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LIBRARY
Michigan State
University

 

 

 

 

This is to certify that the
dissertation entitled
CHARACTERISTICS OF CHARM PARTICLES
PRODUCED BY 800 GEV P-P COLLISIONS
presentedby

Ai Gia Nguyen

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degreein Physics

@7550,“ 4%,

Major professor

 

Mega/Z 7-5; We?

MS U i: an Aflirmatt've Action/Equal Opportunity Institution 0-12771

 

 

 

‘IV1ESI_J RETURNING MATERIALS:
Place in book drop to
LIBRARIES remove this checkout from
—:_——. your record. FINES will

 

 

be charged if book is
returned after the date
stamped below.

 

 

 

 

CHARACTERISTICS OF CHARM PARTICLES
PRODUCED BY 800 GEV P-P COLLISIONS

By

Ai Gia Nguyen

A DISSERTATION

Submitted to
Michigan State University
in partial fullfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1988

ABSTRACT

CHARACTERISTICS OF CHARM PARTICLES

PRODUCED BY soo GEV P-P COLLISIONS
By

Ai Gia Nguyen

This thesis presents the results of Fermilab experiment E743, a study of the pro-
duction characteristics of the D mesons in 800 GeV proton-proton collisions (J3 = 39
GeV), utilizing a high resolution, rapid cycling bubble chamber for vertex detection,
and a multiparticle spectrometer for the momentum determination of charged parti-
cles. A relatively unbiased measurement of the D meson cross section is accomplished
by direct observation of the decay vertices in the bubble chamber, 6(D/D) = 59:3:pb.
Also measured are the longitudinal and transverse momentum distributions of ob-

served D meson decays. The differential production cross sections are described well

by the form

l (130'
0’ dzpdpfr

with n = 11.011: and b = 0.66:3;33 (GeV/c)". For Izrl > 0.3 we observe no events,

 

= (n + mgxl - lzrl)"e"”"

which corresponds to an upper limit of 10 pb at a 95 % confidence level.

Ai Gia Nguyen
When compared with measurements made at lower energies the results of this study
point to a D meson cross section which is slowly rising with center of mass energy.
These results are in sharp contrast with the results from a number of experiments
performed at the CERN Intersecting Storage Rings (ISR) (J3 = 53-62 GeV) which
indicated a dramatic rise in the charm particle cross sections with increasing energy.
These large cross sections were observed in experiments which were sensitive to pro-
duction at large 2;: values (typically my > 0.3). Unusual mechanisms for charm
production invoked to explain these large cross sections do not appear to be neces-
sary below J3 = 39 GeV. Also, our longitudinal momentum distribution of D mesons
shows no evidence of production at large am. A more generally accepted model for

charm hadronic production, the Fusion model, can reproduce most aspects of our

data.

ACKNOWLEDGMENTS

This thesis was written with the support and guidance of Professor Carl
Bromberg of Michigan State University. I would like to thank him, as well as Drs.
Roger Dixon, Howard Fenker, Ian Leedom, John Marraflino, and Steve Reucroft for
invaluable comments and discussions. I would also like to thank our other collabo-
rators and the dedicated staff of the Fermilab Film Analysis Facility. The following
fourteen institutions participated in the LEBC-MPS collaboration: Aachen, Berlin-
Zeuthen, Brussels, CERN, Duke, Fermilab, Kansas, Michigan, Michigan State, Mons,
Notre Dame, Tata (Bombay), Vanderbilt, and Vienna. I thank also the Sage Foun-
dation for providing me with a grant towards publication costs for this thesis.

I thank Trang for her patience and forbearance, and my parents for their con-
stant moral and occasional financial support.

TABLE OF CONTENTS

List of Tables vii
List of Figures viii
1 Introduction 1
2 Theoretical and Experimental Perspectives 3
2.1 Properties of the charm quark ........................ 3
2.2 Parallel attempts to measure charm hadronic cross sections ........ 8

2.3 Attempts to measure charm differential cross sections in 2p and pg. . . . 15

2.4 Two mechanisms for hadronic production of charm ............ 15
2.5 Summary of the goals and results of E743 ................. 21
3 Experimental Apparatus 26
3.1 The beam and beam optics ......................... 26
3.2 LEBC, the hydrogen target and vertex detector .............. 30
3.3 The FMPS spectrometer ........................... 34
3.4 The triggers and data acquisition system .................. 40
4 Data Reduction 44
4.1 Film analysis ................................. 44
4.1.1 Scanning .................................. 45
4.1.2 Measuring .................................. 50
4.2 Event reconstruction ............................. 51
4.2.1 Spectrometer tracking ........................... 51

4.2.2 Hybridization and kinematic fitting .................... 52

4.2.3 Graphical techniques ............................ 55
5 Normalization and Multiplicity Distribution 59
5.1 Scanning of the data sample taken with an unbiased trigger ....... 59
5.2 Determination of the multiplicity distribution ............... 61
5.3 Determination of the interaction trigger bias ................ 68
6 Determination of the Charm Inclusive Cross Section 71
6.1 Normalization and systematic uncertainties ................ 71
6.2 Cross section results ............................. 74
7 D Meson Difi'erential Cross Sections 76
7.1 Observations based on film measurement .................. 77
7.2 Observations based on spectrometer information .............. 78
7.3 Differential cross section results ....................... 86

8 Comparison of Results with the Fusion Model and Other Mecha-
nisms 90

8.1 The experimentally observed energy dependence of the charm cross sec-

tions ..................................... 90
8.2 Predictions by the Fusion model and by other mechanisms ........ 93
9 Conclusions 101

Appendices
A The Impact Parameter of Decay Tracks 104
B Simulating Charm Decays 106

C The O‘C Calculation 110

vi

2.1
2.2
2.3
2.4

3.1

4.1

4.2

5.1
5.2
5.3

6.1

7.1

0.1

LIST OF TABLES

Predicted pseudoscalar charm mesons. ...................
The single charm baryons. ..........................
A partial list of charm cross section measurements. ............

A partial list of measurements for the production parameters n and b. . .
Important LEBC parameters. ........................

Spectrometer acceptance as a function of 2p and topology (V2, C3, V4),

requiring all charged decay tracks to be reconstructed. .........

Spectrometer acceptance as a function of 2p and topology (V2, C3, V4),

requiring at least two charged decay tracks to be reconstructed. . . . .

Scanning efficiency for the multiplicity sample ................
Observed topological cross sections ......................

Lowest moments of the observed inclusive multiplicity distribution.
The D meson sample and effects of the geometrical cuts. .........
Reconstructed D meson decays. .......................

Corrections for the slow O‘C solution .....................

vii

6
7
12
16

36

57

60
63
65

74

85

112

2.1

2.2
2.3

3.1
3.2
3.3
3.4
3.5
3.6
3.7

3.8
3.9

4.1

4.2

5.1
5.2
5.3
5.4

7.1
7.2

LIST OF FIGURES

Charm cross section vs. center of mass energy ................ 13
Charm partial cross section (Izpl > 0.3) vs. center of mass energy. . . . . 14

First order diagrams for the (a)Fusion and (b)Excitation processes. . . . 18

Optics of the MT beam line .......................... 27
Site map showing the location of the MT beam line ............. 28
A photograph of our LExan Bubble Chamber ................ 31
Beam’s eye view of the chamber assembly. ................. 32
Vacuum tank and camera set up for LEBC. ................ 33
The optical system of LEBC. .................... I . . . . 35
Elevation view of the Fermilab Multiparticle Spectrometer in the E743
configuration ................................. 38
The E743 trigger system ............................ 41
Timing of our interaction trigger. ...................... 42

An illustration of (a)important decay parameters and of the charm topolo-

gies (b)C3 and (c)V4. ........................... 46
Photograph of a charm event. ........................ 49
The multiplicity distribution. ........................ 64
The energy dependence of the mean charge multiplicity ........... 66
Energy dependence of the (normalized) higher multiplicity moments. . . 67
Eficiency of our interaction trigger ...................... 70
The longitudinal decay length distribution .................. 79
The transverse decay length distribution ................... 80

viii

7.3
7.4
7.5

7.6
7.7

8.1

8.2

a: ooooooooooooooooooooooooooooooo
8.3 Fusion model predictions of the differential charm hadronic production
cross section 43-. ..............................
1'
RI Simulated D+ —» K ‘1r+1r+ decays, part 1. .................
B.2 Simulated D+ -o K"1I""'u'+ decays, part 2. .................

Maximum likelihood fit of the longitudinal decay length distribution. . .
Maximum likelihood fit of the transverse decay length distribution.

The Feynman x distribution 2;“;- ......................
The invariant distribution E 2% ......................
The transverse momentum distribution a. ................

Fusion model predictions of the integrated charm hadronic production

cross section. ................................

Fusion model predictions of the differential charm hadronic production
cross section ‘N

88
89

96

97

108
109

Chapter 1

INTRODUCTION

This thesis presents the results of Fermilab experiment E743, a study of 800
GeV proton-proton collisions (center of mass energy fl = 39 GeV), utilizing a high
resolution, rapid cycling bubble chamber for vertex detection, and a multiparticle
spectrometer for the momentum determination of charged particles. The study em-
phasizes the measurement of the production characteristics of the meson states con-
taining a charm quark, specifically the D mesons. The most important measurement
made is the D meson inclusive cross section. A relatively unbiased measurement of
the D meson cross section is accomplished by direct observation of the decay vertices
in the bubble chamber. Also measured are the longitudinal and transverse momen-
tum distributions of observed decays, as well as the multiplicity of charged particles

produced in both charm and non-charm associated events.

When compared with measurements made at lower energies the results of this
study point to a D meson cross section which is slowly rising with center of mass

energy. These results are in sharp contrast with the results from a number of exper-

iments performed at the CERN Intersecting Storage Rings (ISR) which indicated a
dramatic rise in the charm particle cross sections with increasing energy. These large
cross sections were observed in experiments which were sensitive only to production at
large values of an» (2:; E $’ where p" is the longitudinal momentum in the center
of mass frame, and Plhm is its maximum value). We show that unusual mechanisms
for charm production, invoked at that time to explain large cross sections, are unnec-
essary to explain the energy dependence of charm production below fl = 39 GeV.
We also show that the longitudinal momentum distribution of D mesons observed in

our study is steeply peaked at my = 0 and shows no evidence for production at large

331"-

We have also compared our data to a more generally accepted model for hadronic
production. This model, which makes use of the fundamental Quantum Chromody-
namic (QCD) scattering amplitudes between quarks and gluons, and a phenomeno-
logical picture of the structure of the proton as well as the hadronization of a quark,

can reproduce most aspects of our data.

This thesis begins with a discussion of the historical background and issues in
charm production physics, the motivation for the configuration of our experimen-
tal apparatus, and is followed by the presentation of the experimental results and

conclusions.

Chapter 2

THEORETICAL AND EXPERIMENTAL PERSPECTIVES

2.1 Properties of the charm quark

Before 1970, in the Cabibbo model1 the up, down, and strange quarks are arranged

in a doublet,

u

dcosoc + ssinflc

expressing the fact that the down and strange quarks participating in the weak in-
teraction are rotated by the Cabibbo angle 0,. The weak neutral current is of the
form

J ° ~ ufi + difcos'Bc + sisinaflc + (s: + id)sin0¢cos0¢,

with a nonzero strangeness changing component (the last term), in conflict with

experimental limits2 established by measurements of decays of the neutral K meson

 

1N. Cabibbo, Phys. Rev. Lett. Q (1963) 531

1Particle Data Group, Revs. Mod. Phys. fl (1980) 1

such as
I'(KZ -’ INF)
F(Kfi —§ all)

 

= (9.1 :1: 1.9) x 10".

In 1970, the charm quark was proposed by Glashow, lliopoulos, and Maiani 3 as
part of a model (the GIM model) to explain the lack of a strangeness changing neutral

current in weak interactions. The charm quark was introduced in an additional

doublet ,

C

scos0c - dsi‘nflc

The weak neutral current gains a term
J" —+ J" - (s3 + 3d)sin0¢cos0¢
and the strangeness changing component is cancelled.

At the time of the proposal of the GIM model, there was yet no experimental
evidence for the charm quark. Indirect but compelling evidence was provided in 1974
by the discovery of the J /¢"‘, a massive (3.1 GeV/c1) spin one particle. The large
mass and low spin of the J /¢ suggested that it was a low lying bound state of heavy
quarks. Subsequently, several resonances were observed at higher masses, including
the W (3685) and 1b” (3770). These resonances were interpreted as excited states of
the CE system. The 1b" in particular played an important role in spectroscopic studies

of the D meson, the first observed quark system with nonzero charm quantum number

 

'S. L. Glashow, J. lliopoulos, and L. Maiani, Phys. Rev. _D_2 (1970) 1285
‘J. J. Aubert et al., Phys. Rev. Lett. fl (1974) 1404

l‘J. E. Augustin et al., Phys. Rev. Lett. fl (1974) 1406

(open charm).

Direct evidence for the existence of the charm quark was obtained in 1976 by
the observation, in e+e‘ annihilations, of narrow mass peaks in the K inf, K *x‘x‘,
and K itfvrl’wr‘ systems at 1.9 GeV/cu”. Following the discovery of the 1/1" in 1977,
large samples of D decays became available. The 2p" is only 40 MeV above the D

meson pair threshold and provides a copious and clean source of these particles.

The existence of four quarks implied an extension of the hadron spectrum. The
SU(3) meson octet of pions, kaons, and 1’ became an SU(4) fifteen-plat, and the SU(3)
baryon octet of nucleons, 2’s, and cascades became an SU(4) twenty-plet’. Table 1
lists the predicted pseudoscalar charm mesons and table 2 gives the single charm

baryons.

Experimental evidence exists for a number of these low lying meson and baryon
states. The TPS collaboration has reported a D, signal in the ¢1r+,¢1r‘,K‘°K ‘,
and I?”K+ channels in photon-nucleon collisions“. The charm baryon Ac has been
observed by experiments at the CERN ISRm. The WA42 collaboration has reported

evidence for the A+ baryonu in E‘Be collisions in the AK “n+1r‘l‘ channel. Excited

 

0G. (301th et al., Phys. Rev. Lett. 31 (1976) 255

'1. Peruin et al., Phys. Rev. Lett. fl (1976) 569

'M. K. Gaillard, B. W. Lee, and J. Rosner, Rev. Mod. Phys. fl (1975) 277
'M. S. Witherell, Procs. of the Salt Lake City Meeting of the DPF (1987) 135
10D. DiBitonto, AIP Conference Proceedings No. 85 (1981) 26

11s. F. 131.51 at al., Phys. Lett. 15013 (1935) 230

Table 2.1: Predicted pseudoscalar charm mesons.

 

 

 

 

 

 

 

Name Content Isospin Strangeness Charm
19+ c2 1/2, 1/2 0 1
D" ciI 1/2,-1/2 o 1
Dj‘(F+) c3 0,0 1 1
5" an 1/2, 1/2 0 -1
D‘ Ed 1/2,-1/2 0 -1
D: (F’) Es 0,0 -1 -1
m c2 0,0 0 0

 

 

states of the D meson, the D‘, have been seen. The D"" was observed as a clear peak
in the D‘1r+ system”. Evidence for the other predicted charm states is statistically

much weaker and not compelling.

A substantial body of spectroscopic information for the D mesons exists, from
the Lead Glass Wall (LGW)13, MARK II“ and MARK III“ detectors at SLAC,
and more recently from the Tagged Photon Spectrometer (TPS)m at Fermilab. The

masses, lifetimes, and branching ratios for Cabibbo favored decays of the charged and

 

"G. J. Feldman et al., Phys. Rev. Lett. _3_8 (1977) 1313
1'1. Perussi et al., Phys. Rev. Lett. _3_9 (1977) 1301

1‘R. H. Schindler et al., SLAC-PUB-2507

1'R.. M. Baltrusaitis et al., Phys. Rev. Lett. 54 (1985) 1976

“M. S. Witherell, Procs. of the Salt Lake City Meeting of the DPF (1987) 135

Table 2.2: The single charm baryons; the S and A baryons have the same quark
contents and are distinguished by their symmetry under simultaneous interchange of

spin and label for the light quark pair.

 

 

Name Content Isospin Strangeness Charm
01++(2;H') cuu 1, 1 0 1
Cf(2;") cud 1, 0 0 1
Cf(2:) cdd 1,-1 0 1
0:01.) cud 0,0 0 1
3+ cus 1 / 2, 1 / 2 - 1 1
5° cds 1/2,-1/2 -1 1
A+ cus 1/2, 1/2 -1 1
A" eds 1/2,-1/2 -1 1
T° css 0,0 -2 1

 

 

 

 

 

 

 

neutral D mesons are relatively well known. Much less information is available for

the decays of the D, and Ac, although their masses and lifetimes are relatively well

established.

2.2 Parallel attempts to measure charm hadronic cross sections

Charm is produced in hadronic collisions with cross sections near 10’3 of the total
cross section, so that charm detection in hadronic processes is difficult. Apart from
our measurements at 800 GeV, results are available at lower energies from fixed
target experiments with 200 to 400 GeV/c hadron beams, and at higher energies

from experiments at the CERN ISR.

There are three general approaches to the measurement of charm production
in hadronic processes: inclusive lepton measurement, a mass peak search, or direct
observation of charm decays. In the first approach, taken by several early experiments
both at Fermilab and at CERN, the rate of prompt neutrinos or muons was used as
an indirect measure of the charm production cross sections 17. Although models for
charm production were needed to calculate the acceptance for the prompt leptons in

the apparatus, copious production in hadronic collisions was ruled out.

Initial high statistics searches for mass peaks in fixed target environments were

unsuccessful". Subsequent experiments attempted to make use of some distinctive

 

"J. L. Ritchie et al., Phys. Rev. Lett. 51 (1980) 230

1"W. R. Ditsler et al., Phys. Lett. QB. (1977) 451

features of charm production, such as the ‘bachelor’ pion from D‘ —» Dr". Due
to the small Q value (5.7 Mev) of this strong decay, the pion is nearly at rest in
the rest frame of the D‘ and the background is restricted to a small region of phase
space. Prompt leptons were also used to enhance the charm signal from pp —+ c5,
with C(E) —» X, and 'c'(c) —+ l + X in invariant mass plots”. These experiments had
large acceptance corrections and the determination of the cross section depended on

the model assumed for charm production.

An additional problem common to both of the above approaches is the nuclear
dependence of charm cross sections. These early experiments were usually performed
with hadron beams incident on nuclear targets such as beryllium. Proton cross sec-
tions were inferred using

where A is the atomic number of the target. One expects the exponent a to be 1
for hard scattering of beam and target nucleon constituents (high Q”, momentum
transfer squared), and 2 / 3 in interactions at lower Q2 where the beam interacts with
the whole nucleus. The only measurement of a for charm production comes from
the prompt neutrino beam dump experiment by the E613 collaboration at Fermilab”1
where several target materials were used, and a was measured to be 0.75. However,

the inferred proton production cross section (03,“) is in disagreement with that

 

1’V. L. Fitch et al., Phys. Rev. Lett. 4_6_ (1981) 761
”R. Bailey et al., Phys. Lett. 2_3_B_ (1983) 237

“M. E. Dufi'y et al., Phys. Rev. Lett. _5_§ 1816

10

derived from measurements made with the bubble chamber used in our experiment.

hrthermore, a has been shown to depend on the momentum of the produced
particle in strange particle production”, contrary to the usual assumption that it is
a constant. Thus extrapolation of nuclear target data to obtain the desired 07'0“?”

appears to be subject to considerable systematic uncertainty.

Mass peak searches were also performed at the ISR. The Lamp Shade Magnet
(LSM) detector took quasi elastic proton triggers pp -+ p' + X where p' is a quasi
elastic proton, and the Split Field Magnet (SFM) took electron triggers pp —» e“ +X.
These groups reported peaks at 2.3 GeV/c2 in the K ‘p1r+ system, corresponding to

the A6 charm baryon”.

The observed longitudinal momentum distribution was flat, leading to a pro-
duction cross section of order 1 mb. These results suffer from very large acceptance
corrections and poorly known branching ratios. In both of these ISR experiments the
charm hadron must have large longitudinal momentum in order for its decay products
to be within the acceptance of the apparatus, and the branching ratio of A, —+ K +p1r‘

is known to no better than 50%.

The third approach to charm production cross sections measurement involves
the direct observation of decay vertices in emulsion or bubble chamber targets. Results

from emulsion exposures are difficult to interpret, due to the problem of nuclear

 

”D. S. Barton et al., Phys. Rev. M (1983) 2580

”D. DiBitonto, AIP Conference Proceedings No. 85 (1981) 26

11

dependence mentioned earlier. Experiments using hydrogen bubble chambers include
NA27 at the CERN SPS by the LEBC-EH8 collaboration, and by our collaboration for
experiment E743 at Fermilab. These are experiments with relatively low statistics but
clean charm samples. Charm decays are unambiguously identified by their topological
signatures in the bubble chamber. Large acceptance corrections are avoided, and cross

sections are inferred from topological rather than exclusive branching fractions.

To summarize the situation for cross section measurements, we present in Table
3 a partial list of results; proton-proton cross sections are given, for heavy target

“1 3" 3°. These measurements are

experiments, assuming an A1 nuclear dependence
plotted as a function on the center of mass energy, J3, in Figures 1 and 2. Figure 1
shows the total charm cross section versus fl (only measurements from experiments

sensitive to most of the cm range are plotted) while Figure 2 shows energy dependence

of the partial cross section a(|zpl > 0.3).

Prior to our experiment the situation could be summarized as follows: there
was an order of magnitude agreement on the cross section in the 24 to 27 GeV J3
energy range, while the ISR results at J; between 53 and 63 GeV implied a dramatic
rise in the cross section with increasing energy. Our result at J; = 39GeV indicates

a more slowly rising cross section.

 

“S. Reucroft, Invited 'Ihlk at the XXIst Reneontre de Moriond, Les Arcs (1986)
”S. L. Olsen, AIP Conference Proceedings No. 85 (1981) 1

”A. Kernan and G. Van Dalen, Phys. Rep. 106 (1984) 299

12

Table 2.3: A partial list of charm cross section measurements; a * denotes experiments

which are sensitive only to Izpl > 0.3.

 

 

 

 

 

 

 

Experiment Reaction ,fi (GeV) 0' (pb/nucleon)
E595 1r‘/Fe —+ ,1 23 17.52;:
NA16 p/p —. 1) 26 31.033"
E595 p/Fe —t p 27 10.7 :h 1.1 :i: 1.8
E613 1r‘ /W —» u 27 7.8 :l: 1.7
NA27 p/p —+ D 27 34.4 a: 4.2
E743 p/p —+ D 39 59:3:
LSM' p/p —-. A. 53 2400 a: 1000
R408‘ p/p —. D 53 210 j: 120
R416‘ p/p -+ A. 62 150 :t 70
R603‘ p/p a A. 62 1800 :l: 600
R606‘ p/p —. A. 62 1000 :l: 400
R606‘ p/p —. A. 63 480 :l: 200
SFM(CBF)‘ p/p —+ A. 63 200 — 1100
SMF(CBF)' p/p —+ D° 63 600 — 5000

 

-MQ-na A4...— -

13

Figure 2.1: Charm cross section vs. center of mass energy; only measurements from

experiments sensitive to most of the 2:;- range are shown.

 

[\J

 

10

0(Mb)
lllll

I
H4

10

llllll
r—a/‘r—e—l

l .

1

 

 

 

O 10 20 3O 4O 50 60 7O

«5(GeV)

 

 

 

14

Figure 2.2: Charm partial cross section (Izpl > 0.3) vs. center of mass energy; upper

limit at J; = 39 GeV is from our experiment.

 

 

 

 

 

 

F
104(:b)

.03... i (I)
102;;- 1 1

10 5:- "

1 l l I l '1 l l ’

O 10 20 30 4O 50 60 7O
6(Cev)

 

 

 

15

2.3 Attempts to measure charm differential cross sections in :1: p- and p}

Several experiments, in a variety of environments, have also attempted to measure
the charm differential cross sections in the Feynman variable am, the longitudinal
momentum fraction of the charm hadron in the center of mass frame of the beam
and target, and in the transverse momentum squared p3“ Charm production is often

parametrized empirically as

(I’d
d3pdp%v

 

~ (1 - lzrl)"ezP(-bpi)-
While in principle the invariant distribution Eda/dz;- ~ (1 - IzFl)" should be used,
this procedure is not always followed and most experimenters used the non invariant

distribution dN/dzp ~ (1 — Impl)" to obtain the exponent 11.

There is general agreement on a value of 5 z 1 (GeV/c)”, corresponding to an
average transverse momentum of 1 GeV/c, independent of the target used, as seen
in Table 4. The up behaviour of charm production on the other hand is not well
understood with results for it, given in Table 4, varying widely, from n z 1 to n z 10.
Although no systematic trend is evident, in using the data in Tables 3 and 4 one
must be aware of the possible distortions in the heavy target data caused by nuclear

effects.

2.4 Two mechanisms for hadronic production of charm

Several mechanisms consistent with our current understanding of QCD have been

proposed to describe charm production. The quark and gluon fusion and excitation

16

Table 2.4: A partial list of measurements for the production parameters 11 and b.

 

 

 

Experiment Reaction J3 (GeV) < pr > (GeV/c) b(GeV/c)‘2 n
NA11 1r'/Be —» D 19 - 1.1 :t 0.5 0.8 i 0.4
NA16 p/p —+ D 26 0.75 :l: 0.12 1.1 :l: 0.3 2.8 :l: 0.8
E595 p/Fe —» ,1 27 0.70 :l: 0.15 - 5.0 :t 0.8
NA27 p/p —+ D 27 - 1.21 a: 0.14 4.8 :h 0.7
E743 p/p —. D 39 - 0.66:“333 11.03;:

 

 

 

 

 

 

models describe charm production as a result of relatively hard collisions between
hadron constituents, while the intrinsic charm model (ICM), based on the postula-
tion of a valence charm component of hadrons, describes charm production as the
dissociation of a charm quark pair from an incident hadron through relatively soft
collisions. Determination of charm production cross section and dynamics can provide

a sensitive test of both the hard and the soft mechanism.

From the perspective of the hard scattering mechanism, the quark and gluon
processes that can give rise to charm hadrons in hadron-hadron collisions fall into

two classes: fusion processes and excitation processes". The fusion processes

gg —> c'é,q_q' -—0 c5

are illustrated in Figure 3(a). Calculation of these diagrams requires knowledge of

 

"B. L. Combridge, Nucl. Phys. 8151 (1979) 429

 

17

the valence and sea quark distributions, known as structure functions, of the col-
liding hadrons. The structure functions of the proton have been measured in deep
inelastic lepton-hadron scattering, while the gluon distribution has been inferred from
these measurements. The structure functions are usually parametrized as functions
of Bjorken x, the fractional momentum of the quark or gluon relative to the parent

hadron, and Q”, the momentum transfer squared in the collision”.

In the proton-proton collisions examined in this experiment an initial state
antiquark can only come from the sea which is peaked at small x. Since the gluon
distribution dominates at small x, gluon fusion is expected to dominate over quark

fusion in charm production.

Excitation processes, illustrated in Figure 3(b), can be expressed as

9‘3 —’ 9°: 9° "" 90:76 —’ 7C:

where, in addition to the gluon, up, down, and strange quark distributions, the initial
state involves the charm sea in the beam or target. To date no measurements of the
charm sea distribution are available, it must be estimated and therefore predictions
of contributions to the cross section from excitation processes have correspondingly

large uncertainties.

Perturbative QCD gives the Feynman amplitude for quark and gluon level pro-
cesses. The production cross section for charm pairs is obtained by summing over

contributing processes 6 and integrating over allowed momenta, from the production

 

”E. Eichten, I. Rinchlifi'e, K. Lane, and C. Quigg, Rev. Mod. Phys. _5_§ (1984) 247

18

Figure 2.3: First order diagrams for the (a)Fusion and (b)Excitation processes.

 

 

 

 

 

 

 

 

 

 

 

A

 

 

_e

 

(b)

(I)

 

 

19

threshold to the initial state invariant mass,

0'63 = 2; (13143255P(31,Q2)P(32:Q2)a

'shS‘S'

The quark gluon process energy is x/i = ,/s:1:13:2, while the sum extends over all
contributing diagrams. Usually the threshold value is taken as the mass of the charm
quark pair (m. 2 1.2-1.8 GeV) and the momentum transfer squared in the structure

functions (P distributions) is taken as Q2 x 4m:.

To convert the pair production cross section 0.; into cross sections for physical
hadrons, hadronization schemes are invoked. The simplest scheme is delta function
fragmentation. Charm quark fragmentation is assumed to be given by the fragmen-
tation function f(2) = 6(2), where z is the momentum fraction of the charm hadron

relative to the charm quark. A more sophisticated fragmentation scheme is imple-

mented in the LUND Monte Carlo 39.

Due to the dominance of small x values for the gluon and antiquark structure
functions in a proton, fusion processes lead to central charm production (% strongly
peaking at x = 0), in proton-proton collisions. Including only the first order processes
of Figure 3(a) the charm cross section at our energy, J3 = 39 GeV, is predicted to

be '31

”fusion z 30l‘b:

 

”T. Sjostrand, Comp. Phys. Comm. fl (1986) 347
”a. K. E111. and c. Quigg, Fermilab FN-445 (1987)

“c. a. Cudell, F. Halsen, and K. nib... MAD/Pam

20

with an energy dependence

afuss'on(\/; = 39GeV) ~

~ 2
dfm(\/: = 27G8V)

 

Predictions for the excitation processes are highly sensitive to assumptions made

on the charm sea distribution. Recent estimates32 gave

aezeitats'on z 2 X firm,
at J3 = 39 GeV.

As the fusion and excitation processes are both hard scattering mechanisms, the
energy dependence of the contribution to the cross section from excitation processes
is expected to be similar to that of fusion processes. However, as the spectator
charm quark is expected to recombine with the beam fragments after the excitation

process, a large forward component was predicted for the longitudinal momentum

(2F) distribution”.

The second, soft scattering, mechanism for charm production involves the hy-
pothesis of intrinsic charm (ICM). In the ICM hadron wave functions are postulated

to contain an intrinsic c2 component distinct from the sea”, so that for a proton

Ip >= qudc'é > .

As opposed to charm pairs from the sea, intrinsic charm pairs exist over relatively long

time scales appropriate for valence quarks. They have the same velocity as the parent

 

”V. Barger, F. Halsen, and W. Y. Keung, Madison preprint DOE-ER/00881-215 (1981)
”R. Odorico, AIP Conference Proceedings No. 85 (1981) 100

“S. J. Brodsky, P. Hoyer, C. Peterson, and N. Sakai, Phys. Lett. £3. (1980) 451

21

hadron and therefore carry a large momentum fraction, leading to forward production
of charm hadrons. In contrast to the hard mechanism of fusion-excitation, production

via the ICM should chiefly occur at low momentum transfers, where perturbative

QCD is not applicable.

The ICM was proposed following the ISR reports of copious forward charm pro-
duction. Charm production by this mechanism is diffractive and the model reproduces

the large ISR cross sections36

”intrinsic ~ 1mb, J; = 6OGeV.

A linear interpolation between the ISR values and measurements made at lower en-
ergies, e.g. the NA27 results“, would predict a dramatic growth of the cross section

over a small energy range,

cintrs'nss'c(fi = 3903V) ~
0;M,;m(fi = 27G8V) ~

 

10,

2.5 Summary of the goals and results of E743

Our proposal to measure the energy dependence of hadronic charm production was
accepted by Fermilab in December, 1983. The experiment was designed to over-
come three major difficulties in the measurement of charm production cross sections:
the nuclear dependence of charm production, the insufficient knowledge of exclusive

branching ratios, and the poor acceptance of charm decay products in the apparatus.

 

”S. L. Olsen, AIP Conference Proceedings No. 85 (1981) 1

”LEBC-EH8 Collaboration, Berkeley Conf. Preprint, presented by M. E. Miehalon and M. Iori

22

First, the nuclear dependence of charm production is not well understood; a
hydrogen bubble chamber target circumvents the problems involved in extrapolating
from heavy target cross sections. Secondly, for the purpose of extracting cross sec-
tions, exclusive or semileptonic branching ratios for charm are not sufficiently well
determined and systematic uncertainties introduced through these branching ratios
can be severe; the active target allows us to see the majority of the important decay
modes. Lastly, charm production kinematics, i.e. the Feynman x distributions, are
virtually unknown; we obtain reliable data on charm hadroproduction via a spec-

trometer with good acceptance in z; and pr.

Our apparatus allowed full reconstruction of charm decay vertices in the rapid
cycling, high resolution Lexan bubble chamber (LEBC). Charm decays were topologi-
cally tagged during scanning of bubble chamber photographs, charged tracks decaying
into three prongs and four pronged decays of neutral tracks are unambiguous charm

signatures.

Identification and momentum measurement of charged decay products were
provided by the Fermilab Multiparticle Spectrometer (FMPS). In the E743 configu-
ration, the FMPS consisted of a superconducting analysis magnet with a 0.7 GeV/c
transverse momentum kick, ten tracking stations, two Cerenkov counters, and a tran-
sition radiation detector. The acceptance of the spectrometer was 100% for charged

particles with 2;- Z 0.

During the third run of Tevatron II (spring and summer 1985), LEBC was

exposed to 800 GeV/ c primary protons from the Fermilab MT beam line and over

23

one million minimum bias triggers were taken.

The most fundamental result is an unambiguous measurement of the D meson

inclusive cross sections”,

0(D/D, J3 = 3QGeV) = 59::gub,

with
«(W/0‘) = 33 4 7ub.a(D°/D‘°) = 26:23.91».
When compared with measurements made at lower energies, such as the D cross

section from experiment N A27 at the CERN SP8“, our value of the cross section

indicates a weak energy dependence,

0(D/D, J3 = 39GeV)
«(D/D: J3 = 27GeV)

= 1.7fg;:,

 

in disagreement with the strong energy dependence implied by measurements made
at the ISR and, correspondingly, with no need for an intrinsic charm component in

the nucleon.

Our fit of the longitudinal and transverse momentum distributions of observed

D meson decays yield

do
tic—F ~ (1 - Izrllflsn = 311-033,

and

da-
—2 ~ ezp(—bp;.),b = 0.66:°:::(Gev/c)".
dPT

 

"a. Ammar et al., Phys. Lett. 1318: (1986) 110

”LEBC-EH8 Collaboration, Berkeley Conf. Preprint, presented by M. E. Michalon and M. Iori

24

The predominantly central Feynman x distribution we observed is, like the inclusive

cross sections reported above, also inconsistent with the predictions of the ICM.

A more generally accepted model for charm hadronic production is the Fu-
sion model (FM), based on perturbative QCD. It is assumed that in proton-proton
collisions the major contribution to the charm cross section comes from first order
processes involving the combination of a pair of gluons to form a c? pair. The FM

prediction

0(D/D, J3 = 39GeV) ~
0(D/D, J3 = 27G'eV) —

 

is in good agreement with our result, although the FM prediction for the total charm
cross section is smaller than the experimental value by a factor K 2 2. This dis-
crepancy can be attributed to the fact that higher order QCD diagrams have not
been included in the calculation. The energy dependence is not expected to change
significantly with the inclusion of second order diagrams, thus the agreement with

the FM prediction should be maintained.

Also measured are the associated charged multiplicity in both charm and non-

charm events. For charm events the mean primary multiplicity was”

< Nd; >= 11.9 :t 1.0,pp -) charm + X

while for inclusive proton-proton events

< N... >= 10.26 i 0.15,” -9 X.

We note that very few charm particles were observed in the low multiplicities. We

 

”R. Ammar et al., Phys. Lett. B178 (1986) 124

25

can attempt to compare our associated multiplicity with all non-diffractive collisions
by removing the multiplicities which are dominated by the diffractive component
(N.;. = 2,4, ~ 6 mb) from the inclusive multiplicity distribution. This yielded a non-
diffractive multiplicity of < Ndhm-dgff,¢¢¢iu >= 11.59 :I: 0.16, which is rather close

to that observed in charm associated events.

In the next two chapters we shall give a detailed description of our apparatus
(Chapter 3) and of our procedures for data reduction and analysis (Chapter 4). Chap-
ter 5 describes our study of the trigger bias as well as our results for the inclusive
multiplicity distribution. Chapters 6 and 7 give detailed results on the D meson total
and differential cross sections. In Chapter 8 we compare these experimental results
with predictions by the FM and other, unusual, mechanisms for charm hadropro-
duction. Finally, a summary of the results presented in this thesis will be given in

Chapter 9.

Chapter 3

EXPERIMENTAL APPARATUS

This chapter gives detailed descriptions of the apparatus of experiment E743.

3.1 The beam and beam optics

During the third run of the Fermilab Tevatron 11, our bubble chamber was exposed
to 800 GeV/ c primary protons from the accelerator. Figure 1 illustrates the optics
of the MT beam line and the site map of Figure 2 shows the beam line location. To
accomodate the low rate capabilities of the bubble chamber, the beam was attenuated
by a four foot beryllium block. Initial collimation of the attenuated beam was per-
formed by a remote-controlled collimator. A kicker magnet with 0.8 GeV/c transverse
momentum kick downstream of this collimator prevented protons from entering the
bubble chamber before it became sensitive. Two additional collimators, five dipole
magnets, and two quadrupole magnets downstream of the kicker provided final beam

tuning.

At the bubble chamber the 800 GeV protons were attenuated to a mean incident

26

27

Figure 3.1: Optics of the MT beam line.

 

lMZ '

Yl

_ \l
l I
133
.00l
I

 

 

Jameson 9

M9

 

 

 

 

 

28

Figure 3.2: Site map showing the location of the MT beam line.

 

. son 5!.
’1 £{ts‘llsfli

!

 

l i "
”3.5.2:...

 

 

 

  
  
  
 
  
   
 

 

 

 

',. . ..'
LAY-ow- 3' ‘

too-0 0“. 0 Issues s.s.

 

 

 

 

FERMlLAB 0

O as a no... 000...!»- \oOOOO-o
.. . coco-.- coed -..- '9‘ m... g...
d—- ‘QOOIO

 

 

29

rate of 1.5 x 10‘ per accelerator spill and collimated to an 8 mm vertical by 1 mm
horizontal spot. The spills were 20 to 23 seconds in duration, with 57 to 120 seconds

between spills.

The beam was defined, prior to entering the bubble chamber, by three stations
of wire planes at 1 mm pitch, approximately one meter apart; the last station was
approximately one meter upstream of the bubble chamber. In addition there were
six scintillators between the last beam wire station and the bubble chamber, four
of which further defined the beam and two vetoed beam halo. These scintillation

counters were part of the trigger system.

During the running period a total of 1.18 x 10° bubble chamber photographs
were taken with a minimum bias trigger (see section 3.4). Subsequent scanning of
these photographs revealed about 5 x 105 recorded proton-proton interactions. Re-
sults reported in this thesis are derived from the first analyzed 25% of the data,

corresponding to an experimental sensitivity of

s = 3.5 :l: 0.1events/pb.

In addition 8.1 x 10‘ photos were taken with an unbiased trigger for multiplicity and

trigger efficiency studies. Scanning these photos revealed 1.6 x 10‘ recorded proton-

proton interactions.

30

3.2 LEBC, the hydrogen target and vertex detector

Figure 3 is a photograph of the Lexan Bubble Chamber (LEBC). LEBC is a high
resolution, rapid cycling hydrogen bubble chamber designed to study short lived par-
ticles. Table 1 shows the most relevant parameters for LEBC. The main body of the
chamber was milled from a single slab of the thermoplastic polycarbonate Lexan. The
beam entry and exit windows, and the flexible expansion membrane were glued to
the main body using a solvent cementing technique which ensured secure sealing at
cryogenic temperatures. A heat exchanger and a filling valve mounted on top of the
main body maintained chamber temperature and pressure. The expansion membrane
was driven by a piston with 0.5 mm stroke. The chamber assembly was housed in a
steel vacuum tank. Figure 4 is a beam’s eye view of the chamber assembly, Figure 5

shows the vacuum tank and camera set up. Greater details for the specifications of

LEBC can be found elsewhere‘.

In order to achieve high resolution, small bubble size and high bubble density
were required. For the bubble size to be small the expansion cycle must be short, so as
not to allow time for the bubbles to grow too large. The cycling rate also must be high
in order to achieve acceptable data rates. Due to the demand of rapid cycling, the
fiducial volume must be made small. Since the short lived particles of interest were
expected to decay near their production vertex, a small fiducial volume was accept-

able. Mechanical integrity dictated that the entire chamber be constructed of lexan,

 

1I. L. Benichou et al., Nucl. Instr. and Math. 192 (1981) 487

31

Figure 3.3: A photograph of our LExan Bubble Chamber.

 

 

     
        
 

1: Gang

 

 

      
 

   
 

   

' i. ' " . . ‘ a 3.32.... p
5‘34. 1."fl§'Pi°.;J':‘.’.‘“¢- 'm‘
' 'Expa.' ion' Hetjntai'at'te,T

,fla'e.

v‘-

  

 

 

 

32

5 eye view of the chamber assembly.

Figure 3.4: Beam’

 

2

 

Em: 93m.

 

.er>Z +
mCDMQZMCr.

 

 

K 8883

 

 

 

 

 

 

 

 

L

 

lr

 

 

 

 

 

 

 

 

 

 

 

 

:0. 3307.- .l .
1 \RN ..

 

 

 

 

 

O

 

m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

33

Vacuum tank and camera set up for LEBC.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.5

 

 

 

I III.
539...: NH
<2 3 mtg:
. /. <3.
<25; «2:.
.
Can; a

$3932. . :3: __ - ,

. 1-: . . 1. l . .ll .1 l. .. P; 5323
M (.2.
p~auau
l . 0.1m“ nbxnn> .
_ .J . ....
1 2.33.3 . f m
‘ I. o s o
7.3.. :32 . H .
3.90 a .
O . . f s
W \... .luu...“ . ..a. . .....11 .7)
t - at. 2235.3? . .. -.. . . . .

. . . . I ......f m
f l . a F s s o .\ . f A Q, Otto?

& r e .o .l a 6 t I 0 . .. 0‘ IO 0‘ o
s O I . l .0 I 1 s a o . . n s e If

a .. .0 our- roowl. s It .a. as .. .s \I\ o\ .

34

a thermoplastic polycarbonate with high impact strength at cryogenic temperatures.

Lexan has the further advantage of being transparent to visible light.

Figure 6 shows the optical system for LEBC. The resolution R of two point
objects is limited by diffraction, R = 1.22%, where A is the wavelength of the light
source and a is the lens aperture. The depth-of-field 6 is proportional to the square of
the resolution, 6 a: 512’. High resolution therefore implies limited depth-of-field. The

optical system must be able to resolve individual bubbles, whose size was z 20pm.

During data taking a resolution of 20pm was achieved for the film image of the

bubbles, with a 2 mm depth-of-field.

Monochromatic illumination by a pulsed dye laser was chosen to circumvent
problems of chromatic aberrations, and correction lenses were used to eliminate dis-
tortions of the image by the cold window of the vacuum jacket and the lexan chamber
body. Photographs were taken in two conventional camera views :l:6.5° from verti-
cal. A pair of optical fibres guided the laser light to condensor lenses focussed at the

camera apertures.

3.3 The FMPS spectrometer

In the E743 configuration, the Fermilab Multiparticle Spectrometer (FMPS) consisted
of one superconducting analysis magnet giving a 0.7 GeV/c transverse momentum
kick in the horizontal plane, ten tracking stations, two Cerenkov counters, and one

transition radiation detector. The analysis magnet was positioned approximately

35

Figure 3.6: The optical system of LEBC.

 

 

     

 

N NSOR
UGHV (0 0‘ n PLANE 0F [ENS
souncs - “70 005" ,mncu WH Hm Punt
T BEAM APERIURE .
/ .....
*--- 33:1 -- _....:
z .‘ \“si
/3:,;:£ (AHERA'
[EXAN 3 Jr b
mucous V

l:l0

 

 

36

Table 3.1: Important LEBC parameters.

 

 

Material

Cycling rate

Cycle duration

Live time

Fiducial volume
Operating T, p, p
Stereo angle
Illumination

Mean bubble diameter

Mean bubble density

 

(H1401603)n

30 s-1

51:23

500;»

50 x 70 x 109mm3
29°K,4.2kgcm”,0.057gcm‘3
:l:6.5°

500 nm dye laser, 200 ns pulses
20pm

706m-l

 

 

37

three meters downstream of the chamber. The magnet apertures were 84 cm in the
vertical plane and 122 cm in the bend plane, corresponding to an angular acceptance

of 3:150 milliradians in the vertical plane. The momentum resolution was
APE“, = 100GeV/c) = 1.5%

for tracks within the aperture of the last tracking station, and 2.5% for wider angled
tracks. The low momentum threshold for tracks to survive bending by the magnet

was 3 GeV/c.

Figure 7 is an elevation view of the FMPS. There were twelve proportional wire
planes in the upstream lever arm of the spectrometer. The downstream arm had
twelve proportional wire planes, eight drift planes, and four planes of proportional
tubes. The four wire planes in the first MWPC station immediately behind the
bubble chamber had 0.5 mm wire spacing and was also part of the trigger logic. The
remaining MWPC planes had wire spacings between 2.0 mm and 2.5 mm, giving a

resolution of z 0.8 mm. The proportional wire stations were filled with a mixture of

argon and 20% 003.

The two drift stations were operated in common stop mode. At 19 mm pitch,
these drift planes had 350 um resolution and provided precision track points for the
downstream pattern recognition. The drift chambers were filled with a mixture of

argon and ethane.

The FMPS was also equipped with two identical stations of proportional wire

tubes. Each station consisted of one horizontal and one vertical plane, with a sensitive

38

Figure 3.7: Elevation view of the Fermilab Multiparticle Spectrometer in the E743

configuration.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u * l
o —:
ls:
l” >< I
» 1 ~ .1.
b ....
.. s ,
9 a
g n
. "1
“in R
~ t»
- " ‘1
3 2
a “ >
1 t~
2 .. E I‘ i
u C
.. i a {g
3‘ l 2
Q .. 3 f
E .. s
“ i a
.. 9
6.-
lb 3
I
.. 0
C
J-
~‘h
. o
a db
‘
.. S
9—_1
‘
~‘P a
“‘ A
q
' III- a
o
“in
O
_—

 

 

 

 

39

area of 365 cm horizontal x 158 cm vertical. Proportional tube cells were 2.5 mm
wide. Except when cells were multiply hit, the proportional tubes provided three
dimensional hit coordinates by the method of charge division. These hit coordinates
aided view matching of tracks during pattern recognition. For the ordinary coordinate
the resolution was 7.3 mm while for the charge division coordinate the resolution was
1.5% of the length of the proportional tube wire. The proportional tube stations were

also filled with argon 00,.

Approximately four meters downstream of the magnet was a nitrogen filled
Cerenkov counter with pion, kaon, and proton momentum thresholds (for a given

particle, the counter does not respond unless the particle momentum exceeds the

threshold pa.)

p¢s(1r/ K/p) = (5/25/38)GeV/6-
The second Cerenkov counter positioned seven meters downstream of the magnet was
filled with helium, with

P:h(1r/K/p) = (17/59/112)GeV/c

momentum thresholds. Behind the last tracking station was the transition radiation
detector. It consisted of alternating planes of xenon filled proportional wire detectors

and carbon fibre radiators.

40

3.4 The triggers and data acquisition system

The trigger system consisted of six scintillator hodoscopes and four planes of 0.5
mm pitch proportional wires, illustrated in Figure 8. Four scintillators positioned
upstream of the bubble chamber signalled the arrival of the beam. Two additional
scintillators approximately 20 cm in front of the bubble chamber and away from the
beam spot vetoed beam halo. Two vertical and two horizontal wire planes downstream

of the chamber counted outgoing tracks.

Figure 9 shows the timing of our trigger. At the beginning of an accelerator spill,
a kicker magnet pulse swept away incident protons as the bubble chamber expansion
cycle started. As the chamber became sensitive, beam was allowed into the fiducial
volume and activated the trigger. The trigger turned on the laser flash, which was

delayed to allow bubbles to grow to photogenic size.

The bulk of the data for charm studies was taken with a minimum bias, or
‘interaction’ trigger, defined as ‘beam’ and at least three tracks in the wire planes.
Some data was also taken with an unbiased, or ‘beam’ trigger, defined by the six
scintillators alone, for inclusive physics studies as well as for studies of the interaction

trigger bias.

The trigger also activated spectrometer data acquisition. The data acquisition
system was based on the Fermilab package MULTI’. Detector channels were read out

from CAMAC crates by a Jorway 411 branch driver controlled by a PDP-ll. From

 

aV. White, B. Burch, K. Eng, P. Heinicke, M. Pyatetsky, D. Ritchie, Fermilab PN—183 (1983)

41

Figure 3.8: The E743 trigger system.

 

 

T 1 V1
LEBC
/_1-2 l_/.

I / l Bear:

 

 

/

 

 

l

 

 

 

 

 

1_

T4 T3 V2 W

 

 

42

Figure 3.9: Timing of our interaction trigger.

 

 

4—15 millisecs
kicker current

 

idl

Al

50 microsecs

 

 

beam (IO khz)

IHIHHHHHI
\ /

_p. ~4———t millisecs

 

 

 

 

 

 

LEBC pressure

 

 

 

 

LEBC gate

 

 

 

Trigger

—>- Flash
150 microsocs

 

 

 

 

 

 

43

there the event data was packed into a half word integer vector for transmission by
a pair of DRll controllers linking the PDP-ll with a VAX 780. From the VAX, the
data was available for logging to magnetic tape, for on-line monitoring, for graphical

display, and for partial on-line analysis with specialized user routines.

In the next chapter we shall give detailed descriptions of the procedures followed

in our reduction and analysis of the data.

Chapter 4

DATA REDUCTION

We discuss at length in this chapter the procedures followed in reducing and

analyzing the data.

4.1 Film analysis

Initially, bubble chamber and spectrometer information were separately processed in
two independent data streams. Identification of charm events took place during the
scanning and measuring of the bubble chamber photographs. The charm candidate
digitizations were stored on magnetic tape in a HYDRA1 data structure. Spectrom-
eter information for selected events was then analyzed and concatenated to the data
structure for further consideration. We describe first the various aspects of film han-

dling.

 

1R. Bock et al., HYDRA Topical Manual, CERN Program Library (1981)

44

45

4.1.1 Scanning

The bubble chamber pictures were recorded on fifty millimeter film. After develop-
ment the film was distributed to scan shops of institutions in our collaboration (50%
of the film was scanned at Fermilab under the author’s direction). Both views of the
bubble chamber were scanned for interactions of interest. Scanning was guided by an
upstream measurement of the beam track that generated the trigger. The primary
interaction was located and secondary activities were searched for. Secondary vertices
were categorized according to their charge multiplicity and by the vertex type. Figure
1 illustrates important decay topologies and parameters. A vertex was of type ‘C’ if
it came from a charged primary track, and ‘V’ if it came from a neutral track. Thus,
for instance, the topology of a D+ -—» K'1r+1r+ is ‘C3’. A second scan was made of
the frames in which a proton-proton interaction was observed, looking specifically for

secondary activity indicative of charm decay.

Charm decays have topologies C-odd or V-even. As charm particles are short
lived and therefore have short transverse flight paths, only those decays which oc-
curred within the ‘charm box’, a space cylinder 2 mm in radius centered on the

interacting beam track, were considered.

In spite of the relatively high multiplicity and the collimation of tracks at our
energy, the efficiency for detection of secondary activity was high. The detection of

secondary activity in scanning is dependent only on the impact parameter

Y = Lsinfl

46

Figure 4.1: An illustration of (a)important decay parameters and of the charm topoloo

gies (b)C3 and (c)V4.

 

 

‘33 Imbst
(b)

\ (c)

 

 

 

47

of secondary tracks, where L is the separation between the primary and secondary

vertices and 0 is the angle between the secondary track and its parent track.

When the daughter is emitted normal to the parent line of flight in the parent
rest frame (denoted by the superscipt I“), the components of the daughter momentum
along and normal to the parent line of flight in the laboratory frame are q i = q",
q” = 7fle‘. In the limit of large Q values (e‘ 2 q‘), the daughter momentum in the
laboratory is approximately q“ 2 7flq“, and the decay angle in the laboratory frame

9

is sin0 = 14- 2 717177;; in the limit of a large Lorentz boost from the parent rest
7

frame to the laboratory (,6 2 1, 7 > 1),

1
sin0 2 —.
'7

The decay angle in the laboratory frame decreases as 7”. On the other hand, the
decay length

L = 7667' 2 7c1'
(1' is the proper decay time) grows as 7, so that the impact parameter is Y 2 c7,

independent of 7, i.e. the parent momentum.

A more complete treatment (see Appendix A) shows that for all angles of emis-
sion, the impact parameter of decay tracks is independent of the parent momentum
for sufficiently high Q values and sufficiently large Lorentz boosts from the parent
rest frame to the laboratory frame. The mean impact parameter is proportional to

the mean life of the parent, with small variations from one decay mode to another.

Figure 2 shows the magnified film image of a charm associated event. After

48

the film had been double scanned by scanners, charm candidates were selected for
measurement by physicists in a third scan of those events tagged as having secondary

activity during either of the two previous scans.

In comparison with data taken with this bubble chamber at lower energies,
scanning of these events suffered from the increased multiplicity and collimation of
tracks but benefitted from the Lorentz boost of decay lengths. On the scanning table,
impact parameters were detected by viewing the magnified film image at glancing
angle. Our scanners placed themselves at eye level with the table onto which the film
image was projected. From this perspective, tracks that did not point back to the
primary vertex were easily detected. With some visual aid, for instance by placing a

straight edge along the secondary track, non pointing tracks with impact parameters

greater than 100 pm were spotted without dificulty.

Both of the two independent scans were done in the above manner. Double
scanning also allowed us to measure the scanning efficiency. Single and double scan
efficiencies were defined as follows. If N,- 5 number of events found in the i"‘ scan,
and N13 E number of events common to both scans, then the efficiency for the two

scans is

_ N12 _ N12
61 — —s€2 - '1?!)

N2

and the double scan efficiency is
e = 1 — (1 -— 61)(1 — 6;).

Our double scan efficiency for the detection of secondary activity was 6 = (90 :l: 5)%.

49

Figure 4.2: Photograph of a charm event.

 

50

Events with secondary activity were tagged for the third scan. During this scan
secondaries with interesting topologies, C-odd or V-even, were selected as potential

charm candidates and sent on for measurement.

4.1.2 Measuring

Film measurement was performed using the Electron Ray Scanning and Measuring
Equipment (ERASME) system at CERN. The film was slice scanned with a light beam
which passed through the film and was detected in a photomultiplier. A jump in the
light intensity at a track bubble caused the position of the bubble to be recorded. In
this manner, track points were measured with an accuracy of 2.7 pm and track angles

and vertex positions were found by fitting.

In addition to decay lengths and impact parameters, the dip and 41 angles of
bubble chamber tracks were also measured for the purpose of hybridization, i.e. the
matching of bubble chamber tracks to tracks found in the spectrometer. The dip and
41 angles were defined as A E (dip) angle between the track and the plane transverse
to the beam direction (-1r/2 S A S 1r/2), and 41 2 angle between the projection of
the track onto the transverse plane and the beam direction (0 S 43 S 211'). Track

images from the two camera views were matched by their bubble pattern.

The film measurements for selected charm decays were stored in HYDRA banks,

to be later concatenated with the spectrometer information on their decay products.

51

4.2 Event reconstruction

In order to determine the identity of the particles and their decay modes the spec-
trometer information on the momentum and mass of the decay tracks was analyzed.
A pattern recognition program was used to analyze the spectrometer tracking system,
followed by steps to combine the bubble chamber and spectrometer information, and
to fit the events to kinematical hypotheses. A final pattern recognition stage using
graphical software developed by the author was used to recover a significant fraction
of those events which would otherwise have been lost. The details of these steps are

provided below.

4.2.1 Spectrometer tracking

The program FLOWERS2 was used for tracking. FLOWERS was a conventional
finder-fitter in four views, with user defined road chambers. The four views were
2,, E bend (horizontal) plane upstream of the magnet,
:4 _=_ bend plane downstream of the magnet,
,, E upstream vertical and slant planes,

yd E downstream vertical and slant planes.

Several passes were made for each event. In each pass the x projections were
found first. The y projections were then found and matched to the x projections.

Downstream tracking was performed first, as the greater track separation there facil-

 

3J. H. Goldman, E623 internal note

52

itated pattern recognition. View matching was done using charge division hits from
the proportional tubes when appropriate, otherwise hits on slant planes were used.
Bubble chamber measurements of the position of the primary vertex aided upstream

tracking.

A distinct set of road chambers pertained to each pass. Road chambers were
selected to cover both large and small angled tracks and redundancy was built into
the selection to cover chamber inefficiencies. Track candidates were selected on the

basis of the number of hits and the goodness of fit.

4.2.2 Hybridization and kinematic fitting

Spectrometer tracks found by FLOWERS were at this point hybridized with tracks
found in the bubble chamber. Bubble chamber tracks were matched with spectrome-
ter tracks on the basis of their dip and 0'1 angles, allowing the identification of charm
decay tracks in the spectrometer. The program GEO743 3 then performed kinematic

fitting of hybridized decay tracks.

Under the assumption that all of the decay products were charged, kinematic
fits of charm decays were divided into constraint classes. For each decay, energy and
momentum conservation gave four equations with four unknowns, the four-momentum
of the parent particle. The angles of all charged tracks were measured on film so that,
when momentum measurements were available for all decay products, there were three

constraints on the fit. This case was termed a 30 (three constraint) fit. When one

 

'J. W. Waters, E743 internal note

53

charged decay product was not reconstructable in the spectrometer its angles are still
measured on film. There remained only two constraints and the fit was a 20. With

two missing charged decay tracks the fit was a 10.

If, on the other hand, there is a missing neutral particle (e.g. a 1r° or K °) then,
even when all the charged decay products were measured, there are no constraints on
the kinematics. A 00 calculation of the parent momentum pp can be made for any
assumption regarding the parent and missing neutral daughter masses my and m,

using the following

 

2 2 2 s
3 11 pm“ 4Eva — u _
pD—pDEz- 2 4(E3“P2||) -0

where

 

pEJmfg+m3—m3

The subscript 1: refers to the visible system, and the subscript || refers to the compo-

nent of the momentum along the direction of flight of the parent.

There are in general two solutions to the above quadratic equation. Unphysical
solutions are immediately rejected in our data, due to the fact that the visible mass
m. is large in most cases. Futhermore we observe, and Monte Carlo studies confirm,
that when there are two physical solutions for the momentum, the two solutions are
always nearly equal to each other. Therefore in such cases the mean of the parent

momentum given by the two solutions was used.

In nearly all of the decays for which constrained fits failed, one can find nu-

merous OC charm decay solutions. It is observed, and has been verified by Monte

54

Carlo studies, that for most decays the parent momentum calculated via the DC as-
sumptions is nearly independent of the charm species and the exact decay mode (only
Cabibbo favored decays are attempted). The following are 00 solutions for a typical

event taken from our data sample

Kinematic hypothesis 2: F.1 3E2 1113, p133

 

D+ —11r"’1r+K"K° -0.034 ~0.008 1.249 1.851

D+—ie+1r+K‘u -0.036 -0004 1.220 1.980
D+-—>1r+e+K’u -0.036 -0003 1.220 1.991
D: —. «+1r+K‘K° .0021 1.589

where 2: 17,1, egg, 111,1, and p1,; correspond to the two solutions of the quadratic equa-

tion in the parent momentum. Note the small variation of the :1: 15 (A2: < 0.1) and p1-

values.

As the OC calculation can only be applied when all charged decay products
were reconstructed, a method was developed to treat those cases where one charged
track was outside the spectrometer acceptance. In this ‘O’C’ calculation the missing
charged track was grouped with the missing neutral into a system with an assumed

invariant mass of 500 MeV/c2 and the calculation proceeds identically to the 00 case.

In contrast to 00 results, the two solutions for the parent momentum from
‘0‘C’ calculations were often widely separated. However, as the geometric acceptance

of the spectrometer was 2 100% for 2F 2 0 (see Tables 1 and 2) the phase space

55

probability for the fast (high laboratory momentum) solution was always negligible.
In other words if the parent had the high momentum of the fast solution, all charged
decay products should have been reconstructable. The fast solution was therefore

eliminated and a correction for the slow solution was calculated by Monte Carlo.

4.2.3 Graphical techniques

A program, E743PIX‘, was written and used to improve our event reconstruction
efficiency through graphical displays. Since the mean event multiplicity at our en-
ergy is 2 10, and each charm decay adds several charged tracks, charm events were
topologically complex. Software tracking and kinematic fitting were performed by
FLOWERS and GEO743. Events were then individually examined with E743PIX,
a package for display and visual pattern recognition. Tracks that were not recon-
structed in software were recovered in this phase by scanning the spectrometer hits,

guided by the film measurements of decay track angles.

Spectrometer events were displayed in two views, the bend plane view x and the
vertical plane view y. The y projections of decay tracks were found using roads defined
by track angles as measured in the bubble chamber. The upstream x projections of
these tracks were also found in that manner. Extrapolation of the upstream x roads
to the mid magnet plane defined the intersection region for up and downstream legs
in the bend plane. Downstream x projections were found by scanning wire chamber

hits in that view. The graphics track candidates were subjected to the same selection

 

‘A. Nguyen, E743 internal note

56

Table 4.1: Spectrometer acceptance as a function of 2p and topology (V2, C3, V4),

requiring all charged decay tracks to be reconstructed.

 

a: F V2 C3 V4

 

<-0.2 0.00 0.00 0.00

-0.20 0.02 0.00 0.00

-0.16 0.04 0.00 0.00

-0.12 0.11 0.00 0.00

-0.08 0.22 0.16 0.00

-0.04 0.46 0.43 0.34

0.00 0.75 0.67 0.59

0.04 0.92 0.85 0.75

0.08 0.95 0.90 0.87

0.12 0.96 0.97 0.92

0.16 0.97 0.98 0.98

0.20 0.99 1.00 0.99

>0.2 1.00 1.00 1.00

 

 

 

 

 

 

57

Table 4.2: Spectrometer acceptance as a function of 2p and topology (V2, C3, V4),

requiring at least two charged decay tracks to be reconstructed.

 

a: F V2 C3 V4

 

< —0.2 0.00 0.00 0.00
-0.20 0.02 0.04 0.12
-0.16 0.04 0.14 0.31
-0.12 0.11 0.28 0.55
-0.08 0.22 0.61 0.83
-0.04 0.46 ‘ 0.89 0.99
0.00 0.75 0.97 1.00
0.04 0.92 1.00 1.00
0.08 0.95 1.00 1.00
0.12 0.96 1.00 1.00
0.16 0.97 1.00 1.00
0.20 0.99 1.00 1.00

>0.2 1.00 1.00 1.00

 

 

 

 

 

 

58

criteria as those found in software and submitted to GEO743 for further kinematic

fitting.

In this and the previous chapter we have given detailed descriptions of our
apparatus and our procedures for data reduction. The next chapter will deal with
the study of our interaction trigger efficiency and the related topic of topological cross

sections.

Chapter 5

NORMALIZATION AND MULTIPLICITY DISTRIBUTION

We describe in this chapter our procedures and results for the multiplicity dis-
tribution in proton-proton collisions at 800 GeV/c. This determination of the topo-
logical cross sections was crucial in our study of the interaction trigger bias. It is also

worth mentioning that these are the only multiplicity data available at our energy.

5.1 Scaning of the data sample taken with an unbiased trigger

A total of 8.1 x 10‘ bubble chamber photographs were taken with an unbiased, ‘beam’
trigger. The trigger required only an incident beam track. Scanning of this film

revealed 1.6 x 10’ proton-proton interactions.

Beam arrived at varying times relative to the beginning of the bubble chamber
expansion cycle. Events that were out of time had anomalous bubble size. To elimi-
nate early and late events from the sample our scanners were equipped with templates
of bubble sizes. Only events with bubbles in the range 20 um S bubble diameter 5

100 um entered the sample. The final selected sample consisted of 11,828 events.

59

60

Table 5.1: Scanning efficiency for the multiplicity sample.

 

 

Multiplicity Double scan efficiency
2 0.61 :l: 0.07

4 0.92 :l: 0.03

6 0.94 :l: 0.03

8 0.99 :l: 0.01

10 0.99 :l: 0.01

2 12 1.00

 

 

 

 

Both views of each event were scanned. When an interaction was seen, the
charge multiplicity was determined and recorded. A fraction of the sample was in-
dependently rescanned to measure the scanning efficiency. Scanning efficiency was
dependent on the event multiplicity. Because there were fewer ionizing tracks the

scanning efficiency was lower for events with low multiplicity (see Table 1).

The raw multiplicity distribution was corrected for scanning losses and for con-
tamination by Dalitz decays of neutral pious. In two pronged events contamination

by energetic knock on electrons (6 rays) and by elastic proton-proton scattering were

evaluated and removed.

61

5.2 Determination of the multiplicity distribution

Our goal was to measure the primary multiplicity of inelastic proton-proton events.
Decay tracks can be mistaken for primary tracks if their impact parameters were less

than 100 um and the decay vertex was close to the primary vertex.

Pions and kaons were copiously produced but due to the relatively long lifetime
of strange particles, the only appreciable background came from Dalitz decays of

neutral pions, 1r° —t 7e+e‘, with branching fraction BR(";,—11——i,f_ = 1.2%.

Since there are two pion charged states and one neutral state with a small
mixture of the 173, isospin invariance dictates that the ratio of the production rates
of charged to neutral pions should be approximately 2:1. Using the fact that roughly

90% of the fragments in hadron collisions are pions
< N(1r°) >2 0.45 < N.;. > .

Due to the short 11” lifetime tracks from their Dalitz decays were not distinguishable

from primary tracks and caused a 0.5% background in our multiplicity sample, i.e. 2

60 obscured decays.

There was no magnetic field across LEBC and therefore 6 rays (atomic electrons
scattered by beam protons) cannot be unambiguously identified. Two pronged events
therefore contained 6 rays as well as inelastic and elastic contributions. A Monte
Carlo simulation based on the expected kinetic energy distribution of 6 rays, on
their multiple scattering, and on their momentum to range relation gave a 6% 6 ray

contamination in the two pronged sample.

62

The total and elastic proton-proton cross section has been measured at sur-

rounding energies’. An interpolation between J3 = 30.7 and 45.0 GeV gave

0'4 = 7.3 :l: 0.11110, that = 41.0 :i: 0.3mb.

The number of inelastic two pronged events was calculated using
a'
N2,s'nel = N161(1 - A) — N>2
01a

where N... is the corrected total number of events in the multiplicity sample, and
N); is the corrected number of events with more than two outgoing tracks. A total

of 1,670 raw two pronged events were recorded. After corrections,

N2 = 2758 :l: 183,N3,.~...1 = 510 :l: 191.

The topological cross sections were determined by normalizing to the above
interpolated value for the total cross section. Table 2 summarizes our topological

cross sections results and the multiplicity distribution is displayed in Figure 1.

Available data on charged particle multiplicity in inelastic proton-proton colli-

sions have been fitted to the form2
< N.;, >= 11 + blog(s) + clog’(s),

a = 0.800 :1: 0.120, b = 0.470 2 0.050,c = 0.114 :1: 0.005.

 

1v. Flaminio et al., CERN-HERA 84-01 (1984)

2A. Breakstone et al., Phys. Rev. mg (1984) 528

63

Table 5.2: Observed topological cross sections.

 

 

 

Topology (Nch) Raw number Corrected number Cross section (mb)
2 1670 2758 :i: 183 8.9 :l: 0.6
2(inelastic) - 510 :l: 191 1.6 :l: 0.6

4 1221 1238 :l: 35 3.88 :l: 0.11
6 1478 1490 :f: 39 4.67 :l: 0.12
8 1582 1590 :l: 40 4.98 :l: 0.12
10 1535 1539 :l: 39 4.82 :l: 0.12
12 1413 1404 i 37 4.40 :l: 0.12
14 1094 1078 :l: 33 3.38 :l: 0.10
16 747 734 :i: 27 2.30 :l: 0.07
18 487 478 :l: 22 1.50 :l: 0.07
20 232 312 :l: 18 0.98 :l: 0.06
22 176 170 :l: 13 0.53 :l: 0.04
24 102 97 :l: 10 0.30 :i: 0.03
26 44 43 2h 7 0.13 i 0.02
28 29 27 :h 5 0.08 i 0.02
30 12 11 :l: 3 0.03 d: 0.01
32 6 6 :i: 3 0.02 :l: 0.01
All 11828 12975 :l: 209 (41.0 i 0.3)

 

 

 

 

 

64

Figure 5.1: The multiplicity distribution.

 

 

 

 

 

?
#10 3
1.75
+
1.5 - + +
a 4*
g 1.25 ~ +
E +
a. 1. "
O
Si 0.75 - +
g +
z 0.5 ‘0
025— ‘.
O 1 1 1 1 1 .10 m .
' O 8 16 24 32
CHARGED PARTICLE MULTIPLICITY, Nd.’

 

 

65

Table 5.3: Lowest moments of the observed inclusive multiplicity distribution.

 

Mean < Nd. > 10.26 :1: 0.15

Dispersion D 5.19 i 0.08

Skewness 5W 0.66 :t 0.03

Kurtosis W 3.27 i 0.08
_ <N' >

Second moment 03 — 71%??- 1.26 :l: 0.01

Third moment 03 = ((7:35;- 1.85 :l: 0.05

Fourth moment 04 = Eggs): 3.09 :l: 0.12

 

 

 

 

Figure 2 shows the energy dependence of < Nd. >. The mean charged multiplicity
calculated from the above expression for fl 2 39 GeV is 10.34 :1: 0.15, so that our

value of < Nd. >= 10.26 i 0.15 is in good agreement with this parametrization.

Figure 3 shows the energy dependence of the lowest normalized multiplicity
moments3 Cg, 2 S i S 5. Our data yielded the results shown in Table 3. As can
be seen, our values for the multiplicity moments smoothly interpolate measurements

made by other experiments at surrounding energies.

Also of interest is the mean multiplicity for non-diffractive proton-proton events.
If we assume that the dominant contributions to the two and four prong multiplicities
are due to a diffractive mechanism, by removing those events with S 4 prongs from

the inclusive multiplicity distribution we obtain a mean multiplicity for an assumed

 

’G. J. Alner et al., CERN-EP/85-62 (1985)

66

Figure 5.2: The energy dependence of the mean charge multiplicity; the solid point

is our measurement.

 

 

 

 

 

1 1 1
1.0 1.5 2.0
Log (V?) -—+

10

 

 

 

67

Figure 5.3: Energy dependence of the (normalized) higher multiplicity moments; the

solid points are from our experiment.

 

 

 

 

Log(V§—>
10‘0 IS 20 25
9 U
8—
7....
6....
111
5... (3
01:13
4~— C U U D
T S Do 0
ca_ 0'
0400000000 1:]
2“ C 1300033.an
3
1_ 0 0000000000 0
2
l l 1 J

 

 

 

 

68

non-difi'ractive mechanism of

< Nch,m_¢;;;,mgve >= 11.59 :1: 0.16,pp —+ X Z 6prongs.

The topological cross section of two and four pronged events was z 6 mb.

We have also measured the charge multiplicity in charm associated events. For

charm events the mean primary multiplicity was

< Nd. >= 12.5 :1: 1.0,pp —+ charm + X.

Charm decays with very short flight times were obscured by the high density of tracks
near the production vertex. A Monte Carlo simulation developed by the author was
used to evaluate contaminations of the primary multiplicity by tracks from such short
lived charm particles. It was found that on average the charge multiplicity included
0.6 :1: 0.2 tracks from obscured charm decays. Including this correction, the mean

primary multiplicity in charm associated events became

< Nd; >—» 11.9 i 1.0.

5.3 Determination of the interaction trigger bias

The interaction trigger bias was determined by comparing the topological cross sec-
tions of ‘beam’ triggered events to those seen in ‘interaction’ triggered events. The
two multiplicity distributions were normalized by requiring that the relative num-

ber of events with twelve or more prongs be the same for both distributions. The

69

interaction trigger efiiciency was taken as the ratio of the two distributions,

Pint(Neh)

€(Nch) = ——Pb¢¢m(N¢h).

Figure 4 shows the two normalized distributions as well as the interaction trigger
eficiency. The interaction trigger was 50% efficient for four pronged events and rose
to 100% for events with more than six prongs. The overall efficiency was (88 :1: 2)%
for Nd. 2 4. Since each charm decay adds several charged tracks, the efficiency was

2 99% for charm associated events.

To summarize, we have described in this chapter our determination of the topo-
logical cross sections in inclusive proton-proton interactions. We have used that in-
formation to study the bias of the interaction trigger used to acquire our charm data
sample. The next two chapters will deal directly with our results on charm hadropro-
duction. Chapter 6 describes the most important measurement made in E743, namely
the cross section for D mesons, and Chapter 7 gives our results for their longitudinal

and transverse momentum distributions.

70

Figure 5.4: Efficiency of our interaction trigger; solid points are the interaction trig-

gered multiplicity distribution, Open points are beam triggered; the curve is the in-

teraction trigger efficiency.

 

 

zooo . . . ' .

OVERALL TRIGGER EFFICIENCY FOR n..24 =- (88:2)2
1750 '

_° 1}

 

 

 

 

u- g —1
.s- - w 2.
g 1250 - l . g
> I I m
L1J l l n
B . ' l I —-—- m

1000 - __L_ +_,_ 1'” l I _100 :2
s —1— ' —r-' ' 5:
D s
E

750 ~ _1_ 1 n
:3 1 _1 ‘<
z . | A

N
500 - l _50
O
25. . 1 , _.
8
t
0 4 6 T2 116 2.0 2:;

Charged Particle Multiplicity. nu.

 

 

 

Chapter 6

DETERMINATION OF THE CHARM INCLUSIVE CROSS SECTION

This chapter describes the most important measurement made in our experi-
ment, the inclusive cross section for D mesons. The results reported here are derived
from the first analyzed 25% of the bubble chamber film, corresponding to an experi-

mental sensitivity of 3.5 :l: 0.1 events per pb. Film scanning and measuring resulted
in forty eight charm candidates, thirty four of which had the C3 topology and fourteen

were V4’s.

6.1 Normalization and systematic uncertainties

Charm decays have topologies C-odd or V-even. Because the C1 and V2 topologies
were heavily contaminated by decays of strange particles, we only considered the C3
and V4 topologies in our cross section determination. By applying geometrical cuts,
twenty five decays including twenty one 03’s and four V4’s were selected from the
initial sample of forty eight charm candidates for the purpose of determining the D

meson cross section.

71

72

The geometrical cuts imposed on the charm sample were designed to ensure
clear definition of decay topologies, to minimize the number of D. and Ac decays in
the D sample, and to remove the residual background of strange decays. The cuts

were

a length cut: the decay length L must be at least 2 mm,

0 angle cuts: no more than one decay track can have qt 2 150 milliradians (<15
is approximately the angle between the track projection onto the film plane

and the beam direction) and the angle between each pair of decay tracks must

exceed 2 milliradians,

a maximum impact parameter cut: for C3’s, 100 pm S Ym 5 2,000 pm and for

V4’s 50 pm 5 Ym S 1,000 pm, and

a minimum impact parameter cut: Ymgn 2 20 pm.

Table 1 shows the statistics for our D meson sample, including the effects of the cuts.

The inclusive cross sections for D mesons were determined according to
N (03) x w(C’3)
s x 312(03) x e’

NLV4) x w(V4)
s x BR(V4) x e,

0(D+/D‘) =

 

 

c(D°/D°) =
where

N E the number of decays observed,

w E a correction factor accounting for losses of events due to bubble chamber accep-

tance and to the geometrical cuts,

73

s E the sensitivity (3.5 :l: 0.1 events per ub),
BR 5 the topological branching ratio, and

e E the scanning efficiency (90 :l: 5)%.

The correction factor 10 was determined for each topology by a Monte Carlo

method (Appendix B) assuming

d’a'

(Imp-(1193. N

 

(1 — Izp|)5ezp(-—1 X pa)

for D meson production, and phase space decay of the D’s into dominant decay modes.
The weights were

w(C3) = 2.5 :1: 0.1,w(V4) = 4.0 i 0.2.

The difference in the weights for the two topologies is due chiefly to the difference in

lifetime between the charged and neutral species.

The topological branching ratios were extracted from SPEAR resultsl",
BR(C3) = 0.43 :l: 0.10, BR(V4) = 0.17 :l: 0.04. Excluding the uncertainty introduced
by the topological branching ratios, the systematic uncertainty in our measurement
due to errors on the correction factor 11:, the experimental sensitivity, and the scanning

efficiency was estimated at 7%. The topological branching ratios are known to 23%.

 

1I. Perussi et al., Phys. Rev. Lett. 31(1977) 1301

’R. H. Schindler et al., Phys. Rev. £24 (1981) 78

74

Table 6.1: The D meson sample and effects of the geometrical cuts.

 

Topology C3 V4
Total number of decays 34 14
‘ Length cut 6 3
Angle cuts 4 1
Ym cut 1 2
Ymgn cut 2 4
Total after cuts 21 4

 

 

 

 

 

6.2 Cross section results

Based on the first analyzed 25% of the charm sample, including twenty one C3 decays

and four V4 decays, the inclusive D meson production cross sections for all my were
a(D+/D-) = 33 :1: 711b,
a(0‘75") = 26331115.
0(D/D) = 59132111).
The errors quoted above are statistical. As previously discussed, systematic

uncertainties were estimated at 7%, excluding contributions from the branching ratios

which are known to 23%.

In the next chapter we will present results for the longitudinal and transverse

momentum distributions for D mesons, from our analysis of the spectrometer infor-

75

mation on topologically identified charm decays.

Chapter 7

D MESON DIFFERENTIAL CROSS SECTIONS

As pointed out in Chapter 2, the production characteristics of charm particles
have been a matter of considerable controversy over the past few years. In this
experiment we have made two independent measurements of the D meson differential
cross sections in am and p}. The first measurement was based on an analysis of the
decay length distributions observed in the bubble chamber. Although indirect, this
technique enabled us to take advantage of the large bubble chamber acceptance. The
second technique, based on the reconstruction of decay products in the spectrometer,
provided a direct measurement of the D meson differential cross sections, although
some charm decays seen in the bubble chamber were lost due to limited spectrometer

acceptance. Results of these two independent measurements were consistent with

each other.

76

77

7.1 Observations based on film measurement

The longitudinal and transverse decay length distributions of topologically tagged
charm decays for the first analyzed 25% of the charm sample are shown in Figures
1 and 2. These distributions were used to obtain an indirect measurement of the

production momentum spectra as follows.

Decay lengths are given by L”: JE, L = 2&5, where t is the proper decay

time. Assuming

4' n
gig ~ (1 - IZFI) 8314—514)

for charm production, the decay length probability distributions were

 

 

dP L; .. —ML d
+1.1. n)""/..5.(1—Ia=r1) cm W") ”"42 .
dP L -b
——f,—L:’—) ~ [05“ ezp(- -bp1)ezp("f ban,

where 1' is the mean life.

The probability distributions were normalized according to

-/L - <L<L (fl 12W — 1

where Lug... was the minimum length cut and Lm was the maximum decay length
allowed by the finite size of the bubble chamber fiducial volume. Since production

vertices were uniformly distributed throughout the fiducial volume, each observed

decay was assigned a weight

 

 

= [exp( —I%nin ) — ezp(-L

"""')]’1

78

where the mean decay length L was directly related to the lifetime of the particle for

a given production n.

Maximum likelihood fits were performed to find the production parameters 11

and b. The likelihood functions were
log[[.(n; L")] = E; log[w;P,-(L”)],

log[£(b; L1)] '2 2&108[w£P£(L1)]1

where the sum extended over all observed decays. Maximization of the likelihood
function with respect to the parameter of interest gives the best fit value for that
parameter, while the standard (10) deviation is given by An = Ina — all where no
is the best fit value and n1 is the value for which %):'—3 = exp(1/2) (similarly for the
parameter b). Fitting the observed transverse decay length distribution (see Figure
4) gave

b = 0.6:8::(GeV/c)‘2.

Because —log[£(n; L“)] had a shallow minimum (see Figure 3), fitting the observed
longitudinal decay length distribution did not give a precise measurement of the

parameter n; the function minimized at n 2 10 and the 20' error excluded 1; S 4.

7.2 Observations based on spectrometer information

Precise measurements of charm production parameters required momentum mea-
surement of the products of topologically identified charm decays. Charm associated

events were tagged in the bubble chamber. Complete tracking and hybridization was

79

Figure 7.1: The longitudinal decay length distribution.

 

GEMS/(0.25611)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.1M 11

0 I 2 J 4 ,5
L I msmnaunou L, (CU

 

 

 

 

 

 

80

Figure 7.2: The transverse decay length distribution.

 

 

[VENUS/(0.0594)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P {ll [ii Ill
. 0.; 0.6 1

0.2 0.8 1.
L.L ousrmaunon L‘L‘c“)

 

 

81

Figure 7.3: Maximum likelihood fit of the longitudinal decay length distribution.

 

 

-Loc uxcuuooomL
m
U a

05
N

61

 
 

60

 
   

 

 

 

58

‘p————————
mF———¢—_-

mb-
.0
C
d
N
-
Q

 

 

82

Figure 7.4: Maximum likelihood fit of the transverse decay length distribution.

 

 

(9L
O b
D to 0
w v

- LOG LlKELlHOOO

‘
\l
U

 

 

 

 

 

 

 

 

83

performed for the event and kinematic fits of the decay products were carried out to

determine the mass and momentum of the parent particle.

Reconstructed charm decays were assigned individual weights to correct for
spectrometer and bubble chamber acceptance. Maximum likelihood fits of the weighted

distributions were used to determine the production parameters 11 and b.

Kinematic fits of decays were categorized by constraint class. Only fits with
at least two constraints (30 and 2C fits) were accepted. When all charged decay
products were momentum analyzed but no constrained fits were found, indicating
that one of the decay products was neutral, unconstrained (OC) calculations were
used to obtain the momentum of the parent. In cases where no constrained fits were
found and one charged decay product was outside the spectrometer acceptance, an

extension of the 0C calculation (‘0‘C’) was used to calculate the parent momentum.

Each decay was assigned a spectrometer weight and a bubble chamber weight,
according to its topology and 211-. The spectrometer acceptance was 2: 100% for
positive 2p, the acceptance depended slightly on the topology. The spectrometer

weight w,” was calculated according to

w 1
are _ e
where e is the spectrometer acceptance.

Given the momentum of the decaying particle, the bubble chamber visibility

weight um, was calculated according to

 

...... = [em 45““) — apt?“ )1“

 

84

where L,,.;fl is the minimum detectable length, Ln.“ is the maximum decay length,
and L the mean decay length uniquely determined by the lifetime and measured

momentum of the parent particle.

The mimimum detectable length ngn was that for which the minimum impact
parameter of the decay exceeded 10 um and the maximum impact parameter exceeded
50 pm. The length Lm was the maximum attainable before the decay vertex either

went out of focus or out of the fiducial volume.

The sample under consideration consisted of forty four events from the first
quarter of our film and included twenty one V2 decays, thirty one C3 decays, nine
V4 decays, and three CS decays. Eliminating decays with K", D,, and Ac fits left
twenty seven reconstructed D meson decays, including one 30 fit, five 20 fits, seven
0C solutions, and seven O‘C solutions (see Chapter 4 for the definition of these fitting

classes). Fitted momenta are listed in Table 1.
Using the method of maximum likelihood, the corrected zp distribution was
fitted to the forms

dN .. dN n.
d—z’: ~ (1 - lzrl) 1192;; ~ (1 — lzrl)

(E is the energy of the charm particle), and the corrected pr distribution was fitted

to the form
(IN 2
Tip—3.— ~ 3314—5”),

to determine the production parameters n, n’, and b.

85

Table 7.1: Reconstructed D meson decays.

 

 

 

Topology Fit 2;: pr W“, W,"
V4 30 -0.03 0.41 1.80 1.01
C3 20 0.07 0.75 1.28 1.00
C3 ZC 0.07 1.39 1.10 1.00
C3 20 0.01 1.34 1.08 1.03
V4 20 0.25 1.68 1.40 1.00
V4 20 0.13 0.82 1.26 1.00
V2 00 -0.05 2.41 1.43 2.53
C3 0C 0.09 2.03 1.18 1.00
C3 OC -0.02 1.53 1.19 1.08
C3 0C 0.00 0.81 1.15 1.03
C3 00 0.09 0.86 1.34 1.00
C3 00 0.02 0.14 1.39 1.00
V4 00 -0.00 0.44 1.68 1.00
C3 0*C -0.11 0.89 1.09 2.70
C3 0*C 0.01 4.64 1.35 1.03
C3 0*C -0.14 0.45 10.41 4.68
V4 0*C -0.02 1.34 2.07 1.01
V4 0*C 0.04 0.24 1.86 1.00
V4 0*C 0.01 0.65 1.96 1.00
CS 0*C 0.14 0.85 1.33 1.00

 

 

 

 

 

 

 

86

7.3 Differential cross section results

Figures 5 through 7 show the longitudinal and transverse momentum distributions
for reconstructed D meson decays with —0.1 S 2F 5 1.0 and 0 5 pr 3 2.5 GeV/c.
Two decays, a V2 and a C3 with my z —0.1 occured in regions of poor spectrometer
acceptance and therefore had relatively high weights. They were excluded from the
fitted sample (fit results were insensitive to their exclusion). One C3 decay with pr =
4.6 GeV / c was also excluded since the probability for that event is very small (< 10“).

The D meson 3p and pr distributions were well described by the parametrization

dN

E ~ (1 - burly," = “-0333;
(IN a.
EE ~ (1 — I317” 91", = 73:35;
dN _
5,; ~ ezP(-bpi),b = 0-66f32§3(Gev/C) ’-

Errors quoted are based on the 10' values found by examination of the likelihood
functions. These results for the parameters n and b consistent with those obtained
from our analysis of decay length distributions. In addition, we observe no events at
lzpl > 0.3, which corresponds to an upper limit of 10 [lb at a 95% confidence level

for D production at large am.

In the next chapter we will present a comparison of our results for the D meson
total and differential cross sections to measurements made by other experiments at
different energies, as well as to predictions made by various theoretical models for

hadronic charm production.

Figure

., , . . . y
1.0: The Feynman x distribution :3?

87

 

 

DN/OX

10

10

10

 

rsvvv

I

Y '1 TTWTI

V

ITYITVI

I

 

nnco N - 11.0 (“.6 -J.6)

NO 01005 A7 X BELOW -0.t5

j
l
l
l
1

N0 EVENTS A7 I ABOVE 0.25

A

 

 

 

- l

 

0.

X

0.2

0.4

 

 

 

Figure 7.6: The invariant distribution Hg.

 

HON/OX)

103

10

10

 

flflCO N - 7.8 (04.5 -J.5)

I rswvvv

F Y V'rVVI I

I

no mm M X BELOW -O.13

 

     
    

 

 

 

no MNYS A! x m 0.25
l
l

 

 

0. 0.2 0.4
X

 

 

 

89

Figure 7.7: The transverse momentum distribution 5:}.
T

 

 

Oil/00’1””

 

 

 

 

 

 

 

 

t0 3
P
b
i. mco s - 0.66 (00.23 -o.:-0)
p
t.

IO 2 :-
;

IO :-
I
b
1.

' E x
t-
b
p-
b

-1

‘0 1 A 1 A

O 2 4 6 8

pruz (col/cw

10

 

 

Chapter 8

COMPARISON OF RESULTS WITH THE FUSION MODEL AND

OTHER MECHANISMS

8.1 The experimentally observed energy dependence of the charm cross

sections

We have seen that from a sample of twenty five observed D meson decays the inclusive

production cross section for D mesons in proton-proton collisions is
0(19m) = 59:32115,

(a(D+ /D") = 33 :l: 7pb, a(D°/Dv) = 26351311”, where the errors are statistical.
Systematic uncertainties were estimated at 7%, excluding the uncertainties introduced

through branching ratiosl", which were known to 23%.

We have also measured the associated charged multiplicity in both charm and

non-charm events. For charm events the mean primary multiplicity was

 

1I. Perussi et al., Phys. Rev. Lett. 32 (1977) 1301

’R. R. Schindler et al., Phys. Rev. _224 (1981) 78

90

91

< Nd. >= 11.9 :1: 1.0, pp —-1 charm + X, while for inclusive proton-proton events
< Nd. >= 10.26:i:0.15(pp —i X). Removing the diffractive component (~ 6 mb) from
the inclusive multiplicity distribution yielded a non-diffractive mean multiplicity of

< Ndhm_d.-H,wgo¢ >= 11.59 :1: 0.16(pp —i X26 prongs) which is rather close to that

observed for charm associated events.

Experiment NA27 by the LEBC-EH3 collaboration at the CERN SPS, using
an identical version of our bubble chamber coupled to the European Hybrid Spec-

trometer, presented the following result3
0(D/D) = 34.4 :1: 4.2pb

(0(D+/D") = 12.5 :1: 1.4pb, c(D°/—D—°) = 21.9 :1: 4.0pb), at center of mass energy
‘5 = 27 GeV (an earlier measurement by experiment NA16‘ , also at the SPS but

at J3 = 26 GeV, gave a'(D+/D‘) = 10.633», d(D°/D°) = 20.4flfa'apb).

Experiments at the CERN ISR (53 GeV 5 J3 S 63GeV)reported very large
charm cross sections“. Measurements of the D meson cross section at the Split Field
Magnet gave values between 0.2 and 5.0 mb, with a flat 2p distribution. The deter-
mination of the cross section in these experiments depended critically on estimates
of the acceptance of charm decay products in the apparatus, and on branching ratios

into exclusive decay channels. A linear interpolation between the NA27 measurement

 

'LEBC-EHS Collaboration, Berkeley Conf. Preprint, presented by M. E. Miehalon and M. Iori
‘M. Aguilar-Benita et al., Phys. Lett. 1358 (1984) 237

'S. L. Olsen, AIP Conference Proceedings No. 85 (1981) 1

92

and the ISR values would predict a dramatic growth of the cross section

0D‘5(J; = 39GeV) z 10

 

over the small energy range from J3 = 27 GeV to 39 GeV.

In contrast, taken together with the NA27 results our measurement of the D

meson cross sections gives an energy dependence of

”DE(\/5 = 38G3V) = 1.1-[+0.0
aD-D-(JE = 27GeV) -°"

 

Our analysis of the spectrometer information showed that the longitudinal mo-

mentum distribution of produced D mesons is well fitted by the parametrization

dN ..
E ~ (1 — le|) in = 1117132:

and that the transverse momentum distribution is well fitted by

dN _
a N €3P(—5Pi~)ib = 0-66:3233(GeV/C) 2
(the LEBC-EH8 collaboration also fitted their observed differential cross sections to

the above forms and reported n = 4.8 :l: 0.7, b = 1.21 :l: 0.14(GeV/c)").

These results show that the charm hadroproduction cross section is increas-
ing relatively slowly with center of mass energy, and that charm production occurs
predominantly in the central 2p region. In addition, when compared to the NA27
measurements, our results indicate that the 2p distribution becomes more central

with increasing energy.

93

8.2 Predictions by the Fusion model and by other mechanisms

A generally accepted model for hadronic production of charm, the Fusion model (FM),
can reproduce most aspects of our data. As discussed in Chapter 2, the FM makes
use of perturbative QCD and a phenomenological picture of the proton structure as
well as the hadronization of quarks to predict charm cross sections and their energy
dependence. Prediction of the absolute cross section is sensitive to input parameters
such as the mass of the charm quark and the QCD scale parameter A, as well as to the
parametrization used for the quark and gluon structure functions. Since the structure
functions are evaluated at Q2 = 47112, variations in the charm quark mass translate
into changes in the longitudinal momentum fraction of the quarks and gluons in the

collision.

Figure 1 shows recent FM predictions“ for the total hadronic charm production
cross section, assuming extreme values 1.2 GeV/c2 3 inc S 1.8 GleV/c2 for the charm
quark mass (the parametrization by Duke and Owens" was used with A = 200 MeV
for the QCD scale parameter). These predictions refer to the cross section for pro-
ducing either a charm quark or antiquark (not summed); as no experimental evidence

exists for correlations between the pair produced charm hadrons, and as the major

contribution to the hadronic charm production cross section at our energy consists of

 

‘R. K. Em. and c. Quigg, Fermilab FN-445 (1987)

' 7D. W. Duke and J. F. Owens, Phys. Rev. E (1984) 49

94

D mesons, the FM would predict
O'FM(D/-fi) 2 40pb,mc = 1.2GeV/cz,

at J3 = 39 GeV “HAD/D.) 2 611b, me = 1.8 GeV/c2). This prediction is smaller
than our observed cross section by a factor K, K 2 1.5 for me = 1.2 GeV/c2 (K g: 10

for m.= = 1.8 GeV/c3). K factors on the order of 2 are not unexpected in calculations

where only first order QCD diagrams are included.

The FM prediction for the energy dependence of the charm cross section is not
expected to be affected by the neglect of contributions from higher order diagrams.

An energy dependence of

O’FM(\/; = 39GeV)
UFM(J3 = 27GeV)

 

2 2,mc = 1.2GeV/c',(2 3,171.; = 1.8GeV/c’)

was predicted for charm production in proton-nucleon collisions. Our measurement

of the inclusive D meson cross section favors light charm quark masses.

In addition, the FM predicted predominantly central production of D mesons in
hadron collisions and, with reasonable assumptions for the mean intrinsic transverse
momentum < 1:1 > of the constituents of the proton, the experimentally observed
transverse momentum distributions were reproducible. Figures 2 and 3 show the
predictions by Ellis and Quigg, superposed on our observed D meson Feynman x and

transverse momentum distributions.

The Excitation model (EM) was proposed as an additional contribution to
charm hadroproduction as an explanation for the dramatic rise in the charm cross

section and the forward charm z 15' distribution inferred from ISR measurements. Sim-

95

Figure 5.1: Fusion model predictions of the integrated charm hadronic production

cross section.

 

 

 

 

 

3 10 3
1 :uppca CUGM: uc - 1.2 CEV/C-oz
v $1.0ch cum uc - i.s CDI/C-ol
b - .
* ISR
,0 2 :- E7l43 __ ..
I NR 2? ,_ .— ——f' " "
L I
‘0 ’ ’ ’ d 4' ’
C
P
' r
I
1.
‘o-‘ A _L A L
20 30 so so so 70
Pa WIECRAKD CROSS SECI’ION
J's‘(CeV)

 

 

 

96

Figure 2: Fusion mudei predictions of the (iii erentiai Charm hadronic production

(I)

. v . .
cross section 415: data pomts are from our experiment.

 

la

 

 

 

as 10
§ {501.10 CURVE - FM PREDICTION
a .oAsseo CURVE - OUR FIT
102 -
:
IO 1..
:

 

 

 

 

 

 

 

 

97

Figure 8.3: Fusion model predictions of the differential charm hadronic production

cross section 5:}; data points are from our experiment.
7'

 

 

 
  

 

 

 

 

 

 

 

3
A ‘0 a a
'2' E SOLID CURVE - FM PREDICTION
3’: ~ DASHED CURVE - OUR FIT
g .
a b
2
to L:-
C
10 :-
: \
—~.
_ \
\
\
\\
t :- “x
s
\
I- \
b \
\
\
i- \
\\
10" ‘ 4 ‘ \\
o 2 s 6 s‘ 10
Piuz (GEN/C)"2

 

 

98

ilarly to the FM, the EM was a perturbative QCD treatment of hard scattering pro-
cesses between hadron constituents. In the EM, a charm quark from the target sea
hadronizes into a physical charm particle after colliding with a quark or gluon from
the beam. As no measurement has been made of the charm sea distribution, this

distribution was evolved from zero at low momentum transfers.

The EM calculations for the charm cross section were strongly dependent on
the sea charm structure function and EM predictions had correspondingly large un-
certainties. An early calculation gave8 as“ m 10 X may, while later estimates” gave

03" z 2 x O'Fu, at J3 = 39 GeV.

As both the FM and the EM are hard scattering mechanisms, these two models
predict similar energy dependence for the cross section. However the EM longitudinal
momentum distribution of charm hadrons is significantly different from FM predic-
tions. The struck (excited) charm quark hadronizes by recombining with quarks from
the sea and the Feynman x distribution of hadrons originating from struck charm
quarks should be central. In addition, a large forward component is expected from
hadrons originating from the spectator charm quarks since they recombine with va-'

lence quarks from the beam or target”.

Our measured D meson cross section is lower than the FM prediction by a factor

of between 1.5 and 10 for various charm quark mass choices, thus some room for an

 

'B. L. Combridge, Nucl. Phys. B151 (1979) 429
’V. Barger, F. Halsen, and W. Y. Keung, Madison preprint DOE-ER/00881-215 (1981)

10R. Odorico, AIP Conference Proceedings No. 85 (1981) 100

99

EM contribution to charm hadronic production at J3 = 39 GeV is available. How-
ever, our observation of predominantly central D meson production contradicts the
expectations of the EM for forward production of D mesons via specific recombination

mechanisms.

The Intrinsic charm model (ICM) was proposed as an alternative to hard scat-
tering mechanisms, to explain forward charm production with large cross sections11
observed at the ISR. The ICM postulates a non negligible uuch component of the
proton wavefunction. Due to the large mass of the charm quark the intrinsic c2 pair
carries a large fraction of the proton momentum and at high energies only a small
momentum transfer is required to excite an intrinsic charm quark into a fast moving

charm hadron in diffractive scattering.

The charm total cross section was expected to be large and to come almost
entirely from diffraction, cm“ x 500ub at J3 = 63 GeV. A linear interpolation
between the above prediction and the N A27 measurement at J3 = 27 GeV would

predict a large charm cross section at our energy, Grands/3 = 39GeV) ~ 200pb

corresponding to a rise in the cross section of

”ICM(\/; = 39G'eV) ~

10
VIOLA“; = 27GeV)

 

with increasing center of mass energy.

The ICM values are inconsistent not only with the observed energy dependence

of charm production but also with the predominantly central longitudinal momentum

 

11S. J. Brodsky, P. Boyer, C. Peterson, and N. Sakai, Phys. Lett. _93_B (1980) 451

100

distribution of D mesons in our study.

Chapter 9

CONCLUSIONS

We have presented in this thesis the results of Fermilab experiment E743 on
hadronic production of D mesons. By directly observing charm decay vertices in the
high resolution, rapid cycling hydrogen bubble chamber LEBC and by reconstructing
charm associated events in the MPS spectrometer, we have made a relatively unbi-
ased measurement of the inclusive D meson cross section in 800 GeV proton-proton
collisions,

”(D/D)‘ — 59:15!“
(a(D+/D" )_ — 33 :l: 7pb, d(D°/D )— - 26:13pb).

We have also measured the longitudinal and transverse momentum distributions of

observed D meson decays. The :1: F distribution was well parametrized by

(UV
2; ~ (1 - IZFD": 71- - 11 0:33:

and the pr distribution was well parametrized by

:7 “wt was: 066i8:§3(GeV/c)"-

101

102

When compared with measurements made at lower energies, our results imply

a slowly rising D meson cross section with center of mass energy,

0DD(\/; = 3BGCV) = 1.7+0.6.
0D5(J3 = 27GeV) ’0'5

 

Furthermore we observe no events at Izpl > 0.3, which corresponds to an upper limit

of 10 pb at a 95% confidence level for D production at large asp.

Also measured were the associated charged multiplicity in both charm and non-
charm events. For charm events the mean primary multiplicity was
< Nd. >= 11.9 :1: 1.0, pp -i charm + X, while for inclusive proton-proton events

< Nd, >= 10.26 :t 0.15, < Nch‘m_d§ff,¢¢fiu >= 11.59 :t 0.16, (2 6 prongs).

The weak energy dependence of the total cross section and the predominantly
central character of D meson production are in sharp contrast with results from a
number of experiments at the CERN ISR which reported copious charm production

in the forward region”, can", z 1mb, 2% ~ flat.

We have shown that the flavor excitation model and the intrinsic charm model,
invoked at the time of the reports from the ISR, are unnecessary to explain our results
on the production dynamics and on the energy dependence of the cross section for D
mesons. There is now a consensus that although the intrinsic charm model cannot

be eliminated, contributions to charm production by that mechanism are likely to be

smalls.

 

1S. L. Olsen, AIP Conference Proceedings No. 85 (1981) 1
2D. DiBitonto, AIP Conference Proceedings No. 85 (1981) 26

’J. L. Ritchie, Procs. of the 1984 Summer Study, Snowmass, Colorado (1984) 237

103

In conclusion, we have made a precise measurement of the hadronic charm
production cross section at J3 = 39 GeV. When compared to measurements made
at lower energies, our results indicate a relatively weak energy dependence for the
charm cross section. Along with our observation of a predominantly central longitu-
dinal production momentum distribution for charm, the observed energy dependence
eliminated the flavor excitation model and the intrinsic charm model for charm pro-
duction at J3 S 39 GeV. The fact that the non-diffractive component of the mean
inclusive multiplicity was approximately the same as that observed for charm asso-
ciated events provides additional evidence that charm production is non-diffractive,
in contrast with the above mentioned models. The more generally accepted fusion

model, on the other hand, can reproduce most aspects of our data.

Appendix A

THE IMPACT PARAMETER OF DECAY TRACKS

The impact parameter of a decay track is defined as Y = L sin0 where L is
the decay length and 0 is the angle of the decay track relative to the direction of its
parent. We show here that, when the Q value of the decay is large and the Lorentz
boost from the rest frame of the parent to the laboratory frame is also large, the

impact parameter of decay tracks is independent of the parent momentum.

Let q" and q .1. be the components of the daughter momenta along and normal

to the parent line of flight in the laboratory frame,

q; = q' sin 0‘,

q” = 7(9‘ cos 0‘ + AM" + m“),

where q‘ is the daughter momentum is the parent rest frame and m is the daughter
mass (the superscript * denotes the parent rest frame). The decay angle in the

laboratory frame is

O ' 0.
sin0=£= q 8m

9 Jq" sin2 0' + 73(q‘ cos 0‘ + fiJq—‘TWP .

104

 

105
In the limit of large Q values (q‘ > m),

sin 0‘
J13(cos 0‘ + 6)2 + sin2 0‘ ,

sin0 2

and in the limit of a large Lorentz boost from the parent rest frame to the laboratory

(321,7>1).

, 0~ sind‘ -ltan0;
8m _ 7(1 +cosd‘) — '1 2 °

 

The decay angle in the laboratory frame decreases as i. The decay length is

L = flier where 1' is the proper decay time, so that the impact parameter is

0.

independent of the parent momentum.
For an isotropic angular distribution of decay products in the parent rest frame

(% = constant), the above approximate expression for Y can be integrated and yields

a mean impact parameter of < Y >2 c1'.

Appendix B

SIMULATING CHARM DECAYS

We describe here an algorithm developed by the author to simulate charm

decays in Monte Carlo calculations used throughout this thesis.

Since flavor is conserved in the strong interaction charm is hadronically pro-
duced in pairs. There has been no experimental indication of momentum or angular
correlations between the pair produced charmed hadrons. Open charm, i.e. hadrons
with nonzero charm quantum number, decays weakly. Due to the vastly different
time scales involved, the production and decay of charm particles can be treated as

independent processes.

Figure 1(a) shows the proper decay time distribution for simulated D+ -—i
K‘11'+1r+ events, and Figure 1(b) shows the D meson transverse momentum dis-

tribution for these events. We have used the inclusive distributions

do da' da'

-— ~ — n — ~ -6P, — N _3/7

hp (1 lel) 9 JP; C T) dt 8 3

to simulate hadronic charm production. Also shown in Figures 1(c) and 1(d) are

the laboratory momentum distribution for these D mesons and the decay length

106

107

distribution.

Assuming that the matrix elements for charm decays are constants, decay mo-
menta are governed solely by phase space probabilities. We have used a cascade
decay model in our simulation of charm decays: a parent particle disintegrates into a
series of two body systems which in turn decay into the daughters of the final state.
The phase space probability dP,,/dpn for the final state momentum configuration

(pmpnd, ..., p1) was calculated according to the recursive formula

 

dPa «”103 i/(8 + m3 - Zen/3 — m2 — mg)2 — 4m§mg
Z;_ 33 8+mg—2e3J3 ’

1% _ 2W1): X (dPn_1
dpn — 8,. dPn—l

 

)

where n is the number of final state particles and J3 is the available energy. Figure
2(a) shows the distribution of daughter momenta for simulated D"' -i K '1r'l'1r'l'
decays and Figure 2(b) shows the daughter transverse momentum distribution, in the
rest frame of the parent particle. Figures 2(c) and 2(d) show the angular distributions
(IN/dd) and dN/d(cos0) of the decay products in the rest frame of the parent. When
Lorentz boosted into the laboratory frame, these daughter momenta and angles give
rise to the impact parameter distribution of Figure 1(e), and the distribution in Figure

1(f) of decay angles with respect to the line of flight of the parent.

108

Figure 8.1: Simulated D‘ ... K‘x":' decays. part I:

(a)d.V/d(ct(mm)). (b)d.\'/d(p'°}((Gel',-'c)"')), (c)d.'V/d(p¢..,(Gel'/c)) .

(d)d.V/dl.(mm), (e)d.\°_."d(sin0), (f)d.V,’di'(mm).

 

 

 

 

 

 

 

l
la) " "
“E- .Wlmlllllll "
g‘ ”1,“,
s F—
.....E- nk:lJ|

 

 

 

‘1-

 

; ...... ml,” 11”“ iii“
L

 

 

 

 

" (e)

 

A
.0

 

 

 

 

 

 

 

 

 

 

 

 

O
o
'b

 

 

109

Figure B.2: Simulated D’ -+ A" :‘x‘ decays. part 2:

(a)d.\',’dq(Cel'/c), (b)d.\°/d(q§((0el°/c)3)), (c)d.~V/d(cosfl). (d)d.\'/d¢}(radians).

 

 

 

 

 

 

'1
'5. NH
5 11“ l
3 H
E“
F1
E1
"1‘
‘ (a) “

 

, "' 1‘

 

"l

l

.. it’ll: '

l

l
llllilllllllluml”l

 

 

 

 

.0 (C) .0

 

 

 

" (b) “

 

i u 1
ill, ”111"1'I,“qu”  

 

 

I (d) 8

 

 

 

 

Appendix C

THE O‘C CALCULATION

We describe here the O‘C calculation, a procedure developed to obtain kinematic

solutions to charm decays‘.

Under the assumption that all of the decay products are charged, constrained
kinematic fits were attempted in order to determine the momentum of the parent.
When all charged decay products were reconstructed in the spectrometer but no
constrained fits were found, indicating that one of the decay products was neutral,
unconstrained (0C) calculations were used to obtain the momentum of the parent.
In cases where no constrained fits were found and one charged decay product was
outside the spectrometer acceptance, the 0‘C calculation was used to obtain the

parent momentum.
The O‘C calculation treats the case
D —’ (Erect) + Xms's

where the sum extends over all reconstructed charged tracks and Xmg, denotes a

 

1C. Bromberg and A. Nguyen, E743 internal note

110

111

system of particles with an invariant mass mmg, = 500 MeV. The parent momentum

pp was calculated using

4E3ech) — [‘4 =
4(E3ee — pagan)

p3) _ pp flaps-cc,“
2
E pace."

rec -

0

 

 

+

where

 

u a Jmi. + m2... — mi...

The subscript M denotes the component of the momentum along the direction of flight

of the parent.

In general there were two solutions to the above quadratic equation in pp, a
fast (high laboratory momentum) and a slow (low laboratory momentum) solution.
Since these events have lost at least one low momentum decay track the phase space
probability of the two solutions heavily favors the slow solution, i.e. if the parent had
the high momentum of the fast solution all charged decay products would have been
within the spectrometer acceptance and would have been reconstructed. Therefore

only the slow solution was used.

Corrections for the slow solution were evaluated by Monte Carlo. D meson
decays were generated and the slow O‘C solution was used to calculate 2',» for de-
cays with one charged daughter outside the spectrometer acceptance. Table 1 shows
< 215' — a} > where 2p is the actual Feynman x of the parent. As can be seen the
corrections were small (< 0.1) over the 2;» range where charged decay tracks were

lost outside the spectrometer.

In order to test the O‘C procedure, charm decays were generated with the al-

112

Table 0.1: Corrections for the slow O‘C solution; R denotes a reconstructed charged

track, L denotes a charged track lost outside the spectrometer acceptance, and O

denotes one or more missing neutrals.

 

 

 

 

 

 

Topology z}.- < 3p — z}.- >

C3 —> RRLO -0.25 0.09 i 0.04
-0.15 0.05 i 0.03

-0.05 0.04 :l: 0.02

0.05 0.04 :l: 0.03

V4 -b RRRLO -0.25 0.09 :t 0.04
-0.15 0.04 :l: 0.02

-0.05 0.02 i 0.02

0.05 0.02 :l: 0.02

 

gorithm described in Appendix A. In decays with missing neutrals and one missing
charged daughter the slow O‘C solution for the parent momentum was used to calcu-

late z}; the a} distribution was corrected using the results in Table 1. The corrected

distribution reproduced well the generated distribution.