cross sections, there is little evi-
dence pointing to such structure. Single pion production without anni-
hilation has already been investigated3 and would require an excitation
curve inconsistent with the data. The double pion production reactions
without annihilation cannot contribute since their cross sections rise
rapidly from the AK threshold which is too great a center-of-mass
energy (2470 MeV) to be associated with any of the enhancements observed

in the total cross sections. The annihilation reactions pd +1p1+21',

34

 

 

 

 

mc.nom.a Pe.nmm.o Fe.hmm.m mm.wme.m am.nm_.m o_.nom.m mF.hmm.e cp.ho¢.e cp.noo.¢ mmcz mcwmmwz
coca m
Np.noo.m Np.n¢m.m m_.hao.m mp.nmm.m NF.Hom.N FF.Hmm.m NF.hmm.m P_.hmo.m mo.hmo.m mmcz asymmez
mecca m
om.hmm.o mm.hmp.m mm.hom.m Fm.mmm.~ mm.nmo.w mp.hm¢.w m—.ho~.m m_.hpp.m mp.nom.m 53m
meo.nmmm. emo.nmop. aeo.homm. ovo.n_m_. meo.nmem. mmo.hpe~. Nco.mmpm. mmo.hom_. omo.h¢mp. rere+eix+xm+
cep.n¢em. Pep.hoom. _mp.nmmm. wep.nomm. oo~.nmmm. mo.neo.P mo.nwo._ oo.nao.~ mo.mmo.P em+eme+
cm.hep.e mm.nOa.c mm.hmo.c mm.mmm.¢ em.n¢o.m m~.nom.m mp.h¢m.m mF.n_w.m mp.ho~.m cerem+e~a+
op.noo.F m_.nom.F c_.nom._ mp.nmm._ m_.new._ mo.hmm._ mo.n~o.m mo.nuo.m wo.nme.m em+e~c+tm
onhu<mm
om.m oo.N me.m om.~ m_.m oo.m mm.” ma.F om.~ 4
a
mmcmopoaoe mecca xcm nee m>wa 0;“ ca Ansv meowuomm mmocu cowuucmm .m wpnce

35

Figure 8. Reaction cross sections for annihilation channels in
the five and six prong topologies. pp data is from
ref. 11

0 (mb)

36

I 13d + p21r+311-1r°
A pd + 11211131'
‘3 <3 pp +'31+31'
i i . 5d + n31+31"
/

 

 

 

7 r r
1.5 2.0 2.5 3.0
PL (GEV/C)
1 W T I fi
2.3 2.4 2.5 2.6 2.7

Ec.m. (GeV)l

37

and 501+ p21+31' both have smoothly decreasing cross sections and fail
to show evidence for any significant structure. The reactions

pd«+ p1+21'1 and Ed +-p21+31‘1 exhibit turnovers in the region of the
11(2350). This turnover, however, appears at the low energy end of the
data and no definite conclusions can be drawn without further investi-
gation at lower energies. As will be seen in the next chapter, this
turnover may be reflected in the resonance production cross section

channels stemming from the reaction pd + 521+31'1°.

CHAPTER 5

RESONANCE PRODUCTION IN
THE MULTIPION ANNIHILATIONS

5.1 Experimental Methods

 

Inspection of the invariant mass distributions M(w+, 0'),

M(fli, Tr°), and M("+, "°, It') shows that 0°(765), f°(1260), oi(765),
and w°(784) are present in the data. Fitting by the method of maximum
likelihood23 showed that the multi-pion annihilations are dominated by
resonance production. The model used assumes that the data can be
described by the incoherent sum of phase space and any resonant pro-
cesses apparent in the invariant mass distributions. In addition,
associated resonance production was included where there was evidence
from the Dalitz plots that such production was possible and where the
inclusion of the associated resonances improved the overall fits.

In the analysis, an approximate matrix element was constructed
assuming that each resonance is represented by a simple Breit-Wigner
shape of the form proposed by Jackson24. The Breit-Wigner intensity
1s

811(0 ) = 111111) t (7)
(E2 - u212 + E2r2(u)

where E is the mass of the resonance, r is the full width and u is the

effective mass of the decay products. The matrix element is written

38

39

2 n n
| = (1 - z oi) + z

a Ro/No (8)
i=1 i-l 1 ‘ ‘

where ai is the fraction of the ith resonant process R1, N1 is the nor-
malization for the ith process, and n is the number of channels with

resonances. The R1 are taken to be the sums of possible Breit-Wigner
line shapes for a particular resonant process or the sums of products
of two such line shapes in the case of associated resonance production.
The normalization, N1, is simply the integral of the function R1 over

phase space.

The masses and widths of the resonances were obtained visually
from the data and were adjusted slightly where there was a significant
improvement in the overall X2 values of the fitted invariant mass dis-
tributions for a particular final state. Although the Bose-Einstein
symmetrization suggested by Goldhaber et al.25 was observed (approxi-
mately a 5% effect) no attempt was made to include it in the model.

The model of phase space plus resonances proved inadequate to
describe the reactions where events involved in the secondary scatter-
ing of the spectator proton by one of the pions were included in the
final sample. An upper limit of 200 MeV/c on the momentum of the
spectator proton was imposed and reasonable fits were obtained. This
limit reduced the effective cross sections by 30% to 40%. The re-
maining cross sections are shown in Table 6. In all references to the
resonance production cross sections any contributions from associated
resonance production have been removed and shown separately (i.e.

p°1+1‘ does not contain any contribution from p°p°).

Table 6.

40

Reaction Cross Sections (mb) for Multipion Fits with

Spectator Cuts

 

 

PL 54+(91111'1' Bejgg)1+1' pd+(p)21+31‘ Bd+(p)21+31‘n°
1.60 .746 e .049 4.25 e .13 1.75 e .08 3.71 e .13
1.75 .573 e .054 3.80 e .14 1.48 e .08 3.60 2 .15
1.85 .553 e .051 3.65 e .13 1.41 e .09 3.93 e .15
2.00 .469 i .048 3.19 e .13 1.41 e .09 3.59 e .15
2.15* .389 i .054 2.23 s .15 1.30 e .15 3.32 e .24
2.30* .250 e .045 2.12 e .20 1.20 e .15 3.38 e .23
2.45* .277 e .043 1.83 e .22 1.10 e .14 3.05 e .25
2.60* .177 e .041 1.81 s .20 .983 e .130 3.08 e .25
2.90* .183 e .045 1.46 e .19 .813 e .100 2.72 s .24

 

* A value of .261 i .055 mb
in the 2.15 GeV/c to 2.90
reaction pd + (p) 1+1'1‘.

was used for the averaged cross section
GeV/c incident momentum range for the

41
5.2 Three Pion Final States

The three pion annihilation channel prominantly exhibits both
0° and f° production. The cross sections for the quasi-two-body final
states fall much more rapidly than the three pion cross section. Re-
sonant production decreases from about 45% of the total cross section
at 1.60 GeV/c to well below 20% at the highest momenta. The resonance
parameters used were (M, r)p = (740, 120)* and (M r)f = (1250, 150)
where M and r are the mass and full width of the resonance in MeV.
Since the three pion cross section is so small at the higher momenta,
the number of events at each momenta (approximately 60) is too small to
fit; hence, only a fit to the combined data was possible in the 2.15 to
2.90 GeV/c momentum range. The resonance cross sections and histogram
X2 values (root mean square deviation of the experimental values from
the fitted values calculated for a particular mass combination) are

shown in Figure 9 and Table 7. Figure 10 shows the fits to the inva-

riant mass distributions from the three pion annihilations.

5.3 Four Pion Final States
Resonance production in the four pion annihilation channel con-
sists primarily of 0°, 9°. 9*, and f°. A small fraction of the quasi-
two-body associated resonance production, 0°0‘, is also present. The
resonance production cross sections fall only slightly faster than the
total four pion cross section. The resonance parameters (M, r) =

(765, 120), (M, r)w = (785, 60), and (M, r)f = (1260, 150) were used to

 

iThe resonance parameters differ slightly from the accepted values.
The parameters used were those which gave the best overall fits to
the data within a given topology.

42

 

 

 

 

 

 

 

 

0.2A
0°1-
3;
£5 0.14
b
1 1 r
1.5 2.0 2.5 3.0
PL (GeV/c)
0.2-1 ,,
f°n'
3 01— i-
D
0 r | l
1.5 2.0 2.5 3.0
PL (GeV/c)
21.3 214 215 2'.6 2.'7
Ec.m. (66v)

Resonance production cross sections

Figure 9.
for the 1+21' channel

43

Table 7. Resonance production cross sections for the n+2,‘ channel

 

 

 

.L /
l.60 .151¢.033 .169:.O4O 68/58 71/58
1.75 .085:.031 .150:.045 54/57 51/56
1.85 .0852.031 .0802.040 56/56 — 52/56
2.00 .051e.030 .108e.040 63/56 60/56
2.15-2 90 .021e.010 .025e.014 75/56 53/56

 

44

Figure 10. Invariant mass distributions for the 1+21’ channel

1455

‘0
N

~.~

A>cov A-e-cv mmcx

 

 

 

 

 

m._ c._ o._ 0.0 N.o
L _ P r ~ P
TOP
10m
10m
o\>mw om.m 1 mp.~
roe
A>mov A1e+ev mmc:
o.~ N.~ m.” v.F o.~ w.o ~.o
r a 1a a a c o
C
r.o_
Tom
r.om
U\>om oo.~ . m_.~
roe

 

A39 VO'/S3U343

A39 tO’/51U343

accmv A-.-ev mmcz

 

 

 

 

N.~ m.p <.— o._ o.o ~.o
_ h P .— b 0
TON
T.oe
i.oo
u\>mo oo.~ 1 om.P
1 cm
A>cmv A-e+ev mmcz
wa mh_ emF oh_ who ~.oo
low
iov
tom
00 .1 .
\> o co N om _ now

 

has to /51u943

A99 30'/S1uana

46

obtain the resonance cross sections and histogram X2 values shown in
Figure 11 and Table 8. Although the A2 was not used in the maximum
likelihood fitting, it was investigated independently. The combined

0

cross sections for A2 and A; was calculated to be approximately

150 i 50 0b at 1.60 GeV/c falling to an upper limit of 40 0b at 2.00
GeV/c. There was no significant evidence for A2 production at any of
the higher momenta. The fits to the invariant mass distributions from

the four pion annihilations are shown in Figure 12.

5.4 Five Pion Final States

In the five pion annihilation channel, the only clear resonance
production was the 0° and the associated p°p°. While the fraction of
resonance production increased from 55% at the lowest momentum to 80%
at the higher momenta, the amount of associated production decreased
markedly. There is a negative correlation between p°n+n'n' and p°p°1‘
which leads to the large errors in the cross sections. The invariant
mass distribution, M(1+,1'), characterizes the 0° as a shoulder on the
high effective mass side of the peak of phase space making fitting dif-
ficult and contributing to the large errors. The mass and FWHM of the
p used in the fitting were 760 MeV/c2 and 120 MeV/c2 respectively.
The 0° and p°p° cross sections and the histogram X2 are shown in Figure

13 and Table 9. Figure 14 shows the fits to the invariant mass distri-

butions from the five pion annihilations.

5.5 Six Pion Final States
Resonance production in this channel was very difficult to

analyze due to the large number of combinations for each process. The

47

 

 

 

 

 

 

 

0.54 O _
(L) 11’
E E
7; II iMi g; I! T?
0 . IJLILJIT.._____'5__‘
1.5 2.0 2.5 3.0
PL (GeV/c)
1.04
+ - -
p n n
E 0.51 i i g
D b
H § § § i
O
1.5 2. 0 3.0
PL (GQV/C)5
1.5-3
1.0- 1 E °°'”'"°
2; E 3
£5 ‘EE
0 0.5.4 ii 1} €£ EE b
0 1
1.5 2.0 2. 3.0
PL»(GeV/c)
T 1 1 T 1
2.3 2.4 2.5 2.6 2.7
Ec.m.(GeV)
Figure 11.

channel

 

 

 

 

 

 

0.54 . _
p p
i i
oJrL—i—r—i—i—EJ—i—i
1.5 2.0 2.5 3.0
PL (GeV/c)
1.0-1
f°n'n
0.5‘1 { i
0 111 i 3]
1.5 2.5 3.0
ZPL (GeV/c)
1.51
1
1.0-1 {{ ° 1'"
0.5- i
01.5 2.'0 2. 3.'0
1 TPL (eeV/cl 1
2.3 2.4 2.5 2.6 2.7
m.(GeV)

Resonance production cross sections for the 11+211'?”

48

 

 

 

 

 

mmxmm ¢e\Fm om\Pm om\P~ om.~
mm\- om\mm om\mm mmxun om.~
mmxmm mmxme mm\e~ mm\pn me.~
mm\mm uwxnm nm\mm om\mm om.~
om\¢m m¢\¢e mm\_m sm\~o mp.m
mm\o¢ me\~e om\mn om\me oo.~
om\oo em\~o om\mn om\mm mm.F
mm\mw ¢m\¢m mm\mm om\oo mn.F
om\mm mm\mm om\mm om\mm oo.p
.=. F .F b. RIF F .=. 4m

I I I o + o + I +

mcwm\~x Emgmopmwz
meo.um~o. oec.npoo. mwo.nw¢m. “no.nmmo. Pmo.nemm. omo.ncoo. om.~
mmo.uwmp. «mo.nm~o. swo.npom. mmo.n_m—. mmo.nmp¢. mmo.ncmo. om.~
oko.nmmo. mmo.no¢o. mop.nem_. mo_.nm-. ¢N_.Hmw~. mmo.nmmo. me.~
Nmo.nxop. moo.n_uo. ___.Mdem. cop.“-m. m~—.Hemm. mmo.neeo. om.m
who.ndup. moo.u-o. m-.HNm¢. moF.H~oN. —~P.neep. wmo.nc¢o. m_.~
mmo.nspm. omo.n_~p. em_.nmmm. mop.“mm_. mmp.oam¢. omo.HN-. oo.~
«mo.uca~. mmo.nmmo. mmF.HFFm. moo.nmo~. oe~.nmmm. omo.nmmp. mm.~
mwo.ns.m. «mo.nmmp. mmp.nmu~. mpF.nF~¢. wep.nmmo. «mo.nmmp. mn.P
mno.nwo¢. _mo.nmeo. mmp.nm__._ mmo.ne¢m. “NF.Hmmo.~ omo.ncmp. oo.P
p+=+ Inc If: I=o=o$ I I... .._n_

Puccmgo oeuem+e mg“ Low as cw meowpumm mmogu :owuuzvoga mucmcommm .m mpnm»

49

Figure 12. Invariant mass distribution for the n+2n'n° channel

 

50

A>ouv “agony «no:

 

 

 

   

 

 

 

. . . . . . ~.o
m»~ ~_~ «_F «_P o._ o.o o
C
row
IomP
Ioem
u\>mu om.~ - mF.~
Io~m
>uo A-e+ev “we:
wh~ ~m~ mm. em_ on. ewe ~.o
C c
Iom
Ioo_
romp
U\>ao om.~ - m_.~
Ioow

 

[132 W ° /5103’\3

A39 70' “10353

1

~.~

N

m...

ml

:08 Aopwev 30:
v...
_

u{>3 oo.~ I on;

A>uuv A-n+=v ”no:
«up

023 oo.~ I 8;

on

 

ad

I omm

I03

I can

 

Io:

IomN

I owe

 

I com

A39 170' #510353

A99 90' ISIUMB

ES].

A>ouv A-u-ev “was

 

 

 

whN NLN mm. em, om. who ~.oo
..om
Ion
roo
U\>ow om.~ - m_.~
+.o~_
A>oav A-:.p+.v no»:
«MN emu om~ amp NM. who ¢.o
o
..om
fi.cop
rem,
U\>aw om.~ - m_.~
f.8~

 

A39 70'/51"3A3

A99 v0'/szuaA3

a>mwv Aupupv mun:

 

 

 

 

 

WWN NHN mw— vw— ow— owe N.oo
Ioc
Iowp
Tom—
0 w . I .
\> o oo N co — Ich
>mw Ankor+:v mmoz
mMN ImmN oh~ on, N“. who e.oo
Iowp
Iovw
flown
U\>ac oo.~ - oo.F I
owe

 

A99 PO'I5103A3

A39 90'/5303A3

52

1.5-4
0+ -
p n n

1.0“

0.5- 1

o(mb)

 

 

I 2.5
PL (GEV/C)

 

1.5—-

1.0-‘

1
I 1 11111

0(mb)

1 L

 

 

 

O 21
1.0 133 210 235
PL (GeV/c) .
211 212 233 234 2f5 23% 2.5
Ec.m. (GeV)

Resonance production cross sections for the
+ p°p°n°

Figure 13.’
2n+3n' channe]. Open points are ppI‘I
from reference 4.

53

Table 9. Resonance production cross sections in mb for the 2n+3n'

 

 

 

channel
Histogram X2/Bins

PL 6° 3n popon- n+n' n'n' n+n+
l.60 .546:.264 .561:.l40 100/56 65/56 64/56
1.75 .451:.287 .498:.l53 lOl/56 54/56 67/54
1.85 .897:.267 .l79:.l48 98/56 42/56 64/53
2.00 .773:.260 .280:.l42 96/56 102/55 52/56
2.15 .0l61.300 .067:.I63 65/56 70/54 52/53
2.30 .935:.278 .lO3:.l44 54/56 7l/56 68/52
2.45 .593:.243 .168i.l27 76/56 63/56 48/54
2.60 .7Io:.210 .069i.ll4 63/56 60/55 40/55
2.90 .5231.l64 .ll0:.087 50/56 59/56 64/56‘

 

54

Figure 14. Invariant mass distributions for the 2n+3n' channel

5555

fi>muv “usury mmoz

 

 

 

 

 

 

m.~ N.N m.” e._ o._ o.o ~.o
_ p _ b — L 0
Ice
1cm.
-omp
6\>oo ca.~ - m_.~
+oe~
“>6wv A-p+=v ”an:
o.~ ~.~ m.p 5., 0.. 6.0 ~.o
LI _ _ L h F O
-ocp
roam
Iowa
6\>6o om.~ - m_.~
[com

 

A39 V0'/51U3A3

A39 PO'/51U353

A>oov Anuuev mmot

 

 

 

 

 

. . . . o. o.c ~.c
ocN ~_~ as. ¢__ __ _ o
..om
Iom_
-oNN
6\>6o oo.~ - ow._
Icon
“>6uv A-.+=v mam:
o 6 o voF . . .
o_N ~_~ m__ 112 o__ m_o N co
Ioow
Iooc
room
o\>ow oc.~ - om._ fi.oom

 

Aag po'/sauaA3

A99 V0'/5109A3

56

only clear resonance in the invariant mass histograms was the 0°. The
0 region appeared only as a slight shoulder on a phase space distribu-
tion and a prediction of 20% 0 looks only slightly different from a
prediction of 80% p production. An attempt was made to determine the
parameters of the 0, however, variations of as much as 45 MeV/c2 in
the central value did not significantly change either the cross sec-

tions or the histogram X2

values. The resonance parameters used,
(M, 1‘)p = (765, l20) and (M, r)w = (785, 40) are those which gave the
best overall X2 values.

There was no evidence for the production of f° and only a small
contribution from 0°. Neither resonance was used in the maximum like-
lihood fitting. The cross section for n° production was less than
50 ub at all momenta.

Initially, the maximum likelihood method was used to fit only the
single resonance 0°, 0°. and 0:. At the three lowest momenta, it was
necessary to include associated production of 0°p° and p°pi. Produc-
tion of 6°p+ decreased rapidly in the lowest four momenta and its in-
clusion was unnecessary above 2.00 GeV/c. The channel p°p°w'n° was
also tried and found to be unnecessary.

The cross section from 0° as well as the associated productions
o°o' and 0°p° at first fall more rapidly than the six pion cross sec-
tions then level out to a constant percentage at higher center-of-mass
energies. The percentage of 0 production increases at first to com-
pensate for the decrease in associated production, then remains essen-
tially constant at higher energies. The resonance cross sections and

2

histograms X values are shown in Figure 15 and Table 10. The fits to

0(mb)
b—fi.——4

0(mb)

 

57

o-+—
00""

”ii;
[1 l h
I 0| l ill; LI
2.0 2.5 . 2.0 2.5 3.
PL(GeV/c) ' PL(GeV/c)

+ _ A - + _
o n+3n 4.; p 21! 211

 

 

 

 

 

 

 

 

 

0

1.5 2.0 2.5 3.0 1.5 2.0 2.5 .0
PL (GeV/c) PL (GeV/c)
I
1.5— °°"+2"_"° 1.54‘
i { w°fi+2fl-
1.0. Al 0. {
.0
ii
° 1
0.5— 0.5— i E i
0 . 1111
1.5 2'0 2 5 To 1.5 2Y0 2 '5 31.0
PL (GeV/c) PL (GeV/c)
233 2'.4 235 2.6 2.'7 213 2.4 2'.5 2.'6 217
Ec m (GeV) Ec m.(GeV)
Figure 15. Resonance production cross sections for the 2n+3w'n°

channel

 

 

58

 

~m\m~ om\oe mm\em mm\oa om\mm ~m\mu om.~
mm\m~ nm\mm wm\mm mm\mm om\em mm\mo oo.~
¢m\mm ~m\om mm\mn mm\mo omxcn ~m\Fm m¢.~
mm\mm mm\mo ~m\mn mm\oo omxms nmx—o om.~
~m\m¢ ¢m\mm mm\om mm\~¢ mm\~m um\mm mp.~
mm\me om\¢o ~m\mm ~m\m¢ ~m\~m mm\~m oo.~
mm\me ¢m\- mm\mm mm\oo mm\mm ~m\oa mm.p
Nm\~¢ om\~m nm\on em\me ¢m\mm mm\mo m~.p
om\mm vm\om mm\mop mm\~w ¢m\om nm\~w cm.—
+p+e Ipun I=ob+ eta: o=+: Ip+= 4m
m=_m\~x Emcmoumwx
8o. 08. RN. “.8. --- 00o. 4:0. 2:. 38. o2. 38. SN. “.08; 9.5.0
8208. 80.08. I. 08.4%». $303. 5.0%. N848: 80
03.450. 80.38. 02.0.00. 5.4.20. 02.480. $.08; 03
mmo.0aop. mm~.0mmp. . III m_F.M¢Fe. oom.npoo. wmp.0meo. mpm.0omm. om.~
cmF.0~m~. mum.fipp_. III mmp.0wue. mpm.0omm. mmP.H—mm. w-.0mom. mp.~
¢~_.0¢mm. emm.0~mp. no~.HP—o. mpp.0¢p~. mop.0mmm. mep.0mmm. u-.0mpo.p oc.~
u¢~.0me¢. mmm.haw~. mo—.Hmpp. mmF.0eom. mm~.n~pm. emp.npm¢. www.0—om. mm.p
emp.0m~¢. mo~.0mem. om—.0~op. wep.0~mP.P o_~.0~mm. cop.0~om. mom.n~o~. mu.p
o-.0mom. Nm_.0mm~. opp.0mmp. ¢m~.0amp.p ~m~.0m~m. amp.0o~m. om~.0m~¢. oo.P
Ikoooa :Nuaoq =N+qoa gmos neua =¢+Q heoo 4m

 

 

Puccmzu oeuem+e~ 0;» go; as cw mcomuumm mmogu cowuuzuoen monocommm .op apnm»

59

the invariant mass distributions from the six pion annihilations are

shown in Figure 16.

5.6 Conclusions

Investigation of the resonance production cross sections in the
annihilation channels has yielded little evidence f0r contributions to
the I=l structures. The only significant channels are the K*an-which
shows an enhancement at 2360 MeV seen both in this experiment and in a
pp experiment8 and the 0°n', the 0°1+n'u' and remotely the 0°p°n'
channels which exhibit possible turnovers in the low energy regions of
the data. All other resonance production cross sections appear to have
a smooth energy dependence and give little evidence for structure. Most
of the resonance production cross sections are decreasing with increasing
incident momentum and those channels which do not decrease are consistent
with smoothly falling cross sections when they are combined with their
corresponding associated resonance production channels.

An enhancement in the p°o°n° channel from pp annihilations at
1.32 GeV/c (2l90 MeV center-of-mass energy) was reported in the forma-
tion experiment of Kalbfleisch et al.4. They determined that this en-
hancement has a cross section of 0.5 i 0.1 mb and a width 20 MeV/c2 <
r < 80 MeV/cz. Their observation of essentially zero cross section
for'pPp°n° at 1.52 GeV/c (no events were observed at either l.ll GeV/c
or"l.52 GeV/c) is confirmed by Parker‘0 in the momentum range from
'l.51 GeV/c to 2.90 GeV/c (p°p°n° cross section of 0.19 i 0.19 mb at
1.51 GeV/c.). If the p°p°1r° channel is isospin one as indicated by

the authors of reference 4, it should be reflected in the p°p°1r‘

60

Figure 16. Invariant mass distributions for the 24+3I'n° channel

ES].

~.~

“>00v A..wev 00.:
0._ .m_

u\>ou cad I m_..~

fl>oav AIu+eV 00.:
0., 1m,

 

I22.

I one

I cum

 

 

0:3 om.~ I m...~

 

I62.

I03

Io—m

 

168

439 tO'ISIuana

A39 90' #311343

A>owv AIenev 00.:

 

 

 

 

o.~ ~.~ a; TP 0... m6 ~.o
I? n h — _ p O
Io-
Ia:
loco
U\>om co.~ I cm.—
[can
:4: 2-..: a...
ohw ~_.~ m_.— v... o__ o.c w oo
Iovw
I63
IONA
o\>oo co.~ I omé Iowa

 

A99 90' “311343

409 v0'lsaua43

62

I!“ .1!

 

:68 A}: 3.:

 

 

 

 

 

0m~ «MN 0“. mm. ch_ ova ~.oo
rag
romp
Iosu
u 0 I I
\>00 om N m. N room
:08 fit; 3.:
om~ New 0mm eh. «m. 0pc «.o
Ioow
Ion
Ions
ux>0¢ oo.~ - 0_.~
Io¢o_

 

A99 PO'/510343

m t0'/s3u943

:08 Aunt; 00-:

 

 

 

 

 

 

0.~ ~.~ 0.. 4., o._ 0.o ~.o
P p _ r b b O
1.on_
:8
I80
6\>o0 o¢.~ - 00._ ..c~m
A>o0v A-...+.. 00.:
WWN epw OWN 0m_ mh_ who ¢.oo
Io~¢
Ioca
woe~p
6:8 8.~ - 8;
Iowa?

 

A39 VO'ISIUOAH

63

channel from the five pion annihilations in in which must be I=l.

Since 5p is an equal mixture of I=l and I=0, the pp I=l cross section

is half the in cross section. Thus, if the p°p°n° channel is isospin
one. it should contribute 1.0 i 0.2 mb to the total I=l cross section

at 1.32 GeV/c incident momentum. Assuming that the pp'+ p°p°n° cross
section of Parker at l.51 GeV/c is a mixture of I=l and I=0 and repre-
sents solely background for the ppn channel, the 0.6 i 0.2 mb observed
for in +-p°p°n' at 1.60 GeV/c would indicate a width for the ppn enhance-
ment much larger than that reported by the authors of reference 4 (see
Figure 13). Further data at lower energies is necessary to confirm an

I=l p°p°n’ enhancement in pn at 2190 MeV.

CHAPTER 6

UPPER LIMIT ON THE DECAY RATE 01+ 2n

Recently, experimental result526’3] have been reported indica-
ting the existence of the G-parity violating decay 0'+ 2“. This decay
has been seen as an interference effect between 0 + 2n and p-+ Zn in
the W n' invariant mass distributions. A knowledge of the coherence
between the o and the 0 amplitudes is necessary to obtain the branching
ratio I

. R = (0 +'n+n')/(0 + n+n°n') (9)

32, the 0 and p

In an e+e' colliding beam experiment at Orsay
production amplitudes are known to be completely coherent and a value
of R = 3.5 :32? % has been obtained. Groups at Daresbury33 and M.I.T.34
from coherent photo-production of pion pairs off nuclei, have obtained
R = 0.80 :8:23 % and R = 1.22 t 0.30% respectively. Their results rely
on the ratio of photon-o and photon-w coupling constants which each
group determined independently. In most strong interaction experiments,
the degree of coherence between the p and 0 production amplitudes is
unknown and only a lower limit on R has been determined. A unique ex-
ception to this case in the strong interactions is the pn interaction
where the p and 0 production amplitudes are completely incoherent.
Nucleon-antinucleon states of total isospin I, total spin 5, and

parity (-l)L+1 are eigenstates of G-parity with eigenvalues35

64

 

 

65
G = (4)L+S+I (10)

Since in is a pure I=l state, G = (-1)L+S+]; therefore, states of oppo-
site total G-parity proceed from states of different spin or different
parity. G-parity is multiplicative in all mesonic states and the p and
0 have opposite G-parity. Thus if G-parity is conserved in the produc-
tion process, for a given pion multiplicity, p and 0 can proceed only
from different states of G-parity which cannot interfere.

In the search for the n n' decay of the 0 in the three and five
pion annihilation channels, the experimental mass resolution was deter—
mined by taking events which fit the three and five pion hypotheses and
reprocessing them through TVGP-SQUAW, fitting them to the hypothesis

d ' n+1r' X°
p ”M )bI+II' (H)

The resolution for two pion invariant mass combinations between 0.7
GeV/cz and 0.8 GeV/c2 from the three and five pion annihilations was
found to be 11 MeV/cz, FWHM, in the 1.60 - 2.00 GeV/c incident momentum
range and 14 MeV/c2 in the 2.15 - 2.90 GeV/c range. Figure 17 shows
the ideogramed mass resolution where the invariant masses have been
fixed at 750 MeV/c. The resolution for 0-+ 3n was determined by the
width of the 0 distributions in the four and six pion final states
since the natural decay width of the w is much smaller than the three
pion resolution. Values of 60 MeV/c2 and 40 MeV/cz, FWHM, were obtained
for the four and six pion final states respectively.

In the interest of maximum statistics, the data from the four
lowest momenta and the five highest momenta were combined into two

groups for both the three and five pion channels. The amount of

Figure l7.

66

Resolution ideogram of the error from invaria t mass

combinations between 0. 7 2GeV/c2 and 0. 8 GeV/c

mass fixed at 0.
l7.l Ideogram
momentum
17.2 Ideogram
momentum
17.3 Ideogram
momentum
l7.4 Ideogram
momentum

75 GeV/c2

for events
range 1.60

for events
range l.60

for events
range 2.15

for events
range 2.15

with the
fitting pd 4 pn+2n- for the
to 2.00 GeV/c
fitting 5d 4 p2n+3n- in the
to 2.00 GeV/c
fitting 66 4 pn+2n' in the
to 2.90 GeV/c
fitting pd 4 p2n+3n- in the
to 2.90 GeV/c

6'7

[.055 o v. .

1! . old.“ «II-L...

>02 AI=+evmmoz

 

 

 

 

 

 

 

m.n—

 

cow cam ooh och own ooh
T p b _ _ o
I p
I N
u\>mw oa.~Imp.~
-em+.~. I em I m
I e
c.5p
>0: 7...... 03:
cow can can ovs on“ com
Fri . . F b o
I F
..N
u\>um ca.~Im—.~
I:N+=n + um In
.Ie

 

satun Kueaniqav

SIIun KJEJIIQJV

>6... Frets...

 

 

 

 

 

 

 

com emu ooh o¢n cum cos
r41 4 . . pi e
I p
rN
4_m
U\>ow oo.NIom.—
I=m+=Nn + vm 4.¢
N.h—
>0: AI=+evmmaz
cow ems own ads own con
W111 p . . . o
I p
I N
U\>mw oo.NIom.p
I m
Ie~+ea i um
f 4

p.5.

 

sIIun KquIIqav

S4100 KJPJIIQJV

68

0 +-n+n' was fitted employing the maximum likelihood method with the mass
and width for the 0 set at 784 MeV/c2 and 15 MeV/c2 respectively. All
other resonance parameters were the same as those found to give the best
overall resultsin the determination of the resonant production cross
sections. The amounts of resonant production other than 01+ 2n were
checked and found to be very nearly the same as those without the inclu-
sion of 0-+ Zn.

In the low momentum data, the branching ratio was determined to be
R = 2.89 i 6.19% from the three pion channel and R = 0.62 i 2.58% from the
five pion channel. There was no eivdence for 04+ Zn in the high momentum
data in either the three or five pion channels with branching ratios of
R = 0.0 i 9.92% and R = 0.0 i 5.11% respectively, however the large errors
do not rule out the possibility for a small amount of 0 + 2n. 0n the
basis of the most significant channel, namely the five pion annihilations
at the lowest momenta, an upper limit of 5.78% can be placed on the value

of R at the 95% confidence level.

 

 

CHAPTER 7

ANGULAR AND MOMENTUM DISTRIBUTIONS

Recently there has been a great deal of interest in single par-
ticle distributions as a means for understanding various reaction pro-
cesses. The results from nucleon-anti-nucleon annihilation studies
have been reported in various journals, however, almost all the data
published is from proton-antiproton reactions.

The center-of-mass angular distributions, relative to the beam
direction, for events fitting the reaction hypotheses 5n +'mn, where
m = 3, 4, 5 and 6, and where the number of neutral pions is less than
or equal to one, are shown in Figures 18, 19, 20 and 21 respectively.
The distributions for the three pion annihilations have been combined
into the two momentum groups for greater statistics. The solid curves

are fits of the data to the first five Legendre polynomials of the

form
P0(x) = 1 (12)
P](X) = X (l3)
P2(x) = 1/2(3x2 - 1) (14)
P3(x) = l/2(5x3 - 3x) (15)
P4(x) = 1/8(35x4 - 30x2 + 3) (16)

where x is cos one m . The fitted coefficients for the Legendre poly-

nomials are shown in Table 11 and Figure 22.

69

70

Figure 18. Angular distributions for the three pion final state.
The solid curves are fits to the Legendre polynomials

IOO

80

60

40

20

4O

 

 

 
 

_ l.60-2.00 GeV/c I

 
    

_

2.I5-2.90 GoV/c

 

 

 

71

240

200

160

l20

80

4O

80

4O

 

 

 

2.I5 -2.90 GoV/c

W

 

 

 

 

 

72

Figure 19. Angular distributions for the four pion final state. The
solid curves are fits to the Legendre polynomials

 

 

 

 

 

20

2.30 GeV/c 3°
20

20

\

\

\l
”g
(N
O

5050‘
ooo\o
l:\l:

\

2.30 GeV/
20

260 * 120
'20.. 220 I00- l.60 GeV/c
l.60 GeV/c
_ l.60 GeV/C IBO- 80'-
N
80” '40 7° 1.75 GeV/c
1.75 GeV/c
60 .. L75 GeV/c l001— 50-
I!
M 80
40F 70
// |.85 GeV/c |.85 GeV/c
60P 60
50 ’
l/ M 60
50 2'00 Gewc I00 2'00 GW‘ 50 2.00 GeV/c
4o~
30 - 60’; G 7/
” 2.I5 eV/c
30 2.15 GeV/c 50 301 2.15 GeV/c Iii
I a

l’ 2.45 GeV/c

\

\ O
\I \I
I"
b
u l
C)
o
<
c}
A
o
‘f i
\

2° 3° 2.45 GeV/c
IO 20 20
30 2.60 GeV/c ” 2.60 GeV/c IO-

\

60 30 2.60 GeV/c

 

 

 

 

 

 

 

 

 

4O 20-
lo” 2.90 GeV/c . /
20°1 II n f 20" 2.90 GeV/c 30
I0 _ 4O 20 2.90 GeV/c
0 ~ 20- 10h _
O 1 O l O l
- LO 0 IO -l.0 O 1.0 -|.O O 1.

cos 6,,+ cos e,- cos 9,0

74

Figure 20. Angular distributions for the five pion final state. The
solid curves are fits to the Legendre polynomials

 

 

120 - I160 GoV/c

 

o).

.80

1.75 GeV/c

4O
80
60
4O

80
2.00 GeV/c
4o
40 2| 5 GeV/c
20E w I]
61

6

2 .30 GoV/c
20 -

J

40 2.45 GoV/c
20

  

1.85 GoV/c

 

2.90 GeV/c

 
      

   
  
 

 

40 2.60 GoV/c
20
4o
0
- I

 

.0 0 1.0

cos 94+

75

' 60 2.1560V/c

 

220‘
180

1.60 GeV/c
I40 -

I00 1.75 GeV/c
/

 

100 1.85 GeV/c
80
60
IOO
2.00 GeV/c
60

40

60 2.30 66M:

20

6° 2.45 GeV/c
4O
20 .
60 2.60 GoV/c

   
  

 

 

 

76

Figure 21. Angular distributions for the six pion final state.
The solid curves are fits to the Legendre polynomials

 

l60
l.60 GeV/c
120
IOO-
ll
l20 r
I75 GeV/c
80
H
'20 ' I.85 GeV/c

80 W
l
'00 P 2.00 GOV/C

60’;-

80 - 2.15 GeV/
WM
40 -

I
30’. 2.30 GeV/c

60%
4o -
8°C 2.45 GeV/c

60_ 2.45 ”F

4°77 2.60 GeV/c

80
60
ll
80 - 2.90 GeV/c

\

\

I

40-

 

 

I

o 1.0
cos 9,4

 

L
b

77

 

240

200 -

|60

\

\

.b
\0
\IE

/
IOO
80

\
\

l20

80

60-
ll
l20-

IOO

ll

 

L75 GeV/c
120-
I
'60 I.85 GeV/c
120 -
l

1401‘ 2.00 GeV/c l:
I00;

‘ZJS GeV/cl] V
H
2.45 GeV/c
80

ll
l20 -
2.90 GeV/c
80

l.60 GeV/c

2.30 GeV/c

     

2 60 GeV/c

 

 

-I.O

o 1.0
cos 9,-

 

8

O

1.60 GeV/c

60

\
\

50- 1.75 GeV/c

3O

71%?

\

60- LBS GeV/c

50 2.00 GOV/C

‘9?

2°,

40- 2.I5 GeV/c
)

50

40 2.30 GeV/c

30
50

3O
60

\ \
\I I I
I“
b
at
6)
a
.5

 

 

 

 

50
40
I
40
30
20
J .
-I.O 0 LG
cos 9,,o

Table 11.

78

Legendre polynomial coefficients

ll.l Legendre Polynomial Coefficients from the three
pion final state

11.2 Legendre Polynomial Coefficients from the four
pion final state.

11.3 Legendre Polynomial Coefficients from the five
pion final state

11.4 Legendre Polynomial Coefficients from the six
pion final state

79

U. .flflqulué—

‘H

 

 

 

 

, «J
3.5 8.408. 02.42:. 08.40%. «8.38... 08.4.8. 8.3-2.0. m
8.2 .863... 08.408. 98.38. 08.403. 8943.... 83-8.: 0.0.
«J
2;. 00.448. .248..- 02.402. 8.408.- 48.420. 82-2.3 m
Au
2...: 4.848.. 03.48.. 08.4.8. $9.03. 08.4.8. 48.0-8... 1+
o

Nx 34. 30. EN. 3:. 3 a 3:08...

.mamum —0=wm sown megs» 0;» son; mpcmpuwemmou Papsocapom 0Lu=0m04 F.—P «Fame

 

80

Table 11.2 Legendre Polynomial Coefficients from the four pion final

 

 

 

State.
PL Po(x) P](x) P2(x) P3(x) P4(x) x2
jGeV/c)
1.60 .993¢.024 .061:.042 .135¢.055 .062:.065 .051¢.076 13.48
1.75 .994:~.03l .lSli.056 .167:.072 .074¢.086 .118:.101 6.49
+ 1.85 .985:.03l .078i.053 .030:.070 .I04i.083 .043:.095 15.63
= 2.00 .971:.035 .045:.062 .206:.079 .132:.094 -.067:.109 23.95
<9 2.15 .965:.048 -.020:.090 .450:.115 -.002:.135 .059:.152 15.44
g 2.30 9244.048 -.059:.084 .048:.105 2024.130 -.213¢.150 30.13
a» 2.45 .948:.055 .026i.097 .062e.129 .175e.154 .l96:.169 16.36
2.60 .946:.046 .077e.081 .018e.099 .077:.120 -.380:.l4l 23.17
2.90 .952e.055 .0513.099 .250:.134 -.087i.159 .349:.I75 15.79
1.60 .997e.017 .032:.031 .348e.040 -.O36:.047 .135e.055 14.18
1.75 .997:.022 -.017:.04l .301:.053 -.013:.062 .046¢.07l 7.98
, 1.85 .996:.022 .022:.040 .339:.052 -.123:.061 .085:.069 10.18
= 2.00 .992:.025 .051:.046 .341:.059 .071e.069 .039:.079 14.66
<9 2.15 .986e.034 .024:.062 .282:.080 .105:.094 .037:.107 12.17
32.30. .975e.035 .001:.066 .456:.085 .053¢.100 .130:.111 21.30
59 2.45 .971:.040 .090e.074 .402:.095 -.065:.111 .070:.126 18.44
2.60 .978:.033 .122i.063 .435:.081 .l36:.093 .ll4¢.l08 20.26
2.90 .959:.039 .058:.073 .490:.100 .133:.111 .574¢.124 28.09
1.60 .994:.024 .036:.044 .362:.056 .023t.066 -.083t.077 11.50
1.75 .979:.031 -.138:.057 .302:.073 -.096:.085 -.o49e.099 21.76
1.85 .987:.031 -.071¢.057 .384:.074 .082:.087 .095t.100 14.92
a. 2.00 .984:.035 -.219:.065 .430:.084 -.2331.097 .089t.ll4 13.96
Cl,2.15 9622.047 .057:.090 .469e.118-.008¢.134 2911.158 17.21
m 2.30 .968e.049, .104:.095 .577:.l23 -.1601.142 .240e.157 13.48
:3 2.45 .937e.055 .152:.100 .267t.134 -.16Lt.l63 .220:.184 19.86
2.60 .974:.047 .0101.089 .487t.ll8 -.067:.133 .355t.152 12.36
2.90 .936¢.054 .394:.105 .543:.l33 -.048:.151 .062:.l79 20.59

L'f-l‘."

 

 

81

Table 11.3 Legendre Polynomial Coefficients from the five pion final

 

 

state.
PL P() P() P() P() M) x2
(GeV/c) 0 x 1 x 2 x 3 x 4 x

1.60 .998:.023 .084i.042 .260:.055 .030:.064 .060t.074 5.40
1.75 .9904.031 -.054¢.055 .l73:.073 -.087¢.086 .134:.098 11.69
+ 1.85 .979:.031 -.015:.057 .292:.075 -.052:.087 .334:.100 23.57
5 2.00 .982:.032 .060:.060 .424:.077 -.072:.090 .091¢.105 17.94
0> 2.15 .967:.042 .100:.076 .254:.100 -.084t.115 .233t.I35 18.81
g 2.30 9774.044 .073:.080 2351.105 0553.120 240.140 12.26
5’ 2.45 .9511.044 .012:.082 .341e.107 .086e.124 .128:.l45 24.45
2.60 .966:.043 .048:.178 .248:.102 .243:.117 .212e.135 18.54
2.90 .946:.049 .1394.092 .408:.120 -.097:.l42 .080:.165 21.57
1.60 .996:.019 .005:.034 .240:.045 .033:.053 .187t.061 14.15
1.75 .987:.025 .064i.046 .264:.060 .015:.07l .157:.081 21.61
1.85 .990:.025 .044:.047 .378:.062 -.022:.073 .242:.082 17.74

'e 2.00 .9921.026 .020:.049 .385:.064 .017:.073 .172:.085 12.69
0’ 2.15 .980:.034 -.074:.063 .277:.083 -.122:.099 .155:.112 17.15
2; 2.30 .985:.036 .053:.067 .363:.086 .121:.lOO .103:.ll8 11.87
F’ 2.45 .992:.037 .030:.070 .450:.089 .020:.104 .019:.120 6.53
2.60 .978¢.035 .041:.065 .338i.084 -.04&t.099 .049:.115 17.62
2.90 .974:.041 .021:.080 .687:.101 .082¢.116 -.008:.134 15.92

 

1F.'. in 1';

Table 11.4 Legendre Polynomial Coefficients from the six pion

82

 

 

final
state.
PL p (x) p (x) p (x) p (x) p (x) x2
(GeV/c) ° 1 2 3 4
1.60 .994:.020 .101:.035 .035:.045 .057:.054 .042:.062 16.57
1.75 .984:.025 .053:.044 .058¢.057 .032:.069 .006:.079 25.28
1.85 .991:.024 .005:.042 .081:.055 -.093:.066 .076:.074 17.20
.4: 2.00 .993:.025 .046:.043 .023:.057 .017i.068 .12ae.079 12.59
In 2.15 .990¢.030 .082:.052 .066:.065 -.160:.079 .240&.092 9.69
3 2.30 .992:.029 -.026:.050 .019:.066 -.047:.077 .168¢.090 11.10
c) 2.45 .993:.030 .076:.053 .091:.069 -.009:.083 -.026e.096 7.93
2.60 .992:.026 -.025¢.046 .0361.059 .051:.07l -.161e.083 10.46
2.90 .986:.030 -.013:.056 .334:.07l .052:.082 -.006t.096 15.29
1.60 .996:.016 -.021:.029 .210t.038 .056e.045 .ll4¢.052 19.68
1.75 .995:.020 .003:.037 .202:.048 -.048:.057 .022:.065 '13.32
1.85 .995:.019 .021:.o35 .165:.045 -.056:.052 .038:.06l 13.61
g: 2.00 .993:.020 .009:.o37 .188:.048 -.069:.057 .054:.065 17.22
CD 2.15 .989:.024 .022e.043 .127:.057 -.021:.067 .l66:.077 19.83
32.30 9903.023 .063:.042 2101.056 -.076e.066 2251.076 20.40
a: 2.45 .993:.025 .094e.044 .177e.057 .015:.068 .036:.079 11.62
2.60 .994:.022 .158e.038 .122:.050 .017:.059 .150t.068 13.51
2.90 .991e.025 .112:.045 .293:.059 .042&.069 .167:.079 16.07
1.60 .986:.028 .022:.o49 .062:.064 .034t.076 .025:.089 18.39
1.75 .982:.035 .046:.062 .IO3t.078 -.081:.094 .238:.110 13.86
1.85 .985e.033 .069:.058 .037:.076 -.l97:.089 .0601.103 13.18
g: 2.00 .987:.035 -.216:.063 .177:.079 -.160t.095 -.l46t.llO 10.43
02.15 .969:.042 -.232:.073 .050:.092 .086¢.108 .183:.127 17.09
g 2.30 .975:.04o -.399:.073 .225:.095 .000:.113 .1196.125 15.72
ca 2.45 .973:.o42 -.664e.o78 .324:.102 .043e.118 .062t.128 15.33
2.60 .985:.037 -.510¢.068 .261:.086 -.023:.102 .043t.IIG 10.95
2.90 .979e.042 -.4891.077 .20&:.099 .114¢.117 .136 11.94

.0343

 

 

1‘55? ‘13 ’3‘}: "
l

 

r 31!. “I. .I

 

Figure 22.

83

Legendre polynomial coefficients

22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8

Legendre
the four
Legendre
the four
Legendre
the'four
Legendre
the five
Legendre
the five
Legendre

polynomial
pion final
polynomial
pion final
polynomial
pion final
polynomial
pion final
polynomial
pion final
polynomial

coefficients
state
coefficients
state
coefficients
state
coefficients
state
coefficients
state
coefficients

the six pion final state
Legendre polynomial coefficients
the six pion final state
Legendre polynomial coefficients
the six pion final state

for
for
for
for
for
for
for

for

n+ from
11" from
11° from
11+ from
11" from
11+ from
11' from

n°,from

F0111

0m

 

0.2— f
0.14 II

84

0.5-1

0.4..
0.3.4

0.2-1

1 1 :z:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0. I T‘ I ‘_ 1
I i l s
-0.L. -0.1- 1
I 1
t
-0.2- *
L 1' .
0.5-
1
0.4 0.4— h
0-3- P3 .- .. 0.3- P4
0.24 IIIfi 0 24 1
0.14 1’ 0,]-
d. I T T
0.- ._ L 0 o
‘F‘ 1 1 I
-o.L -0.1_
. 1 1'
-0.2 -0.2_
1 .,
-o.3- -0.3_
.1.
-0.4.. I
I -0.54 L
115 270 215 310 115 230 255 310
PL(GeV/c) PL(GeV/c)

Figure 22.1 Legendre polynomial coefficients for n+ from the

four pion final state

 

 

0.2-

0.1-

 

..
0.6..

0.5..

0.4-

0.3-4

0.2-1
0.1..

 

 

 

c.mfié I FBI 0.0 1

 

 

-0.1- i 1.
- 1'
0.2- 0 6-4 “I
-0.3_ 0.54
I
0.4-4
0.34
0.3'1 p4
0.24 P 0.2-4

0.1.1

.1
1111111 A‘ M

-o.3_ I
.L
55

 

 

 

-0.l 4

Ff

 

 

 

I

135 210 275 3.0 1
PL(GeV/c)

I , f I

. 2. 3.0
PL(GeV/C)

Figure 22.2 Legendre polynomial coefficients for n‘ from the four
pion final state .

 

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 '1
0.7.4 -
1 1-
0°6_ 1? + T
.1
0.5.. P2
1L. 1
0.4- I ‘L
J. V ¥ ¥ “- 4L
0.3-
0.2-i p'l 0.2"I
0.1. I; 0-1-4
0.0 iE 0.0
l
f L
-0.2. I}
-0.3_ o 511 T
-0'4" 0'04— T v- 7'
ai- -
p 1
0.2.] p3 0 2- 4 T # JL I
L
0.1— - O.I"‘ - JI-
” I
0.0-,iI—44 1+ 1 +~- 0-0 T - . If
-0.I-1 ‘ -0.Ii- ¥ T .1.
-03. T T .L '0'2'1
-0.3— .. .1 -0.3..
.1. JL
1f5 zfo '2T5 330 115 230 215 370
PL(GeV/c) PL(6eV/c)

Figure 22.3 Legendre polynomial coefficients for n° from the four
pion final state

 

 

 

 

 

87

1
0.5-[
0.4% P2 i

 

 

 

 

 

 

 

 

 

 

 

 

 

0'3“ 0.3- i ¥ F
P
o.2~ l o.2~ { a
0.l- é } 0,1s l
0.04 0.0 t
-o.1— -o.1_
'0-2- -o.2
o l
.. 1.
0-5- 0.5..
o.4q 0.4- ._
'1 7’ 1-
0.3— o.3s P4
P 4 k T l P
0.2« 3 0,2- H l
0-1~ 0.1- ; JL L * h L
0,0 l; 'T 't 'T 1. LT 0.0
‘.L J. L i it
Ji-
'°°‘- -o.i—
.L
-o.24
.i I
11? 2.0 215 370 1'3 2.‘0 ‘21.? 310
PL(GeV/c) PL(GeV/c)

Figure 22.4 Legendre polynomial coefficients for n+ from the five
pion final state

88

0.8-

0.7~

0.6-

0.5-

 

o.3«
v i
002"l P 002‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
0.1" i 0.1-1
00-ij ,— l r I
It 1‘

-o 1- -o.1.o
-o.2e

‘ 1r

0.4-1

r

0.3.] 0.3.. P4
WP
0.2” P3 0.2-I { +
0.1.. " 0.1 ~ : ll V
o.o.¢i¥_dE T if _ AILT 0.0 L +r-
I ‘ l 1

-05]- * J. T -O.'| .q L
“0.2—1 4. “0.2‘
-o.3_, -o.3.

.L L

115 270 225 330 ifsi 2fo 2:5 STO

PL(GeV/c) PL(GeV/c)

Figure 22.5 Legendre polynomial coefficients for n' from the five~
pion final state

89

 

0.4..
.11.
0.3-4

 

 

 

 

 

0.2: P] 0.2.. P2

o.l-'iE ii 1E ii 0.1 “_iEjEiE ;E I} I;

0.0 ii T I i. 0'0'1 T i

1 1 1 l
T 0.3- P4

0.2-4 p 0.2 «

1H

r1
h

may l 23‘; i

H
H—fi

 

 

 

 

-o.2.. -o.2—
-o.3.. -o..3d
-o.4_ -o.4'.1
11 J .
“5 2.’o 2i5 37.0 1.? 2.11 215 A 3.10
PL(GeV/c) PL(GeV/c)

Figure 22.6 Legendre polynomial coefficients for n+ from the six‘
pion final state -

 

90

 

0.2+

01- p f on
0:0-T;H§§é i 0:0 f

'0.]--4 '0.]-1

 

 

{F‘- LA --_- L'.-I.‘.‘

 

 

 

 

 

 

 

l'-5 210 2.'5 310 1T5 2.‘o 2.5 3.0
PL(GeV/C) PL(GeV/c)

Figure 22.7 Legendre polynomial coefficients for w' from the six
pion final state

0.2-
0.1-4
0.0
-0.1..

-0.24

-0.5-
-0.6d

-0.7_

 

0.2~

0.1-

0.0

~|

 

 

-0.1«
-0.21

-0.3-

4L

 

Ha—d

H

 

'__

r—-Ir-——1

“0.1 -1
-0.2-

-0.3-a

 

r

1.5

I
2.0

23
PL(GeV/c)

0.4-a

0.3-

0.2-1

 

 

0.1—-

0.0

 

IIFXT'. m-I ’

 

 

JL

 

 

 

 

 

r

1.5

2.'o 215
PL(GeV/c)

3.0

Figure 22.8 Legendre polynomial coefficients for n° from the six

pion final state

92

To discuss the cos one m. distributions, it is convenient to de-
fine the following parameters
‘ no (17)
P/E (l8)

asymmetry A

collimation C

where F is the number of pions going forward in the center-of-mass

(cos 91r > 0), B is the number going backward (cos 91r < 0), and P and E
are the number of polar and equitorial pions (|cos Qfll > 0.5 and
Icos Owl < 0.5 respectively). Unlike pp annihilations, in pn there is .

no charge conjugation, coordinate rotation (CR) invariance, thus one s I .

 

[r

charge state cannot be folded into another and each charge state must
be investigated independently. The asymmetry and collimation parameters
as well as the cosine center-of-mass quadrant values used to calculate
them are listed in Table 12 and ploted in Figure 23.

In the three, four, and five pion annihilations, there is very
little asymmetry in the cos 91T distributions with most of the values
being within one standard deviation of unity. In addition, no clear

trends are present among the none momenta for any particular charge
state. Collimation in these channels is readily apparent but despite
the appearance of effects seen visually in the distributions, the only
discernable trends are in the cos Gfl- distributions for the three and
five pion channels. In these channels, where all the pions are in a
charged state, the collimation of the n' increases with increasing mo-
mentum. As in the four pion annihilations, the collimation of the six
pion distributions remains relatively constant as a function of momen-
tUm and the asymmetry parameter of the n+ is nearly unity. However,‘

contrary to the trends at lower multiplicities, the asymmetry of the

Table 12.

Figure 23.

93

Asymmetry and collimation parameters

12.1 Parameters for n+ from the three pion final state.
12.2 Parameters for n+ from the three pion final state.
12.3 Parameters for n+ from the four pion final state.
12.4 Parameters for n" from the four pion final state
12.5 Parameters for n° from the four pion final state.
12.6 Parameters for n from the five pion final state.
12.7 Parameters for n' from the five pion final state.
12.8 'Parameters for n from the six pion final state.
12.9 Parameters for n' from the six pion final state.

12.10 Parameters for n° from the six pion final state.

Asymmetry and collimation parameters

23.1 Parameters for n+ from the three pion final state.
23.2 Parameters for n: from the three pion final state.
23.3 Parameters for n from the four pion final state.
23.4 Parameters for n‘ from the four pion final state.
23.5 Parameters for n° from the four pion final state.
23.6 Parameters for n+ from the five pion final state.
23.7 Parameters for n; from the five pion final state.
23.8 Parameters for n from the six pion final state.
23.9 Parameters for n“ from the six pion final state.

23.10 Parameters for n° from the six pion final state.

sea.
state.

state.
;tate
tate.
tate.
tate.
ate.
We
'ate.

ate
ate.
:9.
te.

94

Parameters for n+ from the three pion final state.

 

 

 

 

 

Table 12.1
PL Cos 9 center-of-mass
Asymmetry
GeV/c -1<x<-.5<x<0.0<x<0.5<x<l
1.60 133. 113. 114. 148. 1.043 +.096/-.088
1.75 63. 49. 63. 77. 1.250 +.171/-.l48
1.85 71. 57. 55. 78. 1.039 +.137/-.121
2.00 56. 53. 50. 44. .862 +.130/-.114
2.15 33. ’21. 28. 29. 1.055 +.222/-.182
2.30 17. ll. 16. 15. 1.107 +.335/-.254
2.45 22. 15. 8 18. .702 +.204/-.164
2.60 19. 7. 14. 16. 1.153 +.362/-.271
2.90 11. 8. 8. 11. 1.000 +.387/-.279’
2'51 Asymmetry 2°5'“
2.09 2.0.4
1.5)" .1, ‘1" 1.5-1 ¥
1 . . 11
1.0‘1‘i 1.0-1
E .L J- =
1 .
0.5- 0.5-1
0.0 0.0
1.5 1 2‘5 370 1,5

PL(GeV/c) .

d

Collimation

.259 +.118/-.
1.250 +.171/-.
.330 +.181/-
.970 +.146/-
.265 +.272/—
.185 +.362/-
.739 +.571/-
.666 +.578/-
.375 +.566/-

Collimation

 

 

 

107
148

.156
.127
.219
.272
.403
.403
.383

a P rum-0.1.4 (4.1-“WT? ‘-"-1

 

 

 

1‘ 1
2.0 2.5
PL(GeV/c)

Figure 23.1 Parameters for n+ from the three piOn final state

3.0

95

Table 12.2 Parameters for n‘ from the three pion final state.

PL Cos 9 center-of-mass
Asymmetry Collimation
GeV/c -1<x<-.5<x<0.0<x<0.5<x<1

1.60 280. 218. 229. 299. 1.060 +.068/-.064 1.295 +.085/-.079
1.75 135. 127. 101. 141. .923 +.086/-.079 1.210 +.114/-.103
1.85 145. 118. 100. 159. .984 +.090/-.082 1.394 +.132/-.119
2.00 112. .75. 86. 133. 1.171 +.123/-.111 1.521 +.168/-.148
2.15 59. 56. 54. 53. .930 +.133/—.117 1.018 +.146/-.128
2.30 37. 24. 24. 33. .934 +.189/-.158 1.458 +.313/-.249
2.45 39. 17. 33. 37. 1.250 +.250/-.205 1.520 +.318/-.254
2.60 35. 21. 18. 38. 1.000 +.208/-.172 1.871 +.450/-.343
2.90 25. 13. 14. 24. 1.000 +.259/-.205 1.814 +.541/-.391

 

2.5 " Asmtry 2.5"J C0111Mt10n

 

 

T T
2.0- 2.04
.. 1 1 b
1.52 in '
1.5-1 E i . fi ..

 

 

1.04 2 ii;

.11 ,- 1

 

 

 

 

0.5.. .o.5_
0.0 0.0
1.5 2'.o 2.'5 3.0 1.5 2.'o 215 370
PL(GeV/c) PL(GeV/c)

1’igure 23.2 Parameters for n" from the three pion final state

 

96

 

 

 

Table 12.3 Parameters for 1+ from the four pion final state.
PL Cos 0 center-of-mass
Asymmetry Collimation

GeV/c -1<x<-.5<x<0.0<x<0.5<x<1
1.60 441. 419. 425. 492. 1.066 +.051/—.049 1.105 +.053/-.051
1.75 247. 227. 241. 298. 1.137 +.074/-.069 1.164 +.076/-.071
1.85 247. 271. 247. 286. 1.029 +.065/-.061 1.029 +.065/-.061
2.00 211. 194. 189. 221. 1.012 +.073/—.068 1.127 +.082/-.076
2.15 126. 86. 98. 118. 1.018 +.103/-.093 1.326 +.138/-.123
2.30 105. 106. 87. 105. .910 +.095/-.086 1.088 +.114/-.103
2.45 75. 83. 73. 80. .968 +.116/—.104 .993 +.119/-.106
2.60 121. 94. 115. 111. 1.051 +.105/—.095 1.110 +.111/-.100
2.90 77. 77. 79. 85. 1.064 +.126/—.113 1.038 +.123/-.110

2.5.1 2.5-

Asymmetry Collimation

2.0- 2.0-

1.5- 1'51 ‘E

1.0..i ““111 1.o_§.§§ §éi£

0.5.. 0.53

0.0 r I j 0'0 I l 1
1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0

PL(GeV/c) PL(GeV/c)

Figure 23.3 Parameters for 1+ from the four pion final state

-- “‘“J'V'
~h-J.

 

97

Table 12.4 Parameters for n' from the four pion final state.

 

 

PL Cos 9 center-of—mass
GeV/c -1<x<-.5<x<0.0<x<0.5<x<1
1.60 1027. 778. 773. 976.
1.75 574. 447. 450. 555.
1.85 573. 448. 495 586.
2.00 430. 381. 339. 480.
2.15 232. 215. 178. 231.
2.30 223. 183. 172. 228.
2.45 167. 126. 148. 181.
2.60 280. 188. 178. 236.
2.90 173. 133. 145. 185.

2°5'4 Asymmetry
2.0-
1.5-J
0.51
0.0
1.5 2'.o 215 3.'o
PL(GeV/c)

 

 

Figure 23.4 Parameters for n" from_the four pion fina1 state

Asymmetry Collimation
.969 +.033/-.032 1.291 +.044/-.043
.984 +.044/-.042 1.258 +.058/-.055
.058 +.047/-.045 1.229 +.055/-.052
.009 +.051/-.048 1.263 +.065/-.061
.915 +.064/-.060 1.178 +.084/-.078
.985 +.071/-.067 1.270 +.094/-.087
.122 +.094/-.086 1.270 +.108/-.098
.884 +.061/-.058 1.409 +.101/-.094
.078 +.089/-.082 1.287 +.108/-.099

2‘5“ Collimation

2.0-4

1.5- $1

5 ii i 5 i 1 1

1.0-

0.53

0.0 e

1.5 2.'o 2.15 310

PL(GeV/c)

98

Table 12.5 Parameters for 0° from the four pion fina1 state.

PL
GeV/c

1.60
1.75
1.85
2.00
2.15
2.30
2.45
2.60
2.90

2.5-4

2.0-J

1.5-

1.04

0.53

Cos 9 center-of-mass

-l<x<-.5<x<0.0<x<0.5<x<1

497. 379. 370.
297. 235. 204.
301. 253. 203.
277. 160. 174.
123. 83. 99.
110. 77. 84.
94. 72. 68.
121. 100. 89.
114. 66. 66
Asymmetry

55;

531

277.
294.
204.
123.
132.

77.
131.

72.

 

 

 

(3.0

1.5

1
2.0

1
2.5

PL(GeV/c)

 

1‘igure 23.5 Parameters for 0° from the four pion final state

Asymmetry Collimation
1.028 +.050/-.047 1.372 +.068/-.064
.904 +.058/-.058 1.307 +.086/-.080
.897 +.057/-.053 1.304 +.085/—.079
.865 +.063/-.059 1.440 +.108/-.100
1.077 +.109/-.099 1.351 +.141/-.126
1.155 +.122/-.109 1.503 +.166/-.146
.873 +.105/-.094 1.221 +.149/-.131
.995 +.099/-.090 1.333 +.137/-.122
.766 +.092/-.083 1.409 +.174/-.152
2.5~ Collimation
2.0—
1.5- iii E i
1.0‘
0.5-1
0.0
5.0 1.5 25 215 33
PL(GeV/c)

 

 

 

99

Table 12.6 Parameters for 0+ from the five pion final state.

 

 

PL Cos 9 center-of-mass
Asymmetry Col1imation

GeV/c -1<x<-.5<x<0.0<x<0.5<x<1

1.60 476. 421. 428. 541. 1.080 +.051/-.048 1.197 +.057/-.054
1.75 285. 232. 264. 255. 1.003 +.064/-.060 1.088 +.070/-.065
1.85 273. 242. 232. 277. .988 +.063/-.059 1.160 +.075/—.070
2.00 268. 183. 230. 279. 1.128 +.075/—.070 1.324 +.090/-.084
2.15 136. 121. 140. 157. 1.155 +.103/-.094 1.122 +.100/-.091
2.30 ,124. 120. 116. 146. 1.073 +.100/-.091 1.144 +.107/-.097
2.45 136. 103. 119. 128. 1.033 +.098/-.089 1.189 +.ll4/-.103
2.60 132. 131. 116. 147. 1.000 +.091/-.083 1.129 +.103/-.094
2.90 97. 80. 95. 120. 1.214 +.131/-.117 1.240 +.134/-.119
2-5-3 Asymmetry 2.5a Collimation

2.0- 2.04

1.5-- 1.5-

Lo‘iiiiiiii 1,o_ § 5; i

0.5. 0.5-

0°0 1 1 1 0'0 1 _ 1 '1

1.5 2.0 2.5 3.0 1.5 2.0 _ 2.5 3.0
PL(GeV/C) PL(G°V/°)

 

 

(“igure 23.6 Parameters for n+ from the five pion final state

 

100

Table 12.7 Parameters for n" from the five pion final state.

 

 

PL Cos 0 center-of-mass
GeV/c -l<x<-.5<x<0.0<x<0.5<x<1
1.60 747. 653. 654. 745.
1.75 409. 360. 360. 425.
1.85 405. 349. 353. 429.
2.00 400. 311. 310. 419.
2.15 236. 187. 192. 216.
2.30 227. 172. 154. 206.
2.45 206. 148. 158. 217.
2.60 221. 185. 173. 210.
2.90 180. 120. 102. 186.
2'5-7 Asymmetry
2.0-

1.5..

14)— 111515 ii); if iiii 91
0.5-

0'0 1 1 ‘1

1.5 3.

2.0 2.5
PL(GEV/C)

Figure 23.7 Parameters for n“

 

 

 

Asymmetry Collimation
.999 +.038/-.037 1.141 + .044/-.042
1.020 +.053/-.050 1.158 + .050/-.057
1.037 +.054/-.051 1.188 + .052/-.059
1.025 +.055/-.052 1. 318 + .073/-.068
.954 +.059/-.054 1.192 + .085/-.080 5‘4
.902 +.058/-.053 1.328 + .102/-.094 3 1
1.059 +.081/-.075 1.382 + .110/-.100 : “
.943 +.059/-.055 1. 203 + .090/-.083 1
.950 +.082/-.076 1.648 +.153/—.137
g,
2'5" Collimation
2.0-
1.5" ii‘i TE
iiii i
1.0-
0.5 4
0.0
1.5 ' ‘ 310.

2.0 2.5
PL(GeV/c)
from the five pion final state!

101

Table 12.8 Parameters for 0+ from the six pion final state.

PL Cos 9 center-of—mass
Asymmetry Collimation
GeV/c e1<x<-.5<x<0.0<x<0.5<x<1

 

1.60 585. 621. 616. 688. 1.081 +.044/-.042 1.029 +.041/-.040

1.75 391. 378. 391. 420. 1.054 +.054/-.051 1.054 +.054/-.051

1.85 445. 420. 456. 451. 1.048 +.051/-.048 1.022 +.049/-.047 m

2.00 382. 395. 418. 397. 1.048 +.054/-.051 .958 +.049/-.046 1"

2.15 276. 241. 280. 315. 1.150 +.071/-.067 1.134 +.070/-.066 ; F

2.30 312. 304. 305. 295. .974 +.057/-.054 .996 +.058/-.055 T

2.45 265. 257. 260. 306. 1.084 +.068/—.063 1.104 +.069/-.065 .

2.60 372. 343. 350. 357. .988 +.053/—.051 1.051 +.057/-.054

2.90 313. 235. 232. 310. .989 +.061/-.058 1.334 +.085/-.079 . _
3 1
1—1’

2'5" Asymmetry 2'51 Collimation

2.0- 2.0-

1.5- 1.5_

1.0-§§§§ 5 9 § 1.0—65§§§§§§

0.5~ 0.54

 

 

 

0.0 .
1.5 2.0 215 370 0 01.5 210 215 310

PL(GeV/c) PL(GeV/c)

 

Irigure 23.8 Parameters for 5+ from the six pion final state

102

Table 12.9 Parameters for n' from the six pion final state.

 

 

PL Cos 9 center-of-mass
GeV/c -1<x<-.5<x<0.0<x<0.5<x<1
1.60 1012. 886. 860. 1007.

1.75 627. 564. 546. 633.
1.85 710. 602. 643. 703. 1
2.00 637. 532. 593. 626. 1
2.15 426. 394. 421. 427. 1
2.30 461. 400. 452. 511. 1
2.45 400. 385. 378. 469. 1
2.60 475. 504. 541. 613. 1
2.90 422. 354. 376. 483. 1
2'5" Asymmetry
2.0"
1.5-
1.0~ Ii jiiiii ii iii; ‘i
0.5“
0.0
1.5 210 2.5 310
PL(GEV/C)

 

 

Asymmetry Collimation
.983 +.032/-.031 1.155 +.038/-.037
.989 +.041/-.039 1.135 +.047/—.045
.025 +.040/-.039 1.134 +.045/-.043
.042 +.043/—.041 1.122 +.047/-.045
.034 +.052/-.049 1.045 +.052/-.050
.118 +.053/—.051 1.140 +.055/-.052
.079 +.054/-.052 1.138 +.058/-.055
.178 +.052/-.050 1.041 +.045/- 044
.107 +.055/-.053 1.239 +.053/-.05o

2-5" Collimation

2.0-

1.5..

is: :1 '5

1.0- ii‘i 1‘

005—!

0.0 ‘

1.5 2.0 215 310

PL(GeV/c)

Figure 23.9 Parameters for w" from the six pion final state

 

.0.
a

won-o- ..

..‘| '1

“1-0m

103

Table 12.10 Parameters for n° from the six pion final state.

 

 

PL C05 9 center-of-mass
GeV/c -1<x<-.5<x<0.0<x<0.5<x<1
1.60 325. 302. 307. 321.
1.75 206. 179. 195. 210.
1.85 220. 188. 252. 226.
2.00 257. 177. 186. 176.
2.15 168. 144. 124. 120.
2.30 210. 163. 121. 114.
2.45 209. 161. 90. 84.
2.60 265. 178. 143. 125.
2.90 200. 143. 104. 98
2.5-1

Asymmetry
2.0-
1.5-—
1J34 £11;
i
0.5-4 i i i
0.0
1.5 2.0 215 370
PL(GeV/c)

 

 

 

Asymmetry Collimation
1.001 +.058/—.055 1.060 +.061/-.058
1.051 +.077/-.072 1.112 +.082/-.076
1.171 +.082/-.076 1.013 +.070/—.065

.834 +.061/-.057 1.192 +.088/-.082
.782 +.070/—.064 1.074 +.095/-.087
.630 +.055/-.052 1.140 +.097/-.089
.470 +.047/-.044 1.167 +.105/-.096
.605 +.049/—.046 1.215 +.096/-.088
.588 +.056/-.052 1.206 +.109/-.099 :
2. 4
5 Collimation
2.0“
1.5‘
1.0‘1‘:E 11 ‘§
0.5_,
0.0
1.5 210 215 310
PL(GeV/c)

Figure 23.10 Parameter§ for 5° from

the six pion final state

104

n- and 5° distributions is not constant but exhibits an increasing pre-
ference for forward and backward production as the incident beam momen-
tum increases.

The center-of-mass longitudinal momentum and transverse momentum
distribution for the three through six pion annihilations, are shown in
Figure 24. The dashed curves in Figure 24 represent fits of the center-

of—mass longitudinal momentum, pL, and the transverse momentum, pT, to

 

functions of the form36:
'- P
95.. = "tune a" L (19)
dpL
5/2 3/2 -qu
dN = Nt(3 2 191 p1 e T (20)
TI’
1'5

where Nt is the total number of pions. Although these functions, based
on a statistical model, were used by D. B. Smith et al.37 to describe
the momentum spectra of charged pions produced in pp interactions be-
tween 13 GeV/c and 28.5 GeV/c and adequately describe the transverse
momentum distributions, they fail to account for the asymmetry and the

collimation of the fin interactions as is evidenced by the poor fit to
the "oc.m. longitudinal momentum distributions from the six pion

annihilations.

 

105

Figure 24. Center-of-mass longitudinal and transverse momentum dis-
tributions. The solid curves are fits to statistical
model predictions

24.1 Longitudina1 momentum distributions from three
pion final states between 1.60 and 2.00 GeV/c

24.2 Transverse momentum distributions from three
' pion final states between 1.60 and 2.00 GeV/c

24.3 Longitudina1 momentum distributions from four
pion final states between 1.60 and 2.00 GeV/c

24.4 Transverse momentum distributions from four
pion final states between 1.60 and 2.00 GeV/c

24.5 Longitudina1 momentum distributions from four
pion final states between 2.15 and 2.90 GeV/c

24.6 Transverse momentum distributions from four
pion final states between 2.15 and 2.90 GeV/c

24.7 Longitudina1 momentum distributions from five
pion final states between 1.60 and 2.00 GeV/c

24.8 Transverse momentum distributions from five
pion final states between 1.60 and 2.00 GeV/c

24.9 Longitudina1 momentum distributions from five
pion final states between 2.15 and 2.90 GeV/c

24.10 Transverse momentum distributions from five
pion final states between 2.15 and 2.90 GeV/c

24.11 Longitudinal momentum distributions from six
pion final states between 1.60 and 2.00 GeV/c

24.12 Transverse momentum distributions from six
pion fina1 states between 1.60 and 2.00 GeV/c

24.13 Longitudinal momentum distributions from six
pion final states between 2.15 and 2.90 GeV/c

24.14 Transverse momentum distributions from six
pion final states between 2.15 and 2.90 GeV/c

Pions/.02 GeV/c

Pious/.02 GeV/c

 

106

 

 

 

 

 

30‘ PM
50‘ a = 1.89:.11
404
. I ' .
20- . I ' \ I ‘

II r \

0 T T 1' 1 U I 1 T j T
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
p
c.m. (GeV/c)
401
P (n+)

30‘ a = 1,701.06

20‘

10‘ w ” " ‘

r ~
0 f I r I I r 1' U V jfi
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

P (GeV/c)
c.m.

Figure 24.1

Longitudina1 momentum distributions from three pion
final states between 1.60 and 2.00 GeV/c *

Pious/.0 .GeV/c

Pions/.01 GeV/c

107

 

 

 

 

 

 

80‘
P (11‘)
60‘
a = 3.821.10
401 I l
I-» -'-' ‘~ I
20‘ , l I .
/ I
/
0 /
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)
40‘ P (1+)
a = 3.32:.08
30‘
|| 1
I l I I '
- II or I ' II I' I . I
10- 1 1| ' -
I-
0'h I I I I I 1 1 r r T
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8‘ 0.9 1.0
P (GeV/c)

Figure 24.2 Transverse momentum distributions from three pion

final states between 1.60 and 2.00 GeV/c

Pions/.02 GeV/c

Pions/.02 GeV/c

108

 

 

 

 

 

 

160*
. P (11°)
‘20. a = 2.38:.13
/
80i ‘,
\
I \
40.4 x \\ J l
0 r I I I r W I I I T
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P (GeV/c)
4 0.111.
240 / \
'. \ P (w‘)
180‘ , a = 2.75:.08
‘\
/ .
.1
120 ‘, \\
/ \\
60" // \\
x, \\
e' \-
o I I I I T I Y I I ‘1'
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
p
c.m. (GEV/C)
150i
120‘
p (4*)
80. a = 2.74:.13
\
40- " -
//
0 Y T I T F I f l T T
-1'0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
p
c.m. (GeV/c)

Figure 24.3 Longitudina1 momentum distributions from four pion
final states between 1.60 and 2.00 GeV/c

 

Pious/.01 GeV/c Pions/.01 GeV/c

Finns/.01 GeV/c

200i

100: \u\

109

120+
P (I‘)

90‘ a. = 5.34:.16

60" \

30‘

 

 

0 fl I r j r I T T

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)

150‘ P (0")
\ a = 5.771.09

50'

 

 

06.0 031 012 0f3 014 015 036 037 0T8 0T0 1T0

 

 

P (GeV/c)
120 i
90 -
\\ P ("+)
50‘ - a = 5.26:.22
30i .\
o r I I T I 1 I ‘r‘ I r
'0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)

Figure 24.4 Transverse momentum distributions from four pion
final states between 1.60 and 2.00 GeV/c

 

 

ill,

Pions/.02 GeV/c Pions/.02 GeV/c

Pions/.02 GeV/c

80‘

60*

20‘

 

110

P (1°)
a = 1.721.]]

 

120‘

90‘

60‘

30‘

0 1 U T U I I
~1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

P (GeV/c)
c.m.

P (W')
M/\ a = 2.22:.09

I"

 

 

 

JQ.0 -0:8 -0:5 -of4 -0T2 0:0 032 0.4 0.6 0.8 1.0

 

P (GeV/c)
80* c.m.
601 P (1*)

i C! 3 2.181.]3
40‘
\
‘I -
20" //
0 I I r I r r r I f I

-1.0 ~0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Figu

P (GeV/c)
c.m.

re 24. 5 Longitudinal momentum distributions from four pion
fina1 states between 2.15 and 2. 90 GeV/c

 

 

Pions/.01 GeV/c Pions/.01 GeV/c

Pions/.Oi GeV/c

111

 

 

 

 

 

 

 

 

404 P (w°)
a = 4.511.23
30«
204
10 1 l 1 I ' I .
0 T T f T I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)
30+
l P (wr')
60‘ n ' | ‘ I II a =5.17:.18
40 d 4'
'1
20 a ' ~ . .
II -
0 I I I I I I I r I fi
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)
40 i
I P (n+)
3‘” . ' ||' . a =4.61:.17
J " .
I .J
I II II
10 . I ‘ IN
0 l I I I I I I I "I T I5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P (GeV/c)

Figure 24.6 Transverse momentum distributions from four pion
fina1 states between 2.15 and 2.90 GeV/c

 

 

Pions/.02 GeV/c

Pious/.02 GeV/c

112

/‘\

240i . I | P ("-)

‘ .
130+ ‘ a = 3.66:.24
12

01 / \
./ ‘\
60~ /x/ '\ ‘
\

 

g
I I _r T

0 “h I I I I I I
-i.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P (GeV/c) ‘
c.m.

 

 

 

160‘
/\ p (,fi')
120- ' I\ a = 3.621.22
80- I/
l/ ‘\
/’ ‘\
40- -/ \n\
I‘ .l I
c fl'h’ I fl “If I I I I I I
-].0 -0.8 -0.6 -O.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P c.m. (GeV/c)

Figure 24.7 Longitudina1 momentum distributions from five pion
final states between 1.60 and 2.00 GeV/c -

 

- D ‘TIA‘I'I'IL-k AW 1
.

1,

m
d

‘m

Pions/.01 GeV/c

Pions/.01 GeV/c

113

 

 

 

 

200i
P (w')
150 / \ a = 7.49:.12
\\~
100‘ 1 \~
\\
so / ..
f T 1 I I I I T - “1— ‘Inhfi
%.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)
160i
120‘ P (n+)
a = 7.23:.15
80‘
\
\

401

G T I I T I I T “I —I:Th"fi1-r

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P (GeV/c)

Figure 24.8 Transverse momentum distributions from-five pion
final states between 1.60 and 2.00 GeV/c

; is

 

Iri—“f““-
i

I I‘
'V
mana- .

 

7h

C
M_-_._'

..‘nII

Pions/.02 GeV/c

Pions/.02 GeV/c

114

1204
/ P (w‘)

90‘ I \ a = 2.93:.23
60~

/ I

/
304 I \ J
o” r , e I Z

 

 

-1.0 -0T8 -0:5 -014 -0:2 0:0 0.2 0.4 0.5 0.8 1.0
P c.m. (GeV/c)

80+
604 " |‘ P («+)
. I
' I a = 3.01:.20
404 I '
l
| \~

20~ A . _

I, ,i I

0 E; 7 I r . . "L

 

 

-].0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P
c.m. (GeV/c)

Figure 24.9 Longitudina1 momentum distributions from five pion
final states between 2.15 and 2.90 GeV/c

 

Pions/.01 GeV/c

Pions/.01 GeV/c

1204

904

604

304

 

80+

60~

40«

20«

 

0.1

115

P (1")
a = 6.55:.19

I T I I i

0.2 0.3 0.4 0.5 0.6 0.7 0.8

P (GeV/c)

P (n+)
‘ a = 6.33:.36

0.9

‘~

1.0

 

O
0.0

I

0.1

I I I I I

0.2 0.3 014 015 0.6 0.7 0.8
P (GeV/c)

0.9

1.0

Figure 24.10 Transverse momentum distributions from five pion

final states between 2.15 and 2.90 GeV/c

 

Pions/.02 GeV/c

Pions/.02 GeV/c

Pions/.02 GeV/c

116

160i

120i

80‘

40‘

 

 

 

m.- I I T T I

0 I I r I T
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

P c.m. (GEV/C)

440‘ / \

 

330'1

220‘

110*

 

 

 

G I I I I I
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

    

 

P c.m. (GeV/c)
320i / \
240‘
P (TI-I).
160‘ = 5.03:.14
80‘
0 T I I TIL

 

 

-i.0 -0.8 -0.6 -0.4 -O.2 0.0 0.2 0.4 0.6 0.8 1.0
P c.m. (GeV/c)

Figure 24.1] Longitudina1 momentum distributions from six pion
final states between 1.60 and 2.00 GeV/c

Pions/.01 GeV/c Pions/.OT GeV/c

Pions/.01 GeV/c

120+

\O
9’

GI
$3

30‘

 

360i

270-

 

117

P (n°)
a = 8.60:.21

“
.—

I j I I r

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)

 
   

P (0')
a = 8.981.11

  

 

240i
180‘
120‘

60‘

 

0
0.0

I I I

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P (GeV/c)

\ P (19‘)

\ a ’3 8.741.15

'~‘
-

I I I T I I I TI I

0.1 0.2 0.3 0.4 0.5 0.6 0Q7 0.8 0.9 1.0

P (GeV/c)

Figure 24.12 Transverse momentum distributions from six pion

fina1 states between 1.60 and 2.00 GeV/c

- I‘L‘I
an}

 

‘fil o , .

..~ ,4?

I
‘-

‘_‘ "Li.“ ~

 

-§."

Pions/.02 GeV/c Pions/.02 GeV/c

Pions/.02 GeV/c

118

 

 

 

 

 

 

   
 
 
    

 

 

120+
P (n°)
904' / a 8 3.99:.46
60 /
I/
30 / i \'
’,/’ \~ r‘:
a ’ \xa ' '3
Op r. T I I I I I F T I hav- P: ”J
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ‘
P c.m. (GeV/c)
320‘ i
E --"
240‘
160‘
80‘
0“: I T I I I I r T I
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P c.m. (GeV/c) '
240+ /,\
180+ P (17")
= 4.38:.15
120+
60‘
0*... I I I I I I I 'TI Tr Tfl-
-T.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
P c m (GeV/c)

Figure 24.13 Longitudina1 momentum distributions from six pion
fina1 states between 2.15 and 2. 90 GeV/c

Pions/.01 GeV/c Pions/.01 GeV/c

Pions/.OT GeV/c

119

 

120i
90+ P (vr°)
" a =7.80:t.24
60i
30i
0 I T I I I I I T

 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
P (GeV/c)
280.
210. P (11°)
/ a =7.99:.15
1401

70+

‘

‘-
0 I I I I I I I r I

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
P (GeV/c)

 

 

160i

120« \ a = 7.88:.14

40+

 

‘

1.0

OI flHflb~

I I T T I I ‘ I I

0.0 0.] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0. 9
P (GeV/c)

Figure 24.14 Transverse momentum distributions from six pion
final states between 2.15 and 2. 90 SeV/c

1.0

 

Ina:

I‘m-.44.». .

CHAPTER 8

MODELS FOR NUCLEON-ANTINUCLEON ANNIHILATIONS

A Reggeized multiperipheral model for high energy multiple par-
ticle reactions has been proposed by Chan, Loskiewicz, and Allison38,
hereafter referred to as CLA. Many attempts have been made at apply-

ing the CLA model to nucleon-antinucleon interactions, although, to

 

date, none of these attempts have made any eXplicit calculations for
the antiproton-neutron annihilations. Several features of the CLA
model are independent of the charge of the initial particles, re-
quiring only that the interaction be a nucleon-antinucleon annihila-
tion and these features will be discussed.

Chen39, using the CLA model, calculated the total cross sec-
tions as a function of incident momentum for various multiplicities
of proton-antiproton annihilations into pions. Each multiple-pro-
duction process

A+B—>1+2+...+n (.21)

was calculated from incoherently superimposed amplitudes of the form

n-l a. B 12.
MI“ 915i + ca (51+ a 1) 51+ b1- i 1 (22)
i=[ $1 + a a __—E;_—'

where a, bi, c, and 9i are constant parameters, of and Pi are the in-

 

tercept and slope of the ith Regge pole trajectory, and sf and ti are

120

l2l
defined by

(23)

In
_I
II
A
'U

(24)

ff
.1
II
A
U
>
I
M—l
'U
3
v

pA being the center-of-mass momentum of the beam particle.
In the case of nucleon-antinucleon annihilations into pions,
only the N and A trajectories are allowed to exchange. It is well

40 that the cOUpling strength of the A-trajectory is about one

known
order of magnitude weaker than the coupling strength of the N-tra-
jectory. Therefore. only the N-trajectory was used in the calculation
and the independent amplitudes needed for each multiplicity are shown
in Figure 25. In the reaction pn-+ mm, there is only a single ampli-
tude which contributes to the odd multiplicity, m, reactions while
there are m numerically equal but physically distinct amplitudes

needed for each even multiplicity reaction.

Equation 22 was simplified by Chen to

W = 0.4—{0 + 2. )0 + 50a)“ 0 + 500“" (25)
(1+ ila)

where c/g - l was replaced by h and the value 0.077 corresponding to

the c/g ratio determined by CLA was used. The Regge parameters. a

and 3 of the linear nucleon trajectory, were fixed at -0.38 and 0.88

respectively. The energy scale factors of a=0.l and b=3.0 were found

by Chen to give the best fits to available data from the reaction

5p e-MN'fOF multiplicities between 2 and 9. The overall normalization,

 

 

122

 

 

 

 

 

 

 

   

 

   

 

25.1 25.3
- _ 1';
P ‘—“‘—“‘ P P-
i———- 1T- TT+
n -—-—-————- 1T 1T
17’
25.2 25.4
E) ___(2)_ 17' :+
‘H——* 0+ W.
.L_____ TI- 1I+
n ___J____ 0° fl-
“,0
- b - ..
a (b) _ P ( ) 77+ 7T+
__ IT IT
:TT+ 1f- 11'.
— TT° 1I+ 17°
n —_J__— 1r' Ir° 1r+
n It. '0"
- (d) - -
_ C) 1'- p 1T+ ITO
p __ no Ila 3+
1r+ ' "'
—_ II ‘II
n ———-4———— 1" 1r+ 1r+
n 1T- 1T-
- no
i) 4L 1r° D 1T-
__ 1r; 1r+
..____ II “If"
n _____.. 1r' 1!:-
n II’

 

 

 

“' '4 .33"!
I...

#5“

 

 

 

Figure 25. Regge diagrams with nucleon exchange used in the CLA
mo el
,25.l Three pion final state
25.2 Four pion final state
25.3 Five pion final state
25.4 Six pion final state

123

Cm, was then adjusted to give the best fit to the cross sections for a
given multiplicity.

Since the cross sections of the CLA model as applied by Chen to
proton-antiproton annihilations, are only dependent upon the parameters
of the nucleon trajectory for their physical significance, they can q
easily be compared with the cross sections from antiproton-neutron anni- EF-1 A
hilations. To compare the cross sections of 5p with those from 6n, it
is only necessary to scale the overall normalization for a given multi-

plicity. A comparison between an arbitrarily scaled pp prediction and

 

1"
1&2...— .

the pn data is shown in Figure 26 along with a similarly renormalized
comparison of the predictions of the statistical model calculated by
G. van Kuek4]. The scaled pp agrees quite well with the data at all
four multiplicities, however, the scale factors for the three through
six pion annihilations of 0.64, 3.1, 0.30 and 4.9 are somewhat dif-
ferent from the values of 0.33, 4.0, 0.20 and 6.0 respectively, cal-
culated solely from the number of contributing diagrams. This discre-
pancy is not surprising since there was some disagreement between the
calculated and fitted Cm's of Chen and also since the CLA model used
by Chen does not include resonant production which is highly prevalent
in the multipion annihilations.

Due to the lack of CR invariance in 5n reactions, no direct
comparison of the angular and momentum distributions can be made with
the predictions from pp. However, certain features of the model can be
readily deduced and compared with the data. Since the CLA model assumes
that all diagrams contribute equally (i.e. the same number of distinct

couplings occur in each diagram), it is apparent from the diagrams in

124

Figure 26. Comparison of the multipion annihilations with the
multiperipheral and statistical models. Solid (dashed)
curves are predictions of the multiperipheral
(statistical) model

125

10.0“
CLA

. — - — - Statistical
A

1.0

 

0 (mb)

0.2 -

 

 

 

1:5 2:0 2:5 310 3T5
PL (GeV/c1
2.3 234 2:5 2T5 217 2:8

ECJII. (66V)

 

126

Figure 25 that there should be no asymmetry in the cos 9c.m. distri-
butions in any particular charged particle state since each allowed
final configuration may be reflected to f0rm another allowed configu-
ration. The three, four and five pion final states are consistent
with this prediction, however, there is a definite asymmetry which is
increasing with increasing beam momentum in the n' and 0° charge states
of the six pion annihilations. Thus, rather than all diagrams contri-
buting equally, there appears to be an emerging dominance of diagram
25.4a over the others. This asymmetry can be attributed to a charge
following effect of the leading particles. A similar effect may be
seen in the four pion annihilations where the asymmetry values of the
n° mirror those of the n‘. It is not clear whether or not diagram
25.2a is becoming dominant at the higher momenta and additional expe-
riments above 3.0 GeV/c are needed to confirm any definite trend.
Collimation on the other hand, is independent of CR invariance
and therefore independent of the folding used in pp analysis. Although
their results differ significantly, both Chen and Roberts43 predict
that the collimation values should be increasing with momentum in the
1.5 GeV/c to 3.0 GeV/c momentum range. They also find that the rate
of increase is less as the multiplicity increases. Since the CLA mo-
del for nucleon-antinucleon annihilations is essentially a series of
peripheral processes without double charge exchange, it is natural to
expect that the particles on the ends of the chain will make the
greatest contribution to the deviation of the collimation parameters
from unity. In a manner similar to 5p the collimation parameters for

for n‘ in the three and five pion final states in 5n exhibit an

 

 

127

increase with increasing momentum and with a slope which is less in
the five pion final state than in the three pion final state. Like-
wise, the collimation parameters for the n+, which barring double
charge exchange, are always internal to the chain, are consistently
smaller than the corresponding parameters for the n- and n° in all
multiplicities. While the collimation parameters for the n' and n° in
the four and six pion final states exhibit the decrease in magnitude
with increasing multiplicity, they fail to show the momentum depen-

dence seen in pp as well as in the three and five pion final states of

pn.

 

 

CHAPTER 9
SUMMARY AND CONCLUSIONS

Topological and reaction cross sections for antiprotons inter-
acting with deuterons and resonant production cross sections for anti-
proton-neutron annihilations into three through six pions have been
determined fbr incident momenta between l.60 GeV/c and 2.90 GeV/c.

The cross sections for single and double pion production without anni-
hilation as well as the cross sections for the hydrogen like, pp, re-
actions are in good agreement with other experiments lending confidence
in the procedure used to analyze the data. The overall momentum to
momentum dependence of the topological cross sections fail to show en-
hancements sufficient to explain the structures in the isospin one
total cross sections, although their errors do not rule out such struc-
ture in any particular topology. The reaction cross sections, where
any enhancement may be more noticeable, similarly fail to show evidence
for any significant structure with the exception of the cross section
for the reactions pd +'pn+2n'n and 5d + p2n+3n'n° which exhibit turn-
overs in the region of the isospin one structure at 2350 MeV center-of-

mass energy. These turnovers, which may be reflected in the resonance

production reactions pd +»pm°n', pd‘+ pw°n+2n' and remotely pd +-po°p°u',

cannot be conclusively determined to be contributing to the structure
without further investigation at lower energies. Particular emphasis

may be given to the resonance production channel m°n+n'n' which appears

to follow the general trends of the pd‘+ p2n+3w'n reaction cross section.

128

’_ 14...“;

4n“- run

 

129

Investigation of the resonance production cross sections in the
annihilation channels has yielded no evidence for contributions to the
I=l structures with the exception of a K*K enhancement at 2360 MeV seen
both in this experiment and in a pp experiment. The resonance produc-
tion cross sections for 5n + p°p°n- have been investigated for a possi-

ble relation to the p°p°n° enhancement from pp annihilations at

"3.1-Cl l .- '

1.32 GeV/c (2l90 MeV center-of-mass energy) reported by Kalbfleisch et.

al.4. If this enhancement from the pp annihilations is reflected in

 

the pn annihilations, the apparent width is much greater than the '"
r < 80 MeV/cz reported by the authors of reference 4. .
The general features of the multipion annihilations and their
angular and momentum distributions have been compared with various
models. The multiperipheral multi-Regge model of CLA far more accu-
rately describes the slopes of the cross sections for the multipion
annihilations than does the statistical model. Although no direct
calculation of either model was made, it was observed that some mo-

dification is necessary to include the effects of charge following.

. __ 1.. a"

LIST OF REFERENCES

 

1)
2)
3)
4)

5)
6)
7)
8)
9)
10)
ll)

12)

13)
14)
15)
16)
17)
18)
19)

LIST OF REFERENCES

R. J. Abrams gt_al,, Phys. Rev. Ql_(l970) 1917.
R. L. Cool g3_gl , Phys. Rev. 91_(1970) 1887.
w. A. Cooper gt al,, Phys. Rev. Letters, 29_(1968) 1059.

G. Kalbfleisch, R. Strand and V. Vanderburg, Phys. Letters gg§_
(1969) 259.

G. Chikovani §t_al,, Phys. Letters gg_(l966) 233.
. M. Anderson gt_al,, Phys. Rev. Lett. gg_(1969) 1390.
. N. Focacci gt_gl,, Phys. Rev. Lett. lZ_(1966) 890.

E
M
B. Y. 0h gt_gl,, Phys. Rev. Lett. 24_(1970) 1257.
Z. Ming Ma and G. A. Smith, Phys. Rev. Lett. 21_(197l) 344.
D. L. Parker, Ph.D. Thesis, Michigan State University (1971).
F

. T. Solmitz gt_al., Lawrence Radiation Laboratory, Alvarez
Programming Group-Note #117 (1966).

0. I. Dahl et al,, Lawrence Radiation Laboratory, Alvarez
Programming—Group Note #126 (1966).

‘Nathan, w. Dean, Phys. Rev. Lett. gz_(1971) 276.

. J. Moravcsik, Nuc. Phys. Z_(1958) 113.
. J. Glauber, Phys. Rev. lQQ.(1955) 242.

. Nicholson §t_al,, Phys. Rev. Lett. g§_(1969) 603.

M
R
V. Franco and R. J. Glauber, Phys. Rev. lgg_(1966) 1195.
H
J. u. Chapman gt_gl,, Phys. Rev. Lett. gl_(1968) 1718.

H

. Braun gt_al,, Phys. Rev. Qg_(l970) 488.

130

 

20)
21)
22)
23)

24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)

36)
37)

38)

39)
40)
41)

131

T. C. Bacon gt 31,, Phys. Rev. 1§g_(1965) B1420.
T. C. Bacon gt_al,, Phys. Rev. 1§g_(1967) 1320.
T. C. Bacon gt_al,, Phys. Rev. Q§_(1970) 463.

J. Friedman, Lawrence Radiation Laboratory, Alvarez Programming
Group Note #156 (1966).

J. D. Jackson, Nuovo Cimento §4_(1964) 1644.

G. Goldhaber gt_al,, Phys. Rev. 129 (1960) 302.

. Abramovich gt_al,, Nuc. Phys. ng_(1970) 209.

. N. M. Allison gt_g1,, Phys. Rev. Lett. gg_(1970) 618.
. M. Flatte gt_al,, Phys. Rev. 14§_(1966) 1050.

. M. Flatte, Phys. Rev. l§§_(1967) 1517.

. M. Flatte, Phys. Rev. Ql_(1970) l.

..Goldhaber gt_gl,, Phys. Rev. Lett. g§_(l969) 1351.

. E. Agustin gt_gl,, Lett. Nuovo Cimento g_(1969) 214.
. J. Biggs gt_gl,, Phys. Rev. Lett. 24_(1970) 1197.

. Alvensben 3391., Phys. Rev. Lett. _2_7_ (1971) 888.

II'UCafimmmtz

. Pilkuhn: The Interactions of Hadrons, John Wiley & Sons, Inc.,
New York (1967).

J. v. Elbert gt_gl,, Phys. Rev. Lett. gg_(1968) 124.

D. B. Smith, R. J. Sprafka and J. A. Anderson, Phys. Rev. Lett.
lg§_(1969) 1064.

Chan Hang-Mo, J. Loskiewicz, and v. w. Allison, Nuovo Cimento
§ZA_(1968) 93. .

Fong-Ching Chen, Nuovo Cimento 62A (1959) 113.
V. Barger and D. Cline, Phys. Rev. Lett. gl_(1968) 392.

G. van Kuek, DESY Preprint 68/10, "Zur Anwendung des Statistischen
Modells mit Drehimpulserhaltung," 1968.

132

42) J. Benecke £391., Phys. Rev. 188 (1969) 2159.
43) R. G. Roberts, Nuc. Phys.._B_l_3_ (1969) 662.
44) Bettini gta_1_., Nuovo Cimento _1_A_ (1971) 333.

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

11111111111111111111117111131

      

196