ANEiPROTON-PROTON INTERACTIONS FROM 1.51 TO 2.90 GeVIc Thesis for the Degree of PM. MCHSGAN STATE umvmsm DGNALD LESTER PARKER ’ 19m """"" This is to certify that the thesis entitled ANTI PROTON- PROTON INTERACTIONS FROM 1.5] TO 2.90 GeV/c presented by Donald Lester Parker has been accepted towards fulfillment of the requirements for Ph-D- degree in _Ebl$.1£§.__' W Major professor Date ”0-1)“ ”51 97! 0-7839 ABSTRACT ANTIPROTON-PROTON INTERACTIONS FROM 1.51 TO 2.90 GeV/c By Donald Lester Parker In a bubble chamber experiment cross sections have been obtained for zero, two, four, six and eight prong topologies, and the reaction cross sections and resonance production cross sections within each topology for nine antiproton momenta from l.5l to 2.90 GeV/c. The extrapolation of small angle elastic scattering to t = 0 is discussed and compared with the results of other experiments. The differential cross sections are fitted to an adaptation of the Frahn-Venter optical model and also compared to Regge pole model predictions. All other channels are investigated with particular emphasis given to discovering the origin of the structure seen in the total cross section for anti- proton-proton scattering. The structure cannot be explained as thres- hold effects, and viewed as direct channel effects, some channels can be ruled out as the origin of the structure. Pion multiplicity in the all-pionic annihilations has also been investigated and comparisons of the predictions of a statistical model and a multiperipheral model are made. ANTIPROTON-PROTON INTERACTIONS FROM 1.51 TO 2.90 GeV/C By Donald Lester Parker A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics l97l ACKNOWLEDGMENTS I wish to express my appreciation to Professor Gerald A. Smith for his patience and guidance throughout the analysis of this experiment. Many thanks are due also to Professor R. J. Sprafka for all his assist- ance in the data reduction and analysis and for continually reminding me that physics is an experimental science; and to Dr. Benedict Y. Oh for tolerating the many questions I asked him and for many helpful suggest- ions during the data analysis; and to Mr. Paul S. Eastman for his cooperation in the early stages of the data reduction and analysis. I wish also to acknowledge the programming efforts of Mr. Sherwood K. Haynes II, who has shown me many times that computers do only what you tell them to do. I am grateful to our scanning and measuring staff for all their efforts, particularly to Mr. George Sionakides for many hours of assistance in ionization scanning. This research was supported in part by the National Science Foundation. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ...................... 11 LIST OF TABLES ...................... v LIST OF FIGURES ...................... vi Chapter I. INTRODUCTION ................... l 2. ELASTIC SCATTERING ................ 4 2.l Scanning, Measuring, and Event Acceptance 4 2.2 Corrections and Results . I .......... 5 2.3 Differential Cross Sections ......... 18 2.4 Conclusions ................. 37 3. TOPOLOGICAL CROSS SECTIONS ............ 39 4. REACTION CROSS SECTIONS .............. 47 4.l Experimental Methods ............. 47 4.2 Two Prong Cross Sections ........... 48 4.3 Four Prong Cross Sections .......... 54 4.4 Six Prong Cross Sections ........... 63 5. RESONANCE PRODUCTION IN THE MULTIPION ANNIHILATIONS ................... 70 5.1 Experimental Methods ............. 70 5.2 Three Pion Final States ........... 71 5.3 Four Pion Final States ............ 7T Chapter Page 5.4 Five Pion Final States ............ 77 5.5 Six and Seven Pion Final States ....... 86 6. PION MULTIPLICITY IN THE ALL-PIONIC ANNIHILATIONS ................... 88 7. SUMMARY AND CONCLUSIONS .............. 93 LIST OF REFERENCES .................... 97 iv Table 10. 11. 12. 13. LIST OF TABLES Page Results of Fits to do/dt = (do/dt)t=0exp(At) ..... 1] Differential cross sections: do/dn* (mb/sr) .................... 24 Differential cross sections: do/dt [mb'(GeV/c)’2] ................. 27 Optical Model Parameters for Fits Described in Text ......................... 33 Topological Cross Sections in mb ........... 40 Results of Least-Squares Fits to Subtracted Cross Sections Described in Text. "Bkgnd" is the polynomial background term in brackets in equation (5) ...... 46 Reaction Cross Sections (mb) in the Two Prong Topology ....................... 50 Reaction Cross Sections (mb) in the Four Prong Topology ....................... 57 Results of Least Squares Fit to the Subtracted Cross Section [oT(pp) - o(pion prod.)] ........ 64 Reaction Cross Sections (mb) in the Six Prong Topology ....................... 67 Resonance Production Cross Sections in mb for the n+n'n° Channel .................... 72 Resonance Production Cross Sections in mb for the 2n+2n' Channel .................... 78 Resonance Production Cross Sections in mb for the 2n+2n'n° Channel ................... 83 LIST OF FIGURES Figure Page 1. The t-dependence of azimuthal scanning and measuring corrections ...................... 7 2. The low-t data with least-squares fits to do/dt = (do/dt) =0exp(At) in the region 0.03 5 jtl 5 0.20 (GeV/c)2. Arrows indicate the appropriate scale to be read for each momentum . . . . 9 3. Slope parameter from an exponential fit to low-t differential cross sections. Other experiments are: (1) 1.24, 1.32, 1.54, and 1.62 GeV/c, ref. 11; (2; 2.7 GeV/c, ref. 12; (3) 3.3 GeV/c, ref. 13; 4 3.6 GeV/c, ref. 14; (5) 4.0 GeV/c, ref. 15; (6) 5.7 GeV/c, ref. 16; (7) 6.94 GeV/c, ref. 17; (8) 7.2, 8.9, 11.8, and 12.0 GeV/c, ref. 18; and 9) 8.0 and 16.0 GeV/c, ref. 19 ............ 12 4. Momentum dependence of the pp elastic scattering cross section. Other experiments include some of those in figure 3 caption and: (l) 1.14, 1.35, 1.49, 1.64, and 1.78 GeV/c, ref. 20; (2) 1.61 GeV/c, ref. 21; (3) 1.7, 2.0 and 2.8 GeV/c, ref. 22; and (4) 6.9 GeV/c, ref. 23 ............ 14 5. Momentum dependence of diffraction peak slopes in two phenomeno1ogica1 mode1s. ............. 19 6. Momentum dependence of the quantity (1+a2). The solid curve is a dispersion theory prediction ..... 21 7. Differential cross sections, do/d9*, for pp elastic scatterin in the c.m. for (a) 1.51 - 1.95 GeV/c and (b) 2.15 - 2.90 GeV/c. The solid curves represent the best fits obtained with the five parameter Frahn-Venter optical model ....... 30 8. Differential cross sections, do/dt, for pp elastic scattering for (a) 1.51 - 1.95 GeV/c and (b) 2.15 - 2.90 GeV/c. The curves are predictions of a three pole Regge model of Chiu, Chu, and Wang . . 34 vi Figure 10. 11. 12. 13. 14. 15. Page To ological cross sections. Other experiments are: (I) 1.11, 1.33, 1.52 GeV/c, ref. 3; (2) 1.23, 1.27, 1.32, 1.37, 1.43, 1.49, 1.54, and 1.63 GeV/c, ref. 2; (3) 1.2 GeV/c, ref. 28; (4) 1.61 GeV/c, ref. 21; (5) 3.0 and 3.6 GeV/c, ref. 30; (6) 3.28 and 3.66 GeV/c, ref. 35; (7) 3.6 GeV/c, ref. 31; (8) 5.7 GeV/c, refs. 32, 33 and 37; (9) 6.9 GeV/c, ref. 34; (10) 6.94 GeV/c, refs. 35 and 36 ............ 41 Cross sections for the two prong topology. Solid curves in (a) are prediction of a multiperipheral model (see Chapter 6). Other experiments are: (1 1.61 GeV/c, ref. 21; (2) 2.2 GeV/c, ref. 39; 3 2.7 GeV/c, ref. 40; (4) 3.28 and 6.94 GeV/c, ref. 35; (5) 3.6 GeV/c, ref. 41; and (6) 5.7 GeV/c, ref. 32 ........................ 51 Cross sections for the four prong topology. Solid (dashed) curves are predictions of a multiperi- pheral (statistical) model (see Chapter 6). Other experiments are: (1) 1.11, 1.33, and 1.52 GeV/c, ref. 3; (2) 1.2 GeV/c, refs. 28 and 47; (3) 1.61 GeV/c, ref. 21; (4) 1.62, 1.76, 1.82, 1.90, 1.94 and 2.2 GeV/c, ref. 46; (5) 2.2 GeV/c, ref. 39; (6) 2.4 GeV/c, ref. 42; (7) 2.5 GeV/c, ref. 43; (8) 2.7 and 2.9 GeV/c, ref. 44; (9)3.28, 3.66 and 6.94 GeV/c, ref. 35; (10) 3.6 GeV/c, ref. 41; (11) 5.7 GeV/c, refs. 32, 33, and 45. ........... 58 Results of fit to the_subtracted cross section, [oT(Dp) - 0(NNn) - o(fipn+n‘)] ........... 65 Cross sections for 3n+3n' and 3n+3n-n° channels. Solid (dashed) curves are predictions of a multiperipheral (statistical) model (see Chapter 6). Other experiments are: (1) 1.61 GeV/c, ref. 21; (2) 3.0 GeV/c, ref. 30; (3) 3.28 GeV/c, ref. 35; 4) 3.6 GeV/c, ref. 31; and (5) 5.7 GeV/c, refs. 32 and 37 .................... 68 Resonance production cross sections in the n+n-no channel. Other experimental data from reference 50 .......................... 73 Typical invariant mass distributions in the Znizf'channel at 1.80 GeV/c with maximum likelihood fits described in text ................ 75 vii Figure 16. 17. 18. 19. 20. Resonance production cross sections in the 2fl+2n' channel. Other experiments are: (1) 1.2 GeV/c, ref. 28; (2) 2.3 GeV/c, ref. 50; and (3) 2.5 GeV/c, ref. 43 ............... Typical invariant mass distributions in the 2n+2n-n° channel at 1.80 GeV/c with maximum likelihood fits described in text ......... Resonance production cross sections in the 2a+2n’n° channel. Other experiments are (1) 1.11, 1.33, and 1.52 GeV/c, ref. 3; (2) 1.2 GeV/c, ref. 28; (3) 2.3 GeV/c, ref. 50; and (4) 2.5 GeV/c, ref. 43 ................... Cross sections as a function of the number of pions, and the averages N , number of pions independent of charge; N , number of charged pions, and Nneut , number of neutral pions. Solid curve is a prediction of the statistical model discussed in text for the average Nch . . . . Summary of results of subtracted cross section fits. The quantity 0R (see Chapter 3) gives the amount of total cross section bumps which may be accounted for in the indicated channel viii Page 79 81 84 90 94 CHAPTER 1 INTRODUCTION The study of antiproton-proton interactions is interesting for several reasons. The precision measurements of the total cross sections ‘ in 1967 for antiprotons on protons and deuterons by Abrams gt_al. revealed structure in both total cross sections (see figure 12). This discovery is not altogether surprising since other total cross sections show structure as functions of energy in regions where known excited states in the direct channel occur. An example of this occurs in n+p scattering when the total center of mass energy passes through the region of the known strong resonance A++(1236 MeV). In this case, the total cross section peaks strongly, being enhanced by the direct channel formation of the A++ resonant state. Thus one possible inter- pretation of the structure seen in antiproton-proton (pp) scattering is direct channel formation of an excited mesonic state. Another inter- pretation is that some final state is rising sharply from its energy threshold and causing an inflection in the total cross section. Although only two "bumps" are seen in the pp total cross section at 5 momenta of about 1.3 and 1.8 GeV/c, the experimenters in reference 1 were able to determine the isospin components of the antiproton- nucleon scattering by combining the measurements of antiprotons on protons and deuterons. They then find three "bumps" which, assuming Breit-Nigner descriptions, are referred to as th8'n]*(2190, 85), the 2 "1*(2350, 140) and the "0*(2375, 190), where the subscript gives the isospin and (E0, r) are the masses and widths in MeV. Several bubble chamber studies have been made to determine the origin of these 2, attempting to explain the n1*(2190) en- structures. One such study hancement as a threshold effect from single pion production without anni- hilation concluded that an excitation curve inconsistent with the pion production cross section data would be required to do so. A formation experiment3 has reported a narrow enhancement in the pp + p°p°n° final state with a mass of 2190 MeV and 20 MeV 5r$80 MeV which they identify with the "1*(2190). Studies of the antiproton-proton backward elastic scattering”"6 in the c.m. system, while finding 180° structure consistent with one or more direct channel resonances in the 1 - 2 GeV/c momentum range, have been unable to make unique connections with any of the en- hancements seen in the total cross section, especially since the struct- ure is consistent also with diffraction model calculations. A search for the structure seen in the total cross section made in the pp charge exchange scattering from 1 - 3 GeV/c7 yielded no evidence to support such enhancements in that channel. In this thesis a comprehensive study of topological, reaction and resonance production cross sections with particular regard to the structure in the total cross section is presented. This experiment is based on an exposure of 150,000 pictures in the Brookhaven National Laboratory 31-inch hydrogen bubble chamber to antiprotons of incident momenta 1.51, 1.65, 1.80, and 1.95 GeV/c (total c.m. energy 2257, 2308, 2360, and 2413 MeV) and an exposure or 126,000 DTCtUlCS in the Argonne National Laboratory 30-inch hydrogen tubble chamber at antiproton momen- ta 2.15, 2.45, 2.60, 2.75, anr ‘.9O GeV/c (c.m. energy 2482, 2586,2636, 2684, and 2736 MeV). A study of the 1.51 - 1.95 GeV/c film and a 5d exposure in the same energy range lead to a published report8 of a rela- tively narrow (r 5 60 MeV) I=1 enhancement centered at 2360 i 25 MeV in the final state K*Knn. While this enhancement agrees with the mass and width of the U meson reported in the n'p missing mass experimentsg’lo, the fact that the width is inconsistent with that of the I=1 total cross section enhancement rules out a connection with the n]*(2350) unless there are several overlapping structures giving rise to the broad en- hancement in the total cross section. As a by-product of a study of inelastic channels in the two prong topology, the pp elastic scattering channel has been studied. Without a careful study of backward elastic scattering one would not expect to find any connection between elastic scattering and the structures in the total cross section. The extreme backward hemisphere has been studied by other experiments mentioned above. However, independent of direct channel considerations this momentum range has been found to be interest- ing also from the point of view of describing the entire elastic differ- ential cross section distributions in terms of models previously pre- sented in the literature. As will be shown, the model comparisons appear to support the idea that this intermediate momentum range (1.5 - 2.9 GeV/c) represents a transition from the low-energy optical scat- tering description to the high energy Regge pole description. CHAPTER 2 ELASTIC SCATTERING 2.l Scanning, Measuring, and Event Acceptance The 1.51 - 1.95 GeV/c film was scanned for all two prong events and about one-third of the film was rescanned. The 2.15 - 2.90 GeV/c film was completely twice-scanned for two prongs. In each case single scan efficiencies exceeded 93%. A11 cross sections reported in this thesis have been obtained by normalizing total interaction counts to the total cross section data of reference 1. Measurements of 60,000 and 35,000 two prong events in the 1.51 - 1.95 GeV/c film and the 2.15 — 2.90 GeV/c film, respectively, have been completed. These events were fitted* to the following hypotheses: 5p +1319. (1a) + 6w. (Na) + pnn+, (1c) + pfin", (1d) + n+n', (1e) and + “+1.13, (1f) plus all of the corresponding zero-constraint, or "no fit" hypotheses. An event was considered to be an elastic scatter if the four-constraint *The geometric reconstruction and kinematic fitting were done with the standard Lawrence Radiation Laboratory programs, TVGP and SQUAW. 5 hypothesis (la) had a X2 5 50.0. Events which failed the kinematic fits after the first measurement were remeasured. Examination of missing mass, miSsing momentum, and coplanarity distributions indicated that the final sample has negligible contamination from other final states. Further study of the events with X2 > 50.0 for hypothesis (la) and fitting none of the other hypotheses (1b) - (1f) led to the inclusion of about five percent more events in the elastic scattering sample, resulting in a final sample of 27,000 events from the 1.51 - 1.95 GeV/c film and 16,000 events from the 2.15 - 2.90 GeV/c film. 2.2 Corrections and Results In order to minimize the rather severe loss which occurs at low momentum transfers due to the difficulty in finding the short recoil proton tracks, emphasis was placed on finding and measuring properly the small angle elastic scattering events. The final correction for the subsequent systemmatic loss was done in the following two-step fashion: (1) First the azimuthal angular distributions are required to be isotropic. Since the data were obtained from two different bubble chambers, this azimuthal loss due to short tracks being nearly parallel to the average optic axis is expected to possibly show a different t dependence for the two sets of data (t is the square of the four- momentum transfer from 5 to 5 or equivalently from p to p). Thus this correction has been determined for the 1.51 - 1.95 GeV/c and the 2.15 - 2.90 GeV/c data separately, but independent of the individual momenta. This gives the maximum statistical significance, hence allowing a study of the correction in relatively small t bins (0.01 GeV2°c'2). The resulting weights obtained as a function of t are shown for the two sets of data in figure 1. As can be seen, the correc- tions are very smooth functions of the squared momentum transfer, quickly falling to virtually no correction at about -t = 0.04 (GeV/c)2. (2) Using the corrections thus obtained, the differential cross sections were then fitted, using a least-squares method, to the form g3) exp(At) (2) dt t=0 3194 in the region 0.03 5 ltl 5 0.20 (GeV/c)2. This allows us to correct for the extremely low momentum transfer events which are completely lost independent of the azimuthal angle of the proton; e.g., ltl 5 0.01 (GeV/c)2 corresponds to a proton range in hydrogen 5 3 mm. Such short tracks are often not found, and must be corrected for in this manner. Indeed, for ltl 5 0.005 (GeV/c)2, the proton will make at most one bubble in the hydrogen. The corrections for these missed events amount to about 20% of the elastic scattering cross section in the 1.51 - 1.95 GeV/c film, and about 24% in the 2.15 - 2.90 GeV/c film. The low-t data, along with the exponential fits used to obtain these corrections, are shown in figure 2. The errors shown are statistical only for all points with lt|> 0.10 (GeV/c)2 and the quadrature combination of statis- tical errors and errors in the corrections for the azimuthal losses for all points with ltl 5 0.10 (GeV/c)2. Several t-regions were used to make the extrapolation to t = 0. All gave consistent results with the one indicated above, which produced the smoothest behavior in the inter- cept, (do/dt)t=0, and the slope, A. The resulting slopes and intercepts are shown in table 1 along with (do/dt)opt =0 got/19.6 in units of mb°(GeV/c)'2. These slopes are compared to other known values”'19 in Figure 1. The t-dependence of azimuthal scanning and measuring ' corrections. Observed # of Events Corrected # «of Events / 2.0 l.0 MW (o) 1.51- l.95 GeV/c 2.0 r— "%.o + ”51—? (b12.|5 -2.90 GeV/c W 0.02 0.04 0.06 0.08 0.10 ltl (GeV/c)2 Figure 2. The low-t data with least-squares fits to dg/dt = (do/dt)t=0exp(At) in the region 0.03 S |t| 5 0.20 (GeV/c)2. Arrows indicate the appropriate scale to be read for each momentum. [mb/(GeV/dz] da' df 10 l.5l Gev/c l 000 7 1000 100 l l l I l l l l l J 0.0 0.05 0 10 015 0.20 0.25 0.30 0.0 0.05 0.10 0.|5 0.20 0.25 0.30 ltl (GeV/c)2 11 o.Pwm.¢N mom m.ou—.¢~ memmm om.m o._wo.mm mmm o.owo.m_ meovm mN.N o._nm.mm wmm m.owp.m— m—Hmmm om.m P.9Aq.mm mmm m.ow~.vp quomm mv.m N._Hw.om 0mm m.owm.¢_ «muomq ._.N N.qu.mm wmq v.0wm.mF mmuomm mm.” N.—H_.©m mmv c.0un.mp mmwrmm ow.~ N._H—.mm va ¢.oum.m_ mmw¢mm mo._ m.PHv.mm mom v.0flm.op mmuomm Fm.F as .mo .nwmpmwp pamwm AU\>mov q AU\>mov ouwwm . na_ . 3E at N- NIIJmaII A UV AU\>me a .uxmu cw ummmzumwn mcoppumggou unapucw meowpumm mmogu ovummpm omxopuumm mmogu Pmuop seem umumpzopmu och .p mucmgmmmg cw cm>_m men mucwoa Pmuwuao .As b2, a2 a -1, and a] 33.04. The parameter b] ranges from 4.5 - 6.5 and b2 451.5. Thus, instead of having one slope para- meter as in method (4), there is a mixture of three exponentials and no clearly defined "slope" exists. Since b] is the larger of the two slope parameters, the authors of ref. 54 use it as the "slope" and claim no "antishrinkage" based on the three momenta, 1.11, 1.33, and 1.52 GeV/c. Method (5), applied to the data of this experiment, pro- duces much the same behavior in 2b] as obtained for A in method (4). Figure 5 shows the comparison of these two "slopes“; "antishrinkage" is still evident. 2.3 Differential Cross Sections 2 In figure 6 is shown the ratio (do/dtkzO/(do/dt) = 1 + a , opt where a = the ratio of the real part to the imaginary part of the for- ward scattering amplitude. Several points from other experimentslI’IZ’ 15’16’23 are shown with those of this experiment calculated from values in table 1. As with the correction for missed small angle events, this ratio depends strongly on how one extrapolates to t = 0. A11 points shown in figure 6 resulted from the linear fit, (do/dt) = (do/dt)t=0 exp(At). The solid line is a dispersion theory prediction (assuming no spin dependent terms) due to P. Sadin924. The experimental points are somewhat higher than the prediction at the 19 Figure 5. Momentum dependence peak slopes in two phenomenological models. 20 2 __ em .paxw .mmm AV .mmm nu .wmm nu mesh .. <3 VF op mp z_(o/)\ag) aaiaweaed adols 21 Figure 6. Momentum dependence of the quantity (1+a2). The solid curve is a dispersion theory prediction. 0 .328... _n_ o.o_o.m Qm 0.... 0.® O.m 0..» Qm QN m. 0.. . . _ . fl . . ._ . . . . . . . _ ~ —i 22 .— 2238 $3 mezmzamaxm 5.5.0 A. ezmzéuexm 25 m ._ ./W . md ad 10.. N. m. 23 lower momenta; however, the uncertainties in the extrapolation technique and the possibility of spin dependence in the amplitude do not allow any further conclusions than that the pp elastic scattering near 1 GeV/c has a fairly large (perhaps 40%) real part which rapidly falls to nearly pure absorptive scattering above about 3 GeV/c. Tables 2 and 3 show do/dn* and do/dt respectively, the former being expressed in the center of mass. Figure 7 shows the complete angu- lar distributions with minimum X2 fits using an adaptation of the Frahn- Venter optical model25 as described by Daum et_al,26 The model allows for a real part in the amplitude, and absorption which varies as a function of impact parameter. It is parametrized in terms of R, the average radius for the interaction; d, a diffuseness parameter which describes the magnitude of the absorption as the impact parameter varies; ui, which measure the contributions of the total angular momentum states, J = l 1 l, to the real part of the amplitude; and e, where (l — a) des- cribes the amount of absorption. The momentum dependence of these para- meters from the fits are shown in table 4. While this model reproduces the dip-bump structure satisfactorily, it suffers two inadequacies: (1) In the very forward direction it will not give a sufficiently peaked distribution to reproduce the data. This inadequacy gets worse with in- creasing momentum due to a property of the model that as momentum in- creases, it predicts a "shrinking" diffraction peak, whereas pp elastic scattering "antishrinks". While this "shrinking" can be counteracted to some extent by variations in the optical model radius, the dip-bump structure will not allow sufficient variation to overcome the strong mo- mentum dependence; (2) The behavior of the model prediction at large 24 Table 2. Differential cross sections: do/dn: (mb/sr). The first two points for each momentum (cose >O.92) require further model dependent corrections (see text) since the data shown are corrected only for azimuthal anisotropy. (Table continued on next two pages). Plab - 1.51 GeV/c Plab - 1.65 GeV/c P.lab - 1.80 GeV/c COS 6* do/dO* COS 6* do/dO* COS 6* do/dO* 1.00-0.96 31.3:0.7 1.00-0.96 35.310.7 1.00-0.96 38.7t0.8 0.92 34.5:0.8 0.92 33.5:0.7 0.92 33.7:0.8 0.88 21.610.6 0.88 21.0:0.6 0.88 18.5i0.6 0.84 13.110.5 0.84 12.2:0.4 0.84 9.7:0.4 0.80 8.1tO.4 0.80 6.9:O.3 0.80 4.9:0.3 0.76 4.38:0.27 0.76 3.26:0.22 0.76 2.58:0.21 0.72 2.97i0.23 0.72 2.35:0.19 0.72 1.00:0.13 0.68 1.64:0.17 0.68 1.26:0.14 0.68 0.55:0.10 0.64 0.97:0.13 0.64 0.39:0.08 0.64 0.28:0.07 0.60 0.41:0.08 0.60 0.29:0.07 0.60 0.24:0.06 0.56 0.17i0.05 0.56 0.20:0.06 0.56 0.33:0.08 0.52 0.12:0.05 0.52 0.23:0.06 0.52 0.34:0.08 0.48 0.19:0.06 0.48 0.25:0.06 0.48 0.33:0.08 0.44 0.19:0.06 0.44 0.26:0.06 0.44 0.38:0.08 0.40 0.28:0.07 0.40 0.25:0.06 0.40 0.19:0.06 0.36 0.29:0.07 0.36 0.31:0.07 0.36 0.31:0.07 0.32 0.28:0.07 0.32 0.40:0.08 0.32 0.36i0.08 0.28 0.26:0.07 0.28 0.32:0.07 0.28 0.29:0.07 0.24 0.35:0.08 0.24 0.46:0.08 0.24 0.33:0.08 0.20 0.40:0.08 0.20 0.25:0.06 0.20 0.28:0.07 0.16 0.38:0.08 0.16 0.25i0.06 0.16 0.34:0.08 0.12 0.2610.07 0.12 0.19:0.05 0.12 0.14:0.04 0.08 0.35i0.08 0.08 0.17:0.05 0.08 0.22:0.06 0.04 0.26:0.07 0.04 0.12i0.04 0.00 0.12:0.03 0.00 0.19:0.06 0.00 0.14:0.05 -0.08 0.12:0.03 -0.08 0.12:0.03 -0.08 0.09:0.03 -0.24 0.05:0.01 -0.16 0.13:0.03 -0 16 0.08:0.03 -0.40 0.04:0.01 -0.24 0.08:0.03 -O 32 0.05:0.01 -0.56 0.03:0.01 -0.32 0.09:0.03 -0 40 0.07i0.02 -0.72 0.07:0.02 -0.40 0.12:0.03 -0 56 0.05:0.01 -0.88 0.08:0.02 -0.56 0.06:0.02 -0 72 0.07:0.02 -1.00 0.04:0.02 -0.72 0.06:0.02 -0 88 0.05:0.01 -0.88 0.05t0.01 -1 00 0.05:0.02 -1.00 0.09t0.02 . 25 PIab = 1.95 GeV/c Plab = 2.15 GeV/c Plab = 2.45 GeV/c cos 9* dg/d0* cos 9* do/d9* cos 9* do/dn* 1.00-0.96 42.190 9 1.00-0.96 33.9:0.9 1.00-0.96 34.9:0.9 0.92 32.9:0.8 0.92 28.8¢O.9 0.92 26.3:O.8 0.88 17.3:O.6 0.88 12.7t0.6 0.88 10.5:0.5 0.84 8.7:0.4 0.84 6.0:0.4 0.84 3.96:0.31 0.80 3.76:0.28 0.80 2.30:0.24 0.30 1.39:0.18 0.76 2.09:0.21 0.76 1.06:0.17 0.76 0.50:0.08 0.72 0.68:0.12 0.72 0.5420.12 0.72 0.17:0.06 0.68 0.27:0.07 0.64 0.12:0.04 0.68 0.24:0.08 0.64 0.34:0.09 0.60 0.26:0.08 0.64 0.28:0.08 0.60 0.27:0.07 0.56 0.31:0.09 0.60 0.50:0.08 0.56 0.25:0.07 0.52 0.41:0.10 0.56 0.33:0.09 0.52 0.3410.08 0.48 0.28e0.08 0.52 0.42:0.10 0.48 0.27:0.07 0.44 0.39:0.10 0.48 0.54:0.11 0.44 0.34:0.08 0.40 0.49:0.11 0.40 0.38:0.07 0.40 0.42:0.09 0.36 0.28:0.08 0.32 0.19:0.05 0.36 0.42:0.09 0.32 0.34:0.09 0.24 0.23:0.05 0.32 0.40:0.09 0.24 0.18:0.05 0.08 0.09:0.02 0.28 0.27:0.07 0.16 0.15:0.04 -0.08 0.08eo.02 0.24 0.27:0.07 0.08 0.17:0.05 -0.24 0.08:0.02 0.20 0.27:0.07 -0.08 0.08:0.02 -o.72 0.04:0.01 0.16 0.25:0.07 -0 24 0.06:0.02 -1.00 0.0790.02 0.08 0.07:0.03 -o 40 0.06:0.02 0.00 0.13:0.04 -0 56 0.06:0.02 -O.16 0.06:0.02 -0 88 0.05:0.01 -0.4o 0.06:0.01 -1 00 0.07:0.02 -o.56 0.05:0.02 -1.00 0.04:0.01 26 Plab - 2.60 GeV/c Plab - 2.75 GeV/c Plab - 2.90 GeV/c COS 6* do/dn* COS 0* do/dQ* COS 6* do/da* 1.00-0.96 35.6:0.9 1.00-0.96 38.2:1.0 1.00-0.96 37.8:1.0 0.92 24.1:O.7 0.92 23.6:0.8 0.92 20.6:0.8 0.88 9.5:O.5 0.88 8.0:O.5 0.88 7.1:0.5 0.84 3.36i0.27 0.84 2.94: .29 0.84 1.88:0.24 0.80 1.16t0 16 0.80 0.77:0.15 0.80 0.57:0.13 0.76 0.31:0.08 0.72 0.16:0.05 0.76 0.33:0.10 0.72 0.15i0.06 0.68 0.41:0.11 0.72 0.3910 11 0.68 0.31:0.08 0.64 0.38:0.11 0.68 0.18:0.07 0.64 0.46:0.10 0.60 0.65:0.14 0.64 0.36:0 10 0.60 0.29:0.08 0.56 0.62:0.14 0.60 0.33:0.10 0.56 0.35:0.09 0.52 0.27:0.09 0.52 0.18:0.05 0.52 0.4210710 0.48 0.24:0.08 0.44 0.21:0.06 0.44 0.3310306 0.40 0.13:0.04 0.32 0.12:0.03 0.36 0.21:0.05 0.24 0.10:0.03 0.16 0.07:0.02 0.28 0.2310.05 0.12 0.14:0.04 -0.16 0.03:0.01 0.20 0.11:0.03 -O.24 0.04:0.01 -0.56 0.019.005 0.08 0.06:0.02 -O.72 0.011.005 -1.00 0.02+ 007 -0.16 0.03:0 01 -l.OO 0.04:0.01 -O.40 0.0350 01 -0.72 0.03:0 01 -0.88 0.05:0.02 -1.00 0.07:0.02 27 Table 3. Differential cross sections: do/dt [mb-(GeV/c)'2]. The low-t points are corrected for azimuthal anisotropy only; consequently the first three points (|t|<0.03) require further model dependent corrections (see text). (Table continued on next two pages). Plab - 1.51 GeV/c Plab - 1.65 GeV/c Plab - 1.80 GeV/c |t| do/dt do/dt do/dt 0.0-0.01 111:17 114:16 93:15 0.02 379:27 387:26 359:25 0.03 378:27 335:24 337:25 0.04 351:26 307:23 301:23 0.05 274:22 283:22 249:20 0.06 261:21 228:18 238:19 0.07 238:17 219:16 206:16 0.08 195:15 182:14 187:15 0.09 156:11 163:11 151:11 0.10 123:9 144:9 127:9 0.11 113:8 111:8 106:8 0.12 99.3:7.6 90.9:6.8 85.6:6.9 0.16 64.8:2.7 70.9:2.6 64.4:2.6 0.20 33.7:l.9 31.1:1.7 31.2:1.8 0.24 17.8:1.4 19.2:1.4 17.4:1.4 0.28 7.5:0.9 9.7:1.0 6.7:O.9 0.32 3.4:0.6 3.3:O.6 3.7:0.6 0.36 1.4:O.4 2.0:0.4 2.2:0.5 0.40 O.8:0.3 1.4:O.4 l.3:0.4 0.44 l.6:0.4 1.5:0.4 1.7:0.4 0.48 1.8:0.4 1.5:0.4 1.8:0.4 0.52 2.5:0.5 1.9:0.4 1.9:0.5 0.56 2.1:0.5 1.8:0.4 2.1:0.5 0.60 2.3:0.5 2.1:0.5 l.1:0.3 0.64 2.9:0.6 2.7:O.5 2.1:0.5 0.68 2.7:O.5 3.1:O.5 1.7:0.4 0.72 2.3:O.5 2.1:0.5 1.8:0.4 0.76 2.3:O.5 1.5:0.4 2.6:0.5 0.84 1.1:0.3 1.2:0.2 1.1:0.2 0.92 0.98:0.23 0.63:0.17 1.2:0.3 1.04 0.65:0.15 0.61:0.14 0.83:0.17 1.20 0.54:0.12 0.39:0.10 0.51:0.12 1.40 0.39:0.09 0.35:0.08 0.28:0.08 1.60 0.43:0.10 0.41:0.09 0.19: .06 1.80 0.33:0.08 0.37:0.09 2.00 0.06:0.03 0.41:0.09 28 = = ‘ '- :- Plab 1.95 GeV/c Plab 2.19 GeV/c Plab 2.45 GeV/c ltl do/dt |t| do/dt |t| do/dt 0.0-0.01 122:19 0.0-0.01 56:12 0.0-0.01 38:9 0.02 323:25 0.02 196:26 0.02 169:23 0.03 308:25 0.03 239:25 0.03 235:25 0.04 300:24 0.04 258:25 0.04 214:21 0.05 252:21 0.05 223:23 0.05 191:20 0.06 224:20 0.06 184:22 0.06 148:18 0.07 204:16 0.07 177:21 0.07 155:19 0.08 163:14 0.08 139:19 0.08 147:19 0.09 162:13 0.09 136:19 0.09 127:19 0.10 115:9 0.10 120:15 0.10 110:14 0.11 115:9 0.11 83:8 0.11 90:8 0.12 94:8 0.12 81:7 0.12 71.7:6.5 0.16 62.2:2.9 0.16 61.8:3.2 0.16 55.4:2.9 0.20 32.9:2.1 0.20 33.1:2.3 0.20 28.1:2.0 0.24 16.1:l.5 0.24 13.0:1.5 0.24 16.9:1.6 0.28 9.4:1.1 0.28 8.4:l.2 0.28 9.9:1.2 0.32 3.4:0.7 0.32 4.4:0.8 0.32 3.0:0.7 0.40 1.4:o.3 0.40 1.8:0.4 0.40 1.6:0.3 0.48 1.7:o.3 0.56 0.8:0.2 0.56 0.7:0.2 0.56 1.6:0.3 0.64 1.7:o.4 0.64 1.9:0.4 0.64 1.6:0.3 0.72 1.9:0.4 0.72 1.3:0.3 0.68 2.0:o.5 0.84 1.6:0 3 0.84 1.6:0.3 0.72 2.8:O.6 0.92 1.5:0.4 0.92 1.3:0.3 0.76 1.9:0.5 1.20 0.67:0.12 1.04 1.1:0.2 0.84 1.7:o.3 1.80 0.23:0 05 1.20 0.74:0.17 0.92 1.5:o.3 2.60 0.11:0.03 1.60 0.25:0.06 1.04 0.88:0.20 2.20 0.15:0.04 1.40 0.31:0.07 2.80 0.12:0.03 1.80 0.31:0.06 2.20 0.15:0.05 29 Plab 2.60 GeV/c Plab 2.75 GeV/c P.lab 2.90 GeV/c Itl do/dt ltl do/dt ltl do/dt 0 0-0.01 28:7 0.0-0.01 35:9 0.0-0.01 23:7 0.02 139:19 0.02 160:23 0.02 127:20 0.03 213:22 0.03 216:25 0.03 168:21 0.04 204:20 0.04 226:24 0.04 202:22 0.05 162:18 0.05 169:19 0.05 172:20 0.06 165:18 0.06 164:19 0.06 159:20 0.07 152:18 0.07 120:16 0.07 135:18 0.08 125:17 0.08 116:16 0.08 117:17 0.09 118:17 0.09 121:17 0.09 115:17 0.10 105:13 0.10 102:14 0.10 90:13 0.11 75:7 0.11 94:9 0.11 82:9 0.12 70.1:6.2 0.12 59.2:6.6 0.12 72.0:7.3 0.16 58.1:2.8 0.16 54.5:3.2 0.16 43.5:2.9 0.20 30.2:2.0 0.20 31.4:2.4 0.20 30.0:2.4 0.24 18.9:1.6 0.24 19.4:l.9 0.24 15.4:l.7 0.28 8.6:1.l 0.28 7.6:1.2 0.28 7.1:1.2 0.32 5.0:0.8 0.32 5.0:l.0 0.32 3.9:0.9 0.40 l.4:0.3 0.40 2.4:0.7 0.40 l.6:0.4 0.56 0.6:O.2 0.56 0.5:O.2 0.56 0.9:O.2 0.64 1.5:O.3 0.64 1.7:0.4 0.72 0.9:0.2 0.76 1.1:0.2 0.76 1.7:0.3 0.92 0.67:0. 0.84 l.4:0.3 0.84 1.8:0.4 1.04 0.87:0. 0.92 1.2:0.3 1.04 0.52:0.14 1.40 0.25:0. 1.04 0.92:0.21 1.40 0.35:0.08 1.80 0.21:0. 1.20 0.66:0 15 1.80 0.26:0.07 2.60 0.03:0. 1.60 0.25:0 06 2.60 0.10:0.03 2.40 0.05:0.02 30 Figure 7. Differential cross sections, do/d0*, for pp elastic scattering in the c.m. for (a) 1.51 - 1,95 GeV/c (opposite page) and (b) 2.15 - 2.90 GeV/c (next page). The solid curves represent the best fits obtained with the five parameter Frahn-Venter optical model. 31 100 0.2 0.1. 0.05 I I I I I "1'51 '_..__ WF'V'_- "'I . ' A‘ ' ‘ 0.02 I I I 1.0 0.6 0.2 -0.2 -0.6 -|.0 cos 0* 32 ‘\ wPI—fl“ 2 ’5 «>1 \/ \ E 1 \— b ea 2.45 ‘0 ‘6 2. 60 0.5 0.2 A 2. 75 0.1 0.05 1 0.02 * 0.01 2.90 L I I l l 1.0 0.6 0.2 -0.2 06 -1.0 cos 0* 33 mo.owo~.~ No.00—m. mo.ow¢m.p No.0Hmm. mo.oumm.o no.0H m No.0HmF.o mo.ow¢m.o co. m mo.oH¢N.P mo.onm—. oo.oum¢.o vo.owom. o o o mo.owm_.o mo.ow¢o.F mm.m Po.oumm.o No.0Hno.F oo.m po.onmp.o wo.oH—_.~ mv.m mo.owoo.o mo.owo o m o o o .o Fo.ow—_.o mo.owop.P m_.~ o o o o o o o No.0«mm.F mo.onmm.o oo.onmo.o No.0um .o oo.onmo.on No.0HN o o o o No.0wqm.~ No.0HmN No.0wmm.P No.0Hmp. qo.omvo.oi No.owm . po.0flm_.o No.o+m~.— mm.~ NO.OHO¢.~ mo.OHmo. mo.oumo.o No.0How. FO.OH©_.O No.0«m—.— ow.~ No.0Hm¢.~ No.ou¢o. wo.owmo.oi No.0Hmm. FO.OH©F.O No.0wmp._ m©.~ NO.OH@¢.F No.0Hmo. vo.OH~F.Oi No.0Hwo. FO.OHm~.O NO.OHN~.~ —m.~ E C. C. .9998 L 0 -1 +3 n a . amp: .2259: Fence _eu.pqo .xw.e xee_n. 9:: .e 5:: .Feeoe :5:em>-e;ee: 9:: :6. m .1: .+: .n .m ”uxmu cw nmawcummn map: Loy mgmumEmcea .muos Pmowuno .5 anmh 34 Figure 8. Differential cross sections, do/dt, for Ep elastic scattering for (a) 1.51 - 1.95 GeV/c (opposite page) and (b) 2.15 - 2.90 GeV/c (next page). The curves are predictions of a three pole Regge model of Chiu, Chu and Wang. 35 g?- [mb/(GeV/CJZJ I L I L41 1. 1 1 1 1 1 1 p 0.0 0.4 0.8 2 1.6 2.0 111 (GeV/c)2 2.4 2.8 3f“ [mb/(GeV/clzJ 500 1 36 1000 1000 100 1000I 100 10 2.l5 Gev/c L L I I I I I 0'50 0.4 0.8 1.2 ltl(GeV/c)2 I 1.6 2.0 2.4 2.8 37 angles is also inadequate, producing an incorrect shape for the distribu- tion and underestimating the magnitude of the differential cross section for cos 6* < -0.4. Fits have also been made to the "black disk" optical model form do $01 (krsin6*)|2 0—0— (3650* krsin6* l’ (4) in the region 0.60 - cos6* 5 0.92, where k is the incident wavenumber in the c.m. Table 4 gives the resulting radii. Calculations using the "no-compensation mechanism" three pole 27 have been made using (P, P', w) Regge model due to Chiu, Chu, and Wang their parameters obtained from fits to high momentum 6p and pp scattering; these are shown in figure 8 compared to our data. There is substantial disagreement at our lower momenta and, as one might expect, a gradual improvement in the quality of the prediction as the momentum approaches the region of the high energy fits. 2.4 Conclusions The antiproton-proton elastic scattering cross sections presented here are in good agreement with those of other experiments. The data indicate that, in the 1.51 - 2.90 GeV/c range, there is a fairly large, rapidly decreasing, real part to the forward scattering amplitude. The magnitude of this effect is strongly dependent on the method of extra- polating the differential cross section to t = 0. Further evidence has been found for the "anti-shrinkage“ of the pp diffraction peak, which seems to be occurring most rapidly through the momentum range of this experiment. Comparisons of the differential cross sections to a five parameter optical model are not entirely favorable. As the model exists 38 it does not describe the complete angular distributions adequately. The predictions of a high energy Regge pole model are reasonable for several of the higher momentum points of this experiment, but do not adequately describe the distributions at the lower momenta. CHAPTER 3 TOPOLOGICAL CROSS SECTIONS The 1.51 - 1.95 GeV/c film was scanned for all zero through eight prong events with and without neutral decay vees, and one-third of the film was second scanned. The 2.15 - 2.90 GeV/c film was scanned for two prong, four prong, neutral decay vee events, and a total interaction count at all momenta, and in addition, for zero, six, and eight prong events at two momenta and similarly second scanned. Typical single scan efficiencies for the two sets of film are 85% for the zero prong topology, 94% in the two prongs, 96% for four prongs, better than 95% for six and eight prongs, and better than 90% for the vee events. In addition to the random loss accounted for by conflicting independent scans, there is the systemmatic loss due to the very for- ward elastic scattering where the recoil proton is not seen. The quantitative details of this correction were discussed in Chapter 2. Table 5 and figure 9 show the topological cross sections which result from normalizing the corrected total interaction counts to the total cross sections measured by Abrams gtgal,] Also shown are values of these topological cross sections from several other experimentsz’3’28'37. 39 40 Table 5. Topological cross sections in mb. 1— L 1’16 (G:V/c) O-Prong 2-Prong 4-Prong 6-Prong 8-Prong ‘ 27.8:0.4 3.79:0.14 0.039:0.014 1.51 7.22:0.19 59.4:1.0 1.65 6.90:0.17 57.7:1.0 26.8:0.4 4.29:0.14 0.046:0.0l4 1.80 6.71:0.18 55.8:1.0 25.8:O.4 4.61:0.15 0.094:0.021 0 1.95 6.27:0.19 54.2:1. 24.7:0.4 4.50:0.16 0.132:0.028 2.15 49.6:1.1 24.9:0.7 2.45 6.14:0.30 46.5:1.1 23.2:O.6 5.57:0.28 0.200:0.039 2.60 44.9:1.2 22.7:O.7 2.75 44.2:1.2 22.0:0.7 2.90 5.50:0.35 42.9:1.2 21.8:O.7 5.76:0.36 O.388:0.063 41 Figure 9. Topological cross sections (opposite page and next page). Other experiments are: (1) 1.11, 1.33, and 1.52 GeV/c, ref. 3; (2) 1.23, 1.27, 1.32, 1.37, 1.43, 1.49, 1.54 and 1.63 GeV/c, ref. 2; (3) 1.2 GeV/c, ref. 28; (4) 1.61 GeV/c, ref. 21; (5) 3.0 and 3.6 GeV/c, ref. 30; (6) 3.28 and 3.66 GeV/c, ref. 35; (7) 3.6 GeV/c, ref. 31; (8) 5.7 GeV/c, refs. 32, 33 and 37; (9) 6.9 GeV/c, ref. 34; (10) 6.94 GeV/c, refs. 35 and 36. 42 70 §§§§ § This Experiment _ 9 E - _. 6° 9:. 9 itinerarms 50_ 5 9 9-12 PRONG) _ i f §§ § 40— - § § 3 30- o 935890 g _ E 99>? . 514 13110110) \— O i . Q . 5 b 20)- ’ 3 - 9 3 I 9 8 — ._ § §§§§§§ Q i 0'10 PRONG) Q 5 — _ I 4— 5 § - § 2 J I I l I I I §I 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 0- (mb) 43 § § This Experiment O 5 Other Experiments (See Caption) 0(6 PRONGI I 0'18 PRONG) 4 g _ 4 £4 a A ‘ ‘1 1 1 4 1 1 1 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 P196 (GeV/c) 44 The 6p total cross section* in reference 1 has been fitted to a seven parameter function oT(5p) = [.120 3:34 + 96 511(2190) + a7 BW(2360) (5) N - where BW(E ) = . fl 2 with p* the p c.m. momentum, E ° p.52 {tie-so) $1 + 1} the 59 total c.m. energy, and N a normalization factor. The five para- meter polynomial background in brackets is hereafter referred to as "Bkgnd". This was done to determine the best Breit-Wigner parameters for the 5p total cross section where the I = 0,1 enhancements are mixed; in particular, the 2-3 mb bump referred to above as BW(2360) at about 2360 MeV is the result of the 51*(2350) and the 50*(2375) over- lapping. The best values found for 5p are (Eo,r) = (2190, 75) for the first bump and (2360, 195) for the combined I=0,1 higher momentum bumps. The parameter N in the Breit-Wigner expression above is adjusted so that the amount parameters, a5 and a7, equal 4mb and 3 mb, the heights of the BW(2190) and the BW(2360) respectively. Using these fixed values of E0, r, and N fits are made to a number of subtracted cross sections using the function given in (5) above and to a similar six parameter function excluding one or the other of the Breit-Wigner terms. The re- sults of the fits are most clearly displayed in the following fashion: if h1 is the height of the first bump in the total cross section, and a6 is the height for a given subtracted cross section, for example, or - 9(4 prong), then the height of the bump in the indicated channel, 4 prong in this case, is given by “R s h] - a6. Thus °R gives the amount of the bump observed in the total cross section which can be accounted 1EThe errors on 91(pp) in ref. 1 were expanded by 50% based on pri- vate communication with one of the authors. 45 for by the channel being subtracted. Table 6 indicates the results of such fits to the topological cross sections using the compiled data of figure 9. The zero and six prong subtracted cross sections still re- quire bothenhancements, indicating the origin of the structures is not significantly in these topologies. This is in agreement with the obser- vations of reference 7 in regard to 5p charge exchange scattering which dominates the zero prong cross section. The errors on the two and four prong topologies do not allow much discrimination among the three fits, and the resulting amount parameters have such large errors that no con- clusions are possible regarding whether or not the bumps are still pre- sent, with the exception that the 2190 Mev enhancement is still required by three standard deviations in the four prong subtracted cross section. This channel is consistent with 1:1 mb of the 2190 MeV enhancement arising in the four prongs. This is consistent with the findings of reference 3 where the 0.5 : 0.1 mb enhancement in 6p + p°p°n° discussed in Chapter 1 was seen. This method of fitting subtracted cross sections requires data which is as closely matched to the total cross section as possible; i.e., many closely spaced points and small relative errors. Even though the compiled bubble Chamber data falls short on both counts, as seen above some definitive conclusions are still possible. Since a several mb enhancement might appear as a much larger fraction of one or more reaction cross sections or resonance production cross sections these are considered in detail in the next two Chapters. 46 5.555.. 5 5-5: 5.55 5. 5 .555~.35+ue5:5 . 5 5,595.5 55.5 5.55 5_ 5 .55_~.:5+5=5x5 = 5.595.5 5.595.5- 55.5 _.N. 5_ 5 .5555.35+.55_5.35+5e5:5 5.5eoe5o.e-.5m.55. 5.555.N 5 55-5: 5.55 55 5 .555~.35+ue5:5 . 5 5.595.5 5-5: 5.55 55 5 .5555.=5+ue555 . 5.59:.2 5.555.5 55.5 _.55 55 5 .5555.35+.55.~.35+ee5:5 5.5eoe5e.e-.5m.ee. 5._95.5 5 5_.5 o._5 55 5 .5555.35+555:5 . 5 o.:95.5 5_.5 5.55 55 5 .55_5.35+5e5:5 . 5..95.5 5._95._ 55.5 5._N 55 5 .5555.35+.55P~.=5+555:5 5.5eoe55.e-.5m.ee. 5.555.N 5 55.5 5.5 5: 5 .5555.35+u:5:5 . 5 5.595.: 55.5 ..5 5: 5 .55.5.35+5:5:5 . 5.55:.5 5.555.: 55.5 5.5 5. 5 .5555.35+.55.N.35+5:5:5 H.5eoe5m.e-.5m.ee. ..5555 55.5 25>5. 555.55 .55:55 55 .525555 5: «WU5 .mz 55.55555 5555 .Am. cowumzum =_ ecu» ucaogmxuen PMFEocxpoa 05p 55 eucmxme .uxm» :5 nmnweommn mcowpomm mmoeu umuueeunam op mp5: magmacmiumemp mo mp_:mmm .0 «Pack CHAPTER 4 REACTION CROSS SECTIONS 4.1 Experimental Methods The measured events were fitted with rather loose acceptance criteria (e.g., successful fits correspond to confidence levels greater than 10'10). This approach leads to a good deal of ambiguity (i.e., two or more fits to one event) which must be resolved by further confi- dence level cuts and missing mass cuts as well as ionization scanning to finally classify events. It does, however, ensure the least bias in the final samples. Whenever there was reason to expect bias in events which failed at some stage of the processing (e.g., small angle elastic scatters which fail to reconstruct preferentially over other events) the failed events were remeasured in order to minimize bias in the final accepted sample. The overall acceptance into one or more of the final state hypotheses is typically better than 95% in the twice measured events. Ionization scanning was usually necessary on 30 - 40% of the events, primarily in the one-constraint fit class. All ioniza- tion decisions were done or checked by physicists and for the case of pion-kaon separation, the scanning was done twice and all cases of disagreement settled by a third scan. Those events with final state particles too fast to be resolved by ionization (about 10%) are separated on the basis ofimissing mass, missing momentum (for four- constraint events) and confidence level cuts. The final sample of 47 48 measured events is then normalized to the appropriate topological cross section given in table 5 to obtain the reaction cross sections within that topology. 4.2 The Two Prong Cross Sections Approximately 60,000 two prong events have been measured in the 1.51 - 1.95 GeV/c film and 35,000 in the 2.15 - 2.90 GeV/c film. Each measured event was fitted to the following hypotheses: Tip + 513 (6a) + 599° (6b) + 13m+ (6c) + pfin‘ (6d) + n+5” (6e) 5 Mir-5° (6f) and the corresponding zero-constraint "missing mass fits." The elastic scattering events (6a), which amount to a little more than half of the two prong events after correction, were discussed in Chapter 2. The one pion production and pionic annihilation channels (6b) - (6f) are highly ambiguous among themselves and with the missing mass class r+r'MM, MM 3 25°, Ionization constraints allowed virtually complete separation of hypotheses (6b) and (6d) from the others due to the presence of a slow proton in the lab, and missing mass distributions indicate negligible crossing between these two final states after ionization. Hypothesis (6c) generally has a fast antiproton and is therefore inseparable from n+n-MM in a majority of the events. However, since the 5p system is an eigenstate of the combined operations of charge conjugation and spatial rotation (CR)38, then the final states (6c) and (6d) which transform into 49 each other under CR should have equal cross sections, and for an unpol— arized beam and target, the angular distributions for the antiproton and neutron in (Ge) should be reflections of those for the proton and antineutron respectively in (6d). Comparisons of these angular distri- butions indicate that all events fitting hypothesis (6c) which are con- sistent with ionization predictions are acceptable. The number of events accepted into hypothesis (6c) is still somewhat smaller than those of reaction (6d). Interpreting the n+n'MM events as Bn+MM(pn-MM) pro- duces a small neutron (antineutron) signal in the missing mass spectrum. These events were considered as either reaction (6c) or (6d) for cross section purposes and were at most 5% of the events. The four-constraint hypothesis (6e) was successfully fitted to only about 100 events; all were consistent with ionization and were accepted as this hypothesis. Reaction (6f) and n+r'MM were almost always ambiguous. The number of events accepted as reaction (6f) was determined by a missing mass separation. Since the «Tn'MM spectrum contaminates the high mass side of the 9° signal of reaction (6f) the peak is folded about its center from the uncontaminated low mass side to obtain a symmetric pion mass peak. The pion peak is expected to by symmetric since all other one- constraint fits with the 5° (e.g., hypothesis 6b) or neutron (e.g., hypotheses 6c or 6d) where there is much less background problem to indicate that the errors are such that a symmetric, nearly Gaussian shape results for the observed missing particle masses. All of the n+n'MM and other zero-constraint events are added together to form a cross section, 9(2-prong MM). In table 7 and figure 10 the final two prong reaction cross sections from this experiment are shown with 29,32,35,39-41 those of several other experiments The 29 and 30 50 mp.owom.~ m..oa¢m.~ mF.oumm.N mpo.owmmo.o om.m m.oam.o~ m_.owmm.m m_.owom.m 55.0Hmm.m co.owpm.o o—o.OHm_o.o mm.~ ¢5.oum¢.~ mF.OHm~.N mp.05mm.m o—o.own—o.o .oo.m m.ou¢.- ¢~.oupm.m m~.oumo.m mF.Ome.~ no.OHmn.o m—o.OHomo.o m¢.m m.ou~.- mF.OHFm.~ Np.oumm.P mp.owmm.m mo.ow~m.o moo.owooo.o mF.N m.ou~.mp mo.ow~m.— no.OHmo.~ op.oupo.m mo.onpm.o mpo.oumoo.o mm.p 5.0Hm.ep neeoump._ mo.oamm.o mo.oHFm.p mo.onm~.~ mpo.oummo.o om.~ q.oum.¢~ mo.oumm.o mo.oumm.o mo.oumm.P mo.ouom.p upo.onFno.o mo.~ v.onu.mp mo.ouum.o mo.oumm.o wo.owmm.~ mo.oumm._ pmo.owsmo.o Fm.~ Zincocam -1ema +ecm oeam oeie+= 15+: Au\>mm. amp; .111'11 .5mopoao» acogaum egg :5 Age. mcowuumm mmogu cowuummm .5 mpnm» Figure 10. 51 Cross sections for the two prong topolog (opposite page and next page). Solid curves in (a are predictions of a multiperipheral model (see Chapter 6). Other experiments are: (l) 1.61 GeV/c, ref. 21; (2) 2.2 GeV/c, ref. 39; (3) 2.7 GeV/c, ref. 40; (4) 3.28 and 6.94 GeV/c, ref. 35; (5) 3.6 GeV/c, ref. 41; and (6) 5.7 GeV/c, ref. 32. 52 .8583: 0.. 0.0 OK 0.0 0.0 0.0 0.» gm 0.N 0.. . illmlfll 4. _ _ _ m. _ 5 000 1 1 .00 I. «1.3+th b I $0.0 5. 1 N_.0 \\ 1 1 0.0 1 m 1 N. 2.0.800 mom. .ohtk+h.b m mEmEImaxw 350 0 1 255.396 5...... m 1 0.. . 0.N (qua-o 53 .e\>ee.eec 0.. 0.0 0... 0.0 0.0 0.¢ 0.m 0N 0d 0.. d d . _ _ _ _ _ W .+hcmvb+.1hm3b +.oham.b w 321022.535 w W . .5238 88 255.398 350 0.0 w 1 .EoEtmaxw mi... Tw (D (940-0 ¢. 0. m. 54 cross sections are decreasing rapidly as,a function of momentum and show no evidence for structure. There are not enough data points in the 2-prong MM channel to adequately determine the six or seven parameters in subtracted cross section fits; hence, no definitive statements can be made in regard to this channel. The cross section for single pion production without annihilation, hereafter referred to as NNn, is rising rapidly through the region of the bumps. As mentioned in the introduction this channel has been considered as a possible source of the bump at 2190 MeV. In a similar manner the possibility of the structures in the total cross section arising from threshold reactions is considered at the end of the next section, after presenting the data for double pion production without annihilation. 4.4 The Four Prong Cross Sections - Measurements of 60,000 four prong events in the 1.51 - 1.95 GeV/c film and about 42,000 in the 2.15 - 2.90 GeV/c film have been completed. The following hypotheses were fitted to each measured event: 6p + fipw+9' (7a) 5 Epn+n'n° (7b) + finn‘r+n+ (70) + pfin+n'n' (70) + n+n+u'n' (7e) + n+n+n-n-n° (7f) + K+K'n+1r' (7g) .. K+K-11+11-1i° (7h) and the corresponding zero-constraint "missing mass fits." The reactions (7a) - (7d) were quite easily identified by ionization, 55 particularly (7a) and (7b), due to the presence of usually twice mini- mum or greater ionization on a proton or antiproton track. Events fitting one of the four-constraint hypotheses (7a), (7e), or (79) were usually consistent with predicted ionizations. The most difficult identifications were for hypotheses (7f) and (7h) which were normally ambiguous with each other and with the missing mass hypothesis 25+25'MM. After ionization constraints were imposed the ambiguities between hypo- thesis (7f) and 20+Zn'MM still existed and the squared missing mass dis- tribution was folded from the uncontaminated low mass side to obtain the sample of events corresponding to reaction (7f). After ionization identification, the K+K-fl+fl-(fl°) events neces- sarily consisted only of those cases where at least one kaon was distin- guishable from a pion (i.e., PlabIK) 5 0.675 GeV/c, corresponding to Bug/Bi|2 1.5). The Monte Carlo calculations used to correct for the un- seen events in the 1.51 - 1.95 GeV/c film have been discussed elsewhere8. However, the increasing peripheralism of these two final states makes the statistically generated events a less acceptable model for comparison in the 2.15 - 2.90 GeV/c film. In the lab system the K'(K+) tends to be fast (slow); if one Lorentz transforms the fitted four vectors to a frame where the antiproton is at rest (called the "antilab") then the K+(K') should be fast (slow). If there are no experimental losses, CR invar- iance tells us that the K+(K') in the lab should be the same as K'(K+) in the antilab in regard to momentum and angular distributions. Com- parisons of the momentum distributions in the lab and antilab gives the corrections for the K+K-n+n'(n°) events with both kaons too fast to identify by ionization. It was found that by using all events fitting the four-constraint hypothesis (79) no corrections were necessary, 56 indicating that the kinematic constraints were sufficient to identify these events even when both kaons were minimum ionizing. For the one- constraint hypothesis (7h) this was not the case. Since the hypothesis (7f) or missing mass hypothesis 29+29‘MM was almost always ambiguous with this hypothesis, only events with one or two kaons identified were acceptable. The correction due to both kaons having a momentum greater than 0.675 GeV/c for cross section purposes was 20 : 2% and is essen- tially momentum independent from 1.51 - 2.90 GeV/c. This is a feature of the increasing peripheralism that as the incident antiproton momen- tum increases, the peripheral K'(K+) has a higher (lower) average mo- mentum in the lab. Thus, even though the K' becomes increasingly dif- ficult to identify by ionization,the K+ is a much better candidate for ionization identification. This also means that, since one kaon is relied on to identify the event, contamination from the final states KinTnTr'K° becomes more likely. When the K+K-n+n-n° events with only one kaon identified by ionization are interpreted as a missing K° hypo- thesis, a small (m 5%) K° signal is seen in the missing mass spectrum for the higher momenta only. Imposing a 5% minimum confidence level cut on the K+K'n+n-n° events removed these events. In table 8 and figure 11 the cross sections within the four prong topology are shown along with some results of other experimentsza’ 29,32,33’35’39:41’4Z'47. As in the two prong topology, all of the cross sections are statistically smooth; the multipion annihilations are decreasing at least as rapidly as l/Plab' Double pion production without annihilation rises sharply from the AA threshold and reaches a peak around 4 GeV/c. This channel and the single pion production (NNn) channel are the major threshold reactions in this momentum region. 57 ¢.onu.~5 mo.owm¢.o mo.OH¢N.o No.OH N_.c No.o« .5.o 2.9H cm.~ N.owm.¢ no.05mm.o om.~ ¢.oue.mp mo.OHm¢.o mo.ow¢m.o mpo.oummo.o mpo.owmmo.o N56H m~.~ N.owe.m no.owmm.o m5.~ ¢.ono.m_ mo.oam¢.o mo.oen~.o N_o.oaomo.o 05o.oapmo.o 55.09 oo.~ N.oam.m no.OHom.o om.m m.on~.m_ mo.ow~¢.o mo.oaom.o moo.oao~o.o moo.o0o~o.o modH mm.5 N.oem.m mo.OH¢N.. mv.m q.oap.¢5 oo.oamm.o co.OHmm.o moo.ov moo.ov No.05 mm.o m.ou~.u mo.oflmo.. m..m m.OHo.¢P co.oamm.o eo.oam¢.o mNo.OH¢¢~.o N.owm.m mo.oflw~.5 m5.. m.oac.¢~ mo.oum¢.o mo.ou.¢.o F—o.owumo.o N.oae.m No.05mo.m om._ m.owm.¢. «o.o«¢v.o mo.oamw.o moo.ow~_o.o ~.oup.m mo.oumm.m mo.. m.OHm.m_ co.oamm.o mo.onmm.o moo.o0moo.o N.oam.m mo.ow~m.m Pm.5 zzmcogav cpie+eix+¥ 1e+e1¥+¥ 1=me emu“ oeie+eam 1=+eam oeiem+em ie~+eu Aumoww. + + 1 1 .xmopoaop mcogaie mg“ :5 Ana. mcowuumm mmogu cowuommm .m 0.355 Figure 11. 58 Cross sections for the four prong topology (opposite page and next three pages). Solid (dashed) curves are predictions of a multiperipheral (statistical) model (see Chapter 6). Other experiments are: (l) 1.11, 1.33 and 1.52 GeV/c, ref. 3; (2) 1.2 GeV/c, refs. 28 and 47; (3) 1.61 GeV/c, ref. 21; (4) 1.62, 1.76, 1.82, 1.90, 1.94 and 2.2 GeV/c, ref. 46; (5; 2.2 GeV/c, ref. 39; (6) 2.4 GeV/c, ref. 42; 7 2.5 GeV/c, ref. 43; 2.7 and 2.9 GeV/c, ref. 44; (9) 3.28, 3.66 and 6.94 GeV/c, ref. 35; (10) 3.6 GeV/c, ref. 41; (11) 5.7 GeV/c, refs. 32, 33 and 45. 0.5 0.0 59 §,§ This Experiment _ 0. \ 0"(277'+271'_7I'°) 5 Other Experiments (See Caption) \\ ix 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 P|abIGeV/C) 14 12 60 a‘(mb) I I“; 0' (4 PRONG-MM) I 1“} L; This Experiment 6 5 Other Experiments (See Caption) §§ §§ 0' (3p1rT1r') I §§ "‘ b ._ o h g 2 I I I I I I I 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 1.0 P100 (GeV/C) 2.5 61 Li This Experiment 2'O_ §.§ Other Experiments '- (See Caption) 1 - | O _ 0- (EP 1T+17’-1T°) _ —\ Q s, 1; _ 0.0 —- O ' ’° - )7 r A 1.0- - aIBnrr’1r+1r+1-1- 0.0, 0.5 — é -' :4 § 0.0 ‘ ‘IA I l I I I 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 P101) (GSV/C) 62 c.m. 33%: En. ma ma ea ma 0.. v._ N._ 0.. _ _ _ _ O.N _ m._ _ m Aik+hix+x v b w w Auk. uh. +.=. ix+x vb WWWW r m m Wmfl W _ _ a 22800 38 3552095 350% 22:75wa m2... m 0.0 0.0 md 63 These two reactions have been combined and the subtracted cross section, [oT(pp) - o(pion prod.)], has been fitted to the,same functions as used in Chapter 3 with the topological cross sections. Here o(pion prod.) is taken to be the sum of 0(Nhn) and o(ppn+n')* where 0(NNn) = 2[o(ppn°) + o(pnn')], the first being doubled to correct for the unseen channel nfin°, and the second being doubled since it is the better iden- tified of the two CR conjugate states, pfin‘ and pnw+. The results of these fits are shown in table 9 and figure 12. The data allows some [ discrimination among the fits, favoring the seven parameter fit with ' both bumps; the 2190 MeV bump is required by 4 standard deviations, the 2360 by 2.5. Thus, it seems unlikely that a threshold effect can be responsible for the total cross section structure. However, more closely spaced points with smaller relative errors in the 2360 MeV region are required to definitely answer this question. 4.4 The Six Prong Cross Sections Measurements for about 9,000 six prong events in the l.5l - l.95 GeV/c film only have been completed. Each event was fitted to the following final states: 5p + 3n+3n- (8a) .. 31r+3n"1r° (8b) and the missing mass hypothesis, 3n+3n'MM, MM 3 2n°. The n° signal for hypothesis (8b) was symmetric without any folding and no further clean- up was necessary. The cross sections for the six prong events are shown in table l0 and figure l3, including those from other experiments 3l,32,35,37,48 sections. There is no evidence for structure in these cross *In the AZ isobar model, ppn+n' dominates the double pion pro- duction; hence, no correction is made for other channels. 64 N.th.o o o o.—Hm.o F.PHN.o o.FHo.o «0.0 P.om w— mm.o m.mp m— moé _..m_ 2 Aommmvzm+ecmxm Aom_mvzm+ucmxm Aoommvzm+Acm_szm+ucmxm fiAUOLQ coeavo-flamvkog ommm m ompm o .uwwcou _m>m4 x mucwoa N .02 mama .pxmp mgp cw commaumwu .mA.uoLa cowavotfigmvpou .coTpomm mmocu umuomcpnzm mgp cu “we mmcmzcmupmmmp to mppzmmm .m mpnm» 65 Figure l2. Results of fit to the subtracted cross section, [0T(5p) - o(~Nn) - 0(fipn+w')]. |20 66 ||5 IIO I05 IOO 95 9O 0'(mb) 85 80 9 07.459) - O‘(N'h-l1r)- O'(5p1r+1r') § 5/ .Afifl + 0'('5p1r"'1r') 1 l l I l I.2 |.4 LG LG 2.0 2.2 2.4 2.6 2.8 PlabiGeV/c) 67 Table 10. Reaction cross sections (mb) in the 6-prong topology. Plab (GeV/c) 3w+3n' 3n+3n-no 6-ProngMM l.5l l.23:0.10 2.09:0.10 0.47:0.10 1.65 l.30:0.10 2.04:0.l5 0.95:0.08 l.80 1.30:0.10 2.24:0.15 l.07:0.lO 1.95 1.10:0.10 2.32:0.15 1.08:0.10 68 Figure l3. Cross sections for 3n+3n' and 3n+3n'n° channels. Solid (dashed) curves are predictions of a multiperipheral (statistical) model (see Chapter 6). Other experiments are: (l) l.6l GeV/c, ref. 21; (2) 3.0 GeV/c, ref. 30; (3) 3.28 GeV/c, ref. 35; (4) 3.6 GeV/c, ref. 31; and (5) 5.7 GeV/c, refs. 32 and 37. O 3S8: .n. 0d OK 0.9 0.0 of O._m MN ON 9.. 0.. _ d £51me 69 3:238 39 355.896 .35an w WEmfltmaxw mEkm m 1 v.0 mo 90 o._ N. ¢._ 9. m; c.m. Nd ed o.~ m.~ o.» mun-o CHAPTER 5 .RESONANCE PRODUCTION IN THE MULTIPION ANNIHILATIONS 5.l Experimental Methods The invariant mass distributions in the multipion annihilation {AM channels indicate substantial resonance production. Indeed, maximum like- lihood fits to these channels show these reactions to be dominated by re- sonance production. The model used in the maximum likelihood fitting con- sists of an incoherent sum of phase space plus any resonance processes aa— evident in the invariant mass histograms, and further any associated re- sonance processes which significantly reduce the histogram X2 in the data- model comparisons. More precisely, the model assumes the scattering matrix is given by n n |M|=(l-§a)+.§ c.m./N1. (9) where a1 is the fraction of the 1th resonance process Ri’ Ni is the normali- zation for the ith process, and n is the number of processes excluding phase space production. The Ri are taken to be Breit-wigner line shapes, or a product of two such line shapes in the case of associated resonance produc- tion. The normalization, Ni’ is then simply the integral over all phase space of the function Ri' The maximum likelihood fits are made subject to 5 l, and (2) 2 a1 5 l. The masses and widths i l the constraints (1) 0 5 ai 70 71 for the resonances were initially obtained visually from the data and adjusted slightly in some cases to improve the histogram X2. Since reason- able X2 values for invariant mass distributions involving like-charged pion pairs were obtained with this model, no attempt was made to include the effect of Bose-Einstein symmetrization as suggested by Goldhaber, et al.49 5.2 Three Pion Final States The three pion annihilation is about 50% quasi-two-body final states, mainly pin1, p°n°, and f°n°. With only 200-300 events in this channel for each momentum it was necessary to combine the data into overlapping adjacent momenta for the purpose of fitting to resonance production processes. The resonance parameters used were (M, r)p = (770, 110), (M, I‘)f = (1250, 120), and (M, r)g = (l660, 200), in MeV. Initial fits including the above reson- ance processes indicated that g° production is very small, and consistent with zero. Since the 3n cross section is decreasing rapidly as momentum increases, the number of events in this channel in the 2.15 - 2.90 GeV/c film was very small («.200 events); hence, only a fit to the combined data 2 are shown in was possible. The resonance cross sections and histogram X table ll and figure 14. The fractions of the resonance processes are nearly constant as momentum increases; hence, the resonance cross sections fall just as the channel cross.section. 5.3 Four Pion Final States Annihilation into four pions is dominated by p°, f° and associated p°f°, p°p° production. Figure l5tshows typical mass spectra for this channel at l.80 GeV/c. An interesting feature is that associated resonance production is either very small (as for p°p°), or is decreasing far more 72 m¢\m¢ m¢\mv mo.OHmo.o mo.0Ho—.o mo.ou~o.o co.owwp.o om.m mP.N o¢\mm o¢\mo qo.owko.o co.oho_.o mo.onno.o vo.ommm.o mm.— + om.F oe\w¢ o¢\mm wo.0Hmo.o ¢o.onmp.o #o.on~_.o mo.onm~.o ow.F + mm._ o¢\mo o¢\m~ wo.onvo.o ¢o.ownp.o ao.owm~.o ¢o.onmm.o mo.— + —m.~ mp E -e e e m e c e Q E 3:63 a a mcwmmmm Emgmommwx o o o o o o w + I1 It .chcmsu o: e e mzp Low as cw mcowuomm mmoco cowuozuoca mocmmmmmm .FF mpnmh + 73 Figure 14. Resonance production cross sections in the n+n-no channel. Other experimental data from ref. 50. 74 ad 33812.”. Em mam mam _.m m.. E 2 . _ _ % o . _ _m _ _ oo “chomvb m TWI. a loud LT “ TIWI; ¥ rests 86 Tell . \ 23:30 39 mhcmEImaxm 350m 2.95596 3ch AHkHQVb 75 Figure 15. Typical invariant mass distributions in the 2w+2n’ channel at 1.80 GeV/c with maximum likelihood fits described in the text. 76 A>mov Ankakv .2 m._ E o._ 0.0 T . 033 om._...€_n_ 2265958 3% N.0 A>mwzik+kv S. ,m._ S o._ 038 8.. u 3a mcozocBEoo ¢Nm¢ 00. 00m 00m 00v A99 #07 SUNS/13 77 rapidly than single resonance production (as for p°f°). Table 12 and figure 16 show the cross sections from the maximum likelihood fits using (M, I‘)p = (750, 140) and (M, r)f = (1230, 180), in MeV. There is no A; production evident in the p°ni invariant mass plot. This is substantially different from the findings of reference l2 at 1.2 GeV/c where Agn; accounts for approximately 20% of the 4ncross sections. Apparently this final state has essentially gone to zero production at the higher momenta. These results are in good agreement with cross sections from other experiments shown in figure 16. 5.4 Five Pion Final States This channel is nearly 100% resonance dominated. The invariant mass distributions in figure l7, at l.80 GeV/c for example, indicate abun- dant p°, w°, and pi production, and the (nn)° invariant mass opposite the w° indicates both p and f° are produced with the ufi The (nu) invariant mass opposite a p indicates a p signal, but since the p has much greater background than the w°, this is not a clear indication of pp associated production. The maximum likelihood fits do indicate a fairly large p°pin’ final state, and nearly zero p°p°n° production at all momenta. The resonance parameters used were (M, 1")p = (750, 140), (M, r)w = (780, 50), and (M, r)f = (l230, 180), all in MeV. The cross sections are shown in table l3 and figure l8. The large errors assigned by the fit program arise largely because there is considerable anti-correlation between the single and double resonance production; e.g., the amount of popin; can be changed considerably with the opposite (or nearly so) change in p£3n and only a small change in the logarithm of the likelihood function results. Hence large uncertainties must be associated with any of these process 78 fl m¢\¢¢ m¢\mm m¢\mm mo.owo¢.o mo.owmm.o om.N w¢\N¢ m¢\m¢ m¢\m¢ mo.omo~.o mo.owo¢.o mm.N m¢\m¢ m¢\m¢ m¢\o¢ mo.ow¢¢.o mo.ownm.o om.N mv\o¢ N¢\mm m¢\Nm mo.onmm.o mo.oumo.o m¢.~ v¢\wm F¢\mm N¢\m¢ mp.owmm.o mp.owmm.o mP.N mv\om o¢\m¢ FV\NN vo.ow¢o.o Np.oumo.o ¢P.owmm.o mo.ommo.o mm.~ N¢\mm mm\mm o¢\mw 00.0Hop.o op.owmm.o o—.ouwm.o o~.omm~.o om.— ~¢\¢m QM\m¢ o¢\ow mo.ommo.o mp.omxm.o mm.ow¢m.o c~.omom.o mo.~ o¢\mm mM\¢N o¢\mu mo.ova.o m_.ouwm.o m~.ouom.o op.oumu.o Fm.P he“: weneh: ue+e oqoQ ewe“v FNoQ capoQ AU\>mwv amp; mcwm\mx Empmopmw: .chcmco ne~+em any so; as cw mcowuumm mmocu cowpozvoga mucmcommm .NF «Pam» 79 Figure l6. Resonance production cross sections in the 2n+2n- channel. Other experiments are: (l) 1.2 GeV/c, ref. 28; (2) 2.3 GeV/c, ref. 50; and (3) 2.5 GeV/c, ref. 43. 80 0.n §>§€r «w ow o... o._ Arh+homv b 0.3230 :3 2:25.096 3.20 o 2.853”... .2... m . w * W -m w trip. W - m: w W W W o m . 0.0 0v.- 00.. ON.- 0.0 v.0 0.0 0.0 ¢.0 0.0 0.0 #0 0.0 (aw) -0 81 Figure l7. Typical invariant mass distributions in the 2n+2n’n° channel at l.80 GeV/c with maximum likelihood fits described in text. 82 300. .mp1. .2 N. 0.. 0.0 0.0 q 4 4 q d 0;.0 8.. .32... 202050600 ommu. o 9 3 8 N A99 2079.11st v.- N.. $6 8.. . as... 20.803600 mmnw 8 8 8 n N . '- AOQ ZO'IS‘JNSMEI § 300: 0.. 0.. _ 82.0 8.. . ez... 0003003500 000m. n.- u q .0101... or... .s. 0.. 4 V0 00. 00m 00m 1 00¢ $03 Wu: 2 V. N._ 0.. q £60 3.. . .3... 22.2358 :8. 0.0 d d d 0.0 d 000 N0 00. 00N 00m tOOV 000 A 99 £0 '/ SJNBAH A99 30 '/ $1N3/l3 83 . om\_m oo\om oo\- oo\mm om\mm om\m~ om. om\_m oo\m¢ oo\ou om\m~ om\mm om\mn mu.m oo\mo oo\om oo\- oo\wm oo\mm oo\eop om.~ nm\m¢ ~m\mm oo\~m om\F~ oo\m~ mm\ea me.~ ¢m\m~ om\em oo\- oo\mo om\mm mm\m~ m~.~ mm\Pm em\om oo\mm om\m~ o0\~¢ mm\mn mm”. Fm\mop ~m\mm oo\m_p oo\e._ om\emp Nm\mpp om.~ me\nop omxmu om\~op oo\mm oo\¢_p om\on mm.p me\~m m¢\mo om\oep om\mmp oo\m~_ m¢\mm Pm _ :lhl: plhlu. I=1... 2. a. :1... .F t .F o + + $ + + + + i + o + o I + mcwm\mx Emgmoumw: mo.ona~.o mo.onmo.o m_.onm~.o mm.onmm.o «F.0hpo.o “a.onom.P mm.onom.o om.~ __.onmm.o mo.onoo.o -.onmm.o mm.onpm.o o..onon.o m¢.onmm._ mm.onpm.o mn.m mo.ono_.o No.onoo.o e~.onoo.o mm.onmm.o mp.onmm.o «c.0an.N ~¢.onmm.o oo.~ mp.onmm.o mo.onm_.o mP.onmN.o mm.onm_.P m_.onmm.o om.on~o.~ eq.on¢¢.o m¢.~ ap.onnm.o uo.on¢o.o ep.onoo.o ma.onee.. NN.on-.F mm.on¢m._ om.onmm.p m_.~ mp.onmm.o no.onoo.o mp.onm_.o ¢¢.on~m.~ NN.onmm._ Fm.onm~.F mo.onm~.o mm.P wo.onmm.o mo.on~_.o mo.onmo.o en.onon.. up.onm¢.p N¢.onom.~ om.onmo._ om." mp.onpm.o mo.onme.o nm.on~m.o ma.oam~.~ m_.onpm.o o¢.onoo.m eo.onum.p m0._ m..on¢w.o mc.onmm.o mp.onm..o mm.onon.~ mm.ono¢._ om.on-.. em.onn~.p Fm.F owes oaoa oeoaoa weoana emoa emnq emoa .unwww. .chcmso oeue~+e~ 050 com 02 cw mcowuumm mmocu cowuuauoca monocommm .m— 0.00» 84 Figure 18. Resonance production cross sections in the 2n+2n-n° channel. Other experiments are: (l) l.ll, l.33 and l.52 GeV/c, ref. 3; (2) 1.2 GeV/c, ref. 28; (3) 2.3 GeV/c, ref. 50; and (4) 2.5 GeV/c, ref. 43. 85 .850. n.sn. 0.m 0N N.N m _ ¢.. 0.n 0N N N m _ v. 0.. _ 4 d 4 - _ _ - W — f. _ q J. _ . q .1 1% W wow 1. a 4 4 i i w * w W W 1. . m L. a .. J I .. . . - AhNoavb Ahm 003.0 i a .. .. 1 I Automwmvb % .. 1 I i W r 1' J: I4! L: J i a L. 1 222.8 3m. .. 5.3m 350 m .. .. in «a. . b 4 u .20 a...» m -- L m + W o W: 3...... ..... .m.. l Aowoavb W W m 4: rhoiomvb I. _ _ _ 0.0 v0 0.0 N.. 0.. ON ¢.N 0.0 ¢.0 0.0 N._ 0.. ON ¢.N 0N N.» m.» 0.0 V0 0.0 N._ (aw-o 86 amounts. In much the same way as in the 4n channel, the associated re- sonance processes are nearly zero at all momenta (as for p°p°n°), or are decreasing considerably faster than the single resonance processes (as for p°pin7). This may be due to the associated resonance processes being quasi-two-body or quasi-three-body and therefore behaving more as a nucleon exchange process, whereas the single resonance processes may be viewed as final state interactions in a "fireball" type annihilation. However, these observations do not seem to hold in the case of w°nn and w°f°, w°p°; for these processes the w°nn state falls more rapidly than wPf°, and w°p° is essentially zero at all momenta. 5.5 Six and Seven Pion Final States Both of these channels are very difficult to analyze for resonance production due to the large number of combinations involved in any given process. The only clear resonance signal is the w° in 3w+3n'n°, while the nu histograms show only a broad shoulder where the p should be. The maxi- mum likelihood fits obtained in the 3n+3n- channel indicate two solutions: a) (l0 b) (95 H- 15)% p°4n + (75 i 10)%p°p°2n or, 10)%p°4n + (5 i 15)% p°p°2n. H- In either case, the 3w+3n' channel is consistent with at least one p° per event at each of the four momenta l.5l, l.65, l.80, and 1.95 GeV/c. The n+n-no histograms in 3n+3n'n° indicate w° production percentages of 48, 36, 47, and 35 with errors :5% at l.51, l.65, 1.80, and 1.95 GeV/c, respectively. Hhile p° and p: production is evident as a small bump in the appropriate mass spectrum on the high side of phase space, extracting it is difficult. The prediction of 50% p(l/l8 combinations) plus phase space looks only slightly different than phase space alone when compared to the 87 1 data. Hith approximately 50% w° production, there is probably associated w°p°; however no attempt has been made to obtain this cross section due to the very large number of combinations (36) involved. CHAPTER 6 MULTIPLICITY IN THE ALL-PIONIC ANNIHILATIONS For those events in the zero-constraint classes of all charged pions with a missing mass of two or more neutral pions the cross sections as a function of the number of missing neutral pions have been determined. In particular, the possibilities considered were n+n'nn°, 2n+2n'nn°, 3n+3n’nn° where 2 5 n 5 4, and 4n+4n-nn° with n = 1,2. This was done by forming, for example, the invariant mass M(uinn°) in the case of 2n+2n'nn° and fitting this mass distribution to a superposition of Lorentz invariant phase space (LIPS) mass dis- tributions for (n + 1) pions out of an (n + 4) pion final state. Studies of the constrained events indicate that, due to the large number of combinations involved, even with the dominance of reson- ance production the multipion annihilations can be largely described by LIPS. The experimental mass distributions used for determining the number of neutral pions show no obvious resonance signals which is possibly due to (1) poor resolution in the zero-constraint class (m 60 MeV), (2) the combinations involve, for the most part, three or more pions with no direct resonances possible, and/or (3) the number of wrong combinations dilutes the effect of resonance where they exist. Furthermore, excellent agreement was obtained with only two or three phase space distributions entering into the fit indicating that there 88 89 are no serious distortions due to reflections of resonances in other combinations than those used. There are several mass combinations possible in each final state which may be independently treated in this fashion as a check on the method. For example, in the n+n’nn° case, M(n*n'), which showed no appreciable p° signal, was fitted to a combi- nation of two pion LIPS out of an m pion system, 4 5 m 5 6. The re- sults are then compared with fits of M(nw°) to LIPS distributions cor- responding to n pions out of an (n + 2) pion final state. The two prong missing mass channel was the least well determined using this method and good agreement was obtained at only seven out of the nine momenta. The disagreements were averaged giving results compatible with neighboring momenta. The resulting multipion cross sections as a func- tion of the number of neutral pions have been combined with the cons- trained fit cross sections to obtain the overall multipion cross sec- tions as a function of the number of pions, N, regardless of charge. These cross sections are shown, averaged into three groups of three ad- ‘jacent momenta each, in figure 19, with the weighted averagei(N). Also shown is the average number of charged pions,«(Nch), obtained by a weighted average over the number of charged prongs, and the average number of neutral pions,(Nneut), which is the difference between (N) and (Nch). G. van Keuk51 has developed a statistical model which pre- dicts the solid line shown in figure 19 foroo ohmuAav q ox>0o 9N» Aav 1" o\>00 00.. u Aav /.m 0. 0. ON mun-o 92 in figure 11 and 13 are similar predictions from the statistical model mentioned above. The multiperipheral model describes the data reason- ably well for all reactions 2n - 7n. The statistical model prediction for n+n'n° grossly underestimates the data and hence is not shown in figure 9. The 4n and SN predictions are about as good as the multiperi- pheral model, whereas the 6n and 7n predictions considerably overesti- mate the data. The statistical model has virtually no free parameters and the calculations assume (m/E*) + 0, and works best for large N(? 8). Hence it is not too surprising that the agreement using this model is only qualitative. CHAPTER 7 SUMMARY AND CONCLUSIONS Topological and reaction and resonance production cross sections have been determined for antiprotons interacting with protons between 1.51 and 2.90 GeV/c which are in good agreement with other experiments at nearby momenta. Using the data from this experiment and from others the origin of the structures in the pp total cross section have been particularly sought. Assuming the bumps to be direct channel effects we have ruled out the possibility of any significant contribution to them arising from the zero or six prong topologies; however, the fits described in the text do not rule out either the two prong or the four prong topologies as the source of the structures in the total cross section, except that the 2190 Mev bump is still significantly required after subtracting the four prong cross section from oT(pp). Examina- tion of the reaction cross sections, where the enhancements might be more noticeable, shows no evidence for any significant bumps. The data from this and other experiments supports the conclusion that neither of the enhancements in the total cross section can be accounted for as a threshold effect due to a single or double pion production without anni- hilation.- These results are compiled pictorially in figure 20. The technique of fitting subtracted cross sections is highly de- pendent on having a large number of closely spaced data points, parti- cularly in the bump regions, and is not sensitive to the possibility of 93 94 Figure 20. Summary of results of subtracted cross section fits. The quantity PR (see chapter 3) gives the amount of total cross section bumps which may be accounted for in the indicated channel. 95 (_.a+ad_q).a+(a~/_v) .o .0 ._o_. (9NOHd -9) -0 -> r-o-a (QNOHd - t!) -0 -> I——O-—l (QNOHd -Z) -0 -> F {k % (QNOHd -0) -0 + t—O—t a. .1. .k a N . -0. :8 ~. o -"3 8 2; - .0 N E ,, a. o Ci> I 1 3 2 : 3 8 3 1qu (CL)? #514 d_d).o +(aN_/g) .0 -> ._o_i (ONOUd-Q) 9 "D l-O-l (QNOHd-V) -0 -’ l-—O—-| (ONOHd-Z) -0 -' t—-—O-———-i (QNOHd-O) 1’ -> 1-04 I l 1 m V O aw (06/2) ”0 96 these structures being built up from many small effects spread among the seen and unseen channels. The investigation of resonance production cross sections yields no evidence for the enhancements except for the fairly narrow 6N + K*Knn enhancement seen at 2360 MeV in this and a 6d experi— ment; at this juncture, the source of the structures continues to be elusive. The multipion annihilation cross sections have been determined as a function of the number of pions, independent of charge, and indi- cate a rapidly increasing average number of pions in this momentum range. 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