Antiproton-Proton Annihilation Into Four and Five Pions at 2.4 and 2.9 Gev/C Ronald Paul Radlinski Iowa State University

Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations

1970 Antiproton-proton annihilation into four and five pions at 2.4 and 2.9 GeV/c Ronald Paul Radlinski Iowa State University

Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Elementary Particles and Fields and String Theory Commons

Recommended Citation Radlinski, Ronald Paul, "Antiproton-proton annihilation into four and five pions at 2.4 and 2.9 GeV/c " (1970). Retrospective Theses and Dissertations. 4191. https://lib.dr.iastate.edu/rtd/4191

This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 70-18,900 I I RADLINSKI, Ronald Paul, 194-2^ | ANTIPROTdN-PROTON ANNIHILATION INTO FOUR AND \. FIVE PIONS AT 2.4 AND 2.9 GeV/c. l i lowa State University, Ph.D., 1970 ' Physics, elementary particles |

University Microfilms, A )(|ERQ\Company, Ann Arbor, Michigan %

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED ANTIPROTON-PROTON ANNIHILATION INTO FOUR AND FIVE PIONS

AT 2.4 AND 2.9 GsV/C

Ronald Paul Radiinski

A Dissertation Submitted to the

Graduate Faculty in Partial Fulfillment of

The Requi rements for the Degree of

DOCTOR OF PHILOSOPHY

Major Subject": High Energy Physics

Approved:

Signature was redacted for privacy.

Heatr ofvMajor Department

Signature was redacted for privacy.

Iowa State University Of Science and Technology Ames, Iowa

1970 PLEASE NOTE; Not original copy. Several pages have indistinct print. Filmed as received. University Microfilms. 11

TABLE OF CONTENTS Page I. INTRODUCTION 1

II. EXPERIMENTAL PROCEDURE 3

A. Beam Characteristics 3

lo General properties 3

2o Specifics of this experiment 4

Bo Scanning and Measuring 4

Co Identification of Events 5

lo Fitting and biases 5

2o Final state classification 8

Do Data Samples Used for Analysis 11

1. Beam restrictions 11

2. Restrictions on track measurements 12

3o Missing mass squared and chi-squared restrictions 14

4. Final data samples 17

I No CROSS SECTIONS 18

IV. EFFECTIVE MASS DISTRIBUTIONS 23

Ao General Method of Analysis 23

B. Resonance Production in the Four Pion Channel 24

1. General features 24

2o Dipion effective mass distributions 28

3» Three pion effective mass distributions 29

4. Associated production in the four pion channel 34

5. Summary of the production modes in the four pion 37 annihilation channel

Co Resonance Production in the Five Pion Channel 39 Mi

lo General features 39

2o Dipîon effective mass distributions 45

3o Three pion effective mass distributions 46

4o Four pion effective mass distributions 49

5» Associated production in the five pion channel 56

6o Summary of the production modes in the five pion 57 annihilation channel

Do Effective Mass Distributions of the 4itMM Events 57

ANGULAR DISTRIBUTIONS 64

A. Production Angles of Pions 64

Bo Pion Correlation Angles 72

Co Angular Distributions of Resonance Production 82

lo Production angles of resonances 82

2o Decay angular distributions 85

CONCLUSION 89

BIBLIOGRAPHY 91

ACKNOWLEDGMENTS 94 1

I» INTRODUCTION

This dissertation is an investigation of the four-prong reactions

(1)

(2)

(3) at incident antiproton momenta of 2.4 and 2»9 GeV/c. The film analyzed

in this experiment was exposed in the Brookhaven National Laboratory's

31 inch hydrogen bubble chamber during June, I967. Approximately 60,000

pictures were taken at 2.4 GeV/c and 40,000 pictures at ,2.9 GeV/c. Other experiments involving the above reactions have been reported at momenta of

1.1 to 1.52 GeV/c (0,1.2 GeV/c (2,3), 1.2 to 1.6 GeV/c (4,5), 1.51 to 1.95

GeV/c (6), 1.6 GeV/c (7), 2.5 GeV/c (8,9), 2.7 GeV/c (10), 3.28 GeV/c

(11), 3.6 GeV/c (12), 3.66 GeV/c (11), 5.7 GeV/c (13-15), and 6.9 GeV/c (16).

\The opportunity to study single and associated resonance production

• Is.a prime consideration for analyzing the above final states. The

investigation of the energy dependent properties of the resonance

particles over a limited momentum range is made possible by performing the

experiment at both 2.4 and 2.9 GeV/c. The cross sections for resonance

production as well as for the total cross section of the above final states

are found, in general to decrease as the incident antiproton momentum is

increased from 2.4 GeV/c to 2.9 GeV/c. A high percentage of the pion

annihilations is found to proceed through an intermediate three meson

state. In the four pion channel, the dominant modes of production at both

momenta are through the following three meson reactions — o + • PP -» p ît ît 2

— -O + - pp f jr 3t ,

.where both the neutral rho meson (p°) and f meson (f°) subsequently decay into a 3t ït pair* Indications of associated production are found in the four pion channel at both momenta. A significant fraction of the five pion events proceed via

— o o o PP p P 3C

— ± o T pp p p It

— o + - pp CU 3t

The charged rho (p^) decays into a pair while the omega (iu°) decays

via a* ïC jr°. There are also indications of Aj (_> pir), AgC^. p#), and B(-, m%)

resonance production in the five pion channel. Evidence for A^ production

as well as for a possible f°jt resonance is found in the four pion channel

at 2.4 GeV/c. The analysis of the unconstrained pp _• lit nit® (n > 1)

events gives evidence only for p° production.

Single pion and dipion production angles are investigated in the center

of mass system. The tendency of the jt (it ) to be emitted in the direction

of the p(p) increases, in general, with energy and decreases with multiplicity.

Quantitative measurements of the asymmetry characteristics of angular dis

tributions are obtained from the forward to backward ratio (F/B), the

polar to equatorial ratio (P/E) and the correlation parameter (7).

The dependences of the F/B and P/E ratios on pion momentum are investi

gated for chosen momentum intervals. Production angles and decay angular

distributions are given for resonance production in which the signal is

strong enough to allow a meaningful background substraction. 3

11. EXPERIMENTAL PROCEDURE

Ao Beam Characteristics

]o Genera1 Proper ti es

To obtain an antiproton flux of specified properties from the Brook- haven National Laboratory's AGS (Alternating Gradient Synchrotron), hydrogen ions are initially preaccelerated to an energy of 750 keV by a Cockcroft-Walton generator. The ions are further accelerated by a linac

(linear accelerator) which increases their energy to 50 MeV. The parti cles are then injected into a vacuum tank which is inside the magnets of the synchrotron. The magnetic field then rises in step with the increasing momentum of the protons as they are accelerated by successive traversais of one or more gaps across which R. F. fields are provided. After the protons have reached a desired momentum, a portion of the beam is spilled onto a suitable metallic target. The interaction of the deflected beam and the target results in a flux of secondary particles such as pions, kaons, antiprotons, and muons. This secondary beam of particles passes through a transport system which consists of dipole magnets, quadrupole magnets, and mass slits that focus the beam and select particles of a desired momentum. The next stage, which consists of an electrostatic separator and another mass slit, is tuned to allow only the passage of antiprotons. The beam separator is comprised of crossed electric and mag netic fields that pass only particles of a designated velocity. Since all particles have approximately the same momentum at this stage, the process

is equivalent to selecting particles of a particular mass. The beam is

subsequently refocussed, sent through another momentum selection stage,

another mass separator stage, and finally into a beam shaping section that h spreads the beam for a uniform coverage of the bubble chamber in which the reactions are to occur.

2. Specifics of this experiment

By placing a scintillation counter behind the second separator during the tuning of the beam, a distinct separation of pions, kaons, and antiprotons was found at each momentum. To insure constant running conditions throughout the experiment a Cerenkov counter was placed behind the second

\ mass slit to monitor the pions and muons. Since the beam was estimated to consist of more than 99% antiprotons, no corrections have been made for beam contaminations. A counter at the entrance to the bubble chamber trig gered the cameras only when the incident antiproton flux was between six and sixteen particles/pulse. Acceptance of less than six incident particles per picture would decrease the interaction statistics while more than six

teen incident tracks per picture is too high a density for efficient scanning and measuring of the film.

In a later analysis of the beam momenta from events with a unique final state (pp ^ pp It ) (17) the distribution of the beam momentum for the

two exposures was determined to be 2375 + 75 MeV/c and 2885 ± 80 MeV/co

Although the film was processed with the above values for incident momenta,

the two data samples will be referred to in this presentation as having

incident antiproton momenta of 2.4 and 2.9 GeV/c.

B. Scanning and Measuring

From the 100,000 picture exposure, 58,277 pictures at 2.4 GeV/c and

37,189 pictures at 2«9 GeV/c were found suitable for scanning. A scan of

these samples for four-pronged topologies in a restricted fiducial volume

of the chamber resulted in 17,613 events at 2.4 GeV/c and 10,246 events at 5

2.9 GeV/co From the events found in the restricted fiducial volume^

15^965 events at 2.4 GeV/c and 9,393 events at 2.9 GeV/c were measured. An event would be classified as unmeasurable if the tracks were too faint or obscured in some manner. An event was measured in three views by recording points on the tracks relative to fixed fiducial marks. Most of the measure ments were recorded on punched cards as input to the special reconstruction program which provided calculations of momenta, angles, and positions together with their associated errors, for all measured tracks. If an event failed to reconstruct properly or did not obtain an acceptable fit, it was submitted for remeasurement. After about 85% of the film was measured by the above procedure, the measuring machines were interfaced to a computer

(18). This system provided immediate knowledge about event reconstruction and eliminated long remeasurement delays.

Co Identification of Events

1. Fittinq and biases

For all events which passed the reconstruction routines, kinematic

fits, consistent with the laws of strongly interacting particles, were

attempted for various mass assignments. Since, for a four particle mass

hypothesis to a four-pronged event, all variables (azimuth, dip, momentum)

associated with each particle are known, the energy-momentum relations

made this assignment a four-constraint fit. The inclusion of a neutral

particle in the above mass hypothesis introduces three missing variables

and thereby reduces the number of constraints to one. The addition of more

than one neutral particle to the four particle mass assignment obviously

makes the fit unconstrained.

The kinematic program GUTS (19, 20) was used to fit all reconstructed 6

four-pronged events. The program subjects each attempted fit to tests on missing mass and chi-squared. The missing mass for a given mass assignment is defined by the relativistically invariant equation

(NM)^ = - (jS E.)]2 - [P^ - (J, P.)]2 (4)

—& where and are the total energy and momentum of the incident particles, •H while E. and P. are the total energy and momentum of the jth outgoing track. ' J The chi-squared is related to the confidence level of a fit and is defined by (13)

S S 3 (5) k=l ^=1 ^ Kt

Here n, the number of variables associated with each track, is 3 and m, the total number of tracks, is 5 for a four—constraint fit and 6 for a one-constraint fit. is the measured azimuthal angle, A^g 's the tangent of the measured dip angle, and Aj^ is the measured curvature, of the kth track. The quantities B», are the associated fitted values and aA„. are the associated uncertainties in the measured quantities.

A kinematic fit was attempted to the four pion hypothesis if the missing mass was within six standard deviations of zero and accepted if the chi- squared was less that 31. A fit to the five pion assumption resulted if

the missing mass was less than three standard deviations from the mass of

the jt° and the chi-squared was less than 13. More restrictive selections

would have eliminated real fits from the samples. A greater missing mass

range was allowed for the four pion fits because these events have a smaller

background contamination than do the five pion fits. The contaminations

are discussed in the follow! ng paragraphs. 7

Four-pronged events classified in the following categories were eliminated-from the sample:

pp pp 3r 3t

— + - o pp Jt at jt

— + + - pn It 31 Jt

^ mm np :t Jt It

These events have been investigated in a separate study (I?)* Events obtaining a four constraint fit to the 2K 2jt hypothesis were eliminated 1 from the samples if x 2jt2K less than the chi-squared for a correspond ing four pion fit and/or the chi-squared probability for the kaon-pion fit was less than that for a corresponding five pion fit. The contamina tion in the four pion final state which arises from four-constraint reactions involving nucléons or kaons is small in view of the kinematically over determined nature of these fits and the use of ionization criteria.

Events which were identifiable on the basis of ionization as four-constraint nucléon or kaon events frequently had a fit to the five pion hypothesis.

These one-constraint fits characteristically had the jt° moving backward in the center of mass system. This result is understandable in that the kinematic program^ in making the incorrect five pion fit, introduces a slow

jt° in the laboratory. This result is equivalent to a jt° going strongly backwards in the center of mass» No fits were attempted to the KK jt jt jt

hypothesis because there is no reliable method of distinguishing these one-

constraint fits from fits to the five pion hypothesis. Since the cross

section for the KK at jc at reaction is believed small compared to the cross

section for the five pion annihilations in"the 2.4 to 2.9 GeV/c momentum

range (21), no corrections have been made for this contamination. 8

The largest contamination in the five pion category consists of pp _» 2i^ 2ît nrt° (n > 1 ) reactions. These multineutral pion events are introduced into the sample through the errors associated with the missing masso : As noted previously, the missing mass had to be consistent with the mass of the assumed neutral pion within three standard deviations. If MM is the missing mass, m^, the mass of the neutral pion and ^KM the error in the missing mass, this implies iMM - m^l - 3 6MM must be less than or equal to zero. With a large aMM, a fit might be attempted for an event with uncertainty in the missing mass of order of one or two pion mass and thereby allow for the inclusion of multineutral pion events in the sample.

Various selection criteria discussed in later sections were imposed on the five pion sample to reduce this contamination.

2. Final state classification

Many events that received a fit to four pions also satisfied the five pion hypothesis. Such kinematically ambiguous events having a four pion 2 fit with X less than 20 were retained in the four pion sample if either 2 • o the five pion fit had a ^ greater than 1.5 or the momentum of the it was less than 175 MeV/c in the center of mass system. The reliability of such low momentum 3t° assignments is small because of the characteristic high uncertainty in the 3t° direction. A subsample of the ambiguous events had a missing mass near that of the jt° mass and obtained high probabili

ties for both the four and five pion fits. These small sanples of events were placed in 5it) Ambiguous" categories and not considered in the analysis of either final state. Four-pronged reactions that did not

satisfy a constrained pion fit or a fit to reactions involving nucléons or kaons were classified as unconstrained events. The number of events in the 9 various categories at each momentum are shown in Table 1.

Table lo Number of events in the four-pronged pion categories at 2.4 and 2.9 GeV/c

Category 2.4 GeV/c 2.9 GeV/c

860 events 405 events

(4it, Sît) Ambiguous 83 18

5* 5184 2752

Unconstrai ned 8405 5007

Estimates of the multineutral pion background in the Sit category were

determined by the percentages of Sit and 6jt Lorentz invariant phase space

predictions for the distribution. Contributions from 3#/7#

and Bjr/Sit phase space predictions were negligible. This procedure gave

values for multineutral pion background of 34 + 5% at 2.4 GeV/c and of

39 ± 6% at 2.9 GeV/c.

Figure 1 shows the plots of the missing mass squared of the unconstrained

events at 2.4 and 2.9 GeV/c where four pions have been assigned, to the

charged tracks. From phase space consideration as discussed above, events

with a missing mass squared less than zero are believed to be missed four

and five pion events and appropriate corrections were made in cross section

calculations. Events with a missing mass squared value greater than zero

were determined to be mainly multineutral pion events and will be referred

to as the 4ïtMM sample. The background in this category consists of KK it jr it

events and any other constrained events which were missed by the fitting 10

2.4 6eV/c 8405 UNCONSTRAINED 300 (O EVENTS

5200

-3.00 -2.00 -1.00 0.00 100 2.00 300 g (MM)2 (GeV/c2)

2.9 GeV/c 5007 UNCONSTRAINED H150 EVENTS

5100

3 50

-3.00 -2.00 -1.00 0.00 100 2.00 300

Figure 1. MM distributions for the unconstrained events when pion masses are assigned to the four charged tracks 11

procedureo

Estimates of pion multiplicity in the multineutral events were made ± ± T by fitting the jt it it invariant mass distributions of the 4itMM sample with 3it/6it, 3it/7it and 3%/8# phase space predictions and also by considering

the multi neutral pion background determined in the git sample. The frequencies

for 6it, yitj and 8it occurrences are given in Table 2o

(

Table 2. The frequencies for 6it, 7ît and 8it reactions at 2.4 and 2.9 GeV/c

Reaction frequency at 2.4 GeV/c frequency at 2.9 GeV/c M M C C ?p T 2it° 0.34 + 0.08 0.35 +0.10

pp _» 2/ 2it" 3*° 0.61 + 0.19 0.56 + 0.21

pp _ 2/ 2it" 4it° 0.05 + 0.04 0.09 + 0.05

Do Data Samples Used for Analysis

To obtain data samples for the analysis of the constrained final

states with the minimum amount of background, restrictions were imposed on

beam characteristics, track measurements, missing mass, and chi-squared.

Each of these selections is discussed below in detail.

1. Beam restrictions

;o Restrictions on the vertex position, dip, and azimuth of the incident

beam tracks were obtained by plotting these quantities for four, pronged

events at each ^omentum. The x-vertex for the beam track was required to

lie between 2.5 and 20.0 inches. .The dip was restricted to be within five 12

degrees of zero and the azimuth as a function of the vertex position along the incident beam direction was required to be within the outlined areas shown in Fig. 2a for events at 2.4 GeV/c and Fig. 2b for events at 2.9

GeV/c. Additional restrictions were placed on the fitted beam momentum.

For the four pion events, the momentum was required to be within 165 MeV/c of the central fitted beam values of 2375 MeV/c and 2885 MeV/c. For the 5# events, the beam momentum was restricted to the ranges 2275 MeV/c to 2450

MeV/c at the lower momentum and 279O MeV/c to 2950 MeV/c at the higher momentum. Only the above restrictions on the vertex position were imposed in the study of the 4jt MM events.

2c Restrictions on track measurements

To eliminate poorly measured events in the one-constraint Sit fits and

4ît MM categories, loose cuts were made on the error in momentum divided by the momentum (Ap/p) from graphs displaying regions of outgoing urack lengths and particle momentum. The Ap/p restrictions at 2.4 GeV/c are given in

Table 3 and at 2.9 GeV/c in Table 4,

Table 3® Ap/p (error in momentum/momentum) restrictions as a function of track length (L) and momentum (p) at 2o4 GeV/c.

P < 400 MeV/c 400 MeV/c ^ p ^ 800 MeV/c p > 800 MeV/c V L C 0.58 0.60 0.57 4 in < L <8 in 0.25 0.275 0.30 L > 8 in 0.105 0.11 0.115 13

1- 1 111"T"]" •

—

—4——1—1—I- • I

2.4 GcV/c 4: PRONGS f 5000 EVENT SAMPLE • /ix'l . J

J1 I.. 1 U,„ 1 -10-8 -6 -4 -2 0 2 4 6 AZIMUTH or- BEAM DEGREES

2.9 GeV/c 4-PRONGS 5000 EVENT SAMPLE

-10-8 -6 -4 -2 0 2 4 6 AZIMUTH OF BEAM DcGFÎEES

Figure 2. Scatter plots of the beam azimuth versus the position of the vertex along the incident beam direction. The boxes indicate the restrictions used in determining the final data samples 14

Table 4. Ap/p (error in momentum/momentum) restrictions as a function of track length (L) and momentum (p) at 2.9 GeV/c

p < 400 MeV/c 400 MeV/c ^ p ^ 800 MeV/c p > 800 MeV/c

L < 4 in ' 0.56 0.60 0.49 4 in < L < 8 in 0.24 0.27 0.30 L > 8 in 0.105 0.125 0.125

These restrictions eliminated about 12% of the events in the 5Jt sample

at each momentum. These same cuts reduced the 4aMM samples about 11%.

3» Missing mass squared and chi-squared restrictions 2 2 From the distributions of MM and for the four pion events at both

momenta displayed in Figure 3, the following restrictions were applied to

the 4it categories: 2 ,i) the missing mass squared had to be within the range -0.16 (GeV/c )

to Ob 16 (GeV/c^)^

ii) the chi-squared maximum was set at 20.

Similar restrictions for the five pion fits were obtained from scattergrams

of the missing mass squared plotted against chi-squared as shown in Figure

4a for 2.4 GeV/c and Figure 4b for 2.9 GeV/co The asymmetry in the scatter- 2 plot indicates the inclusion of multineutral pion events for MM greater

than zero. The restrictions that

i) the missing mass squared of the 5îr fit had to be within

-0.115 (GeV/c^/ to 0.115(GeV/c2)2

ii) the chi-squared value of these one-constraint fits had to be less

than two

were chosen so as to eliminate as much background as possible without 1 rr "1 2.4GeV/c (a) 860 4Tr EVENTS 2.4 GeV/c (b) 860 4 TT EVENTS w PÙI60 u. 40 lu o 0 0: w 3 m 1 80 S 20h D 3 Z Z " unJne'^J 1 1 -0.40 -0.20 0.00 0.20 0.40 16 24 32 (MM)^ (GeV/c2)^

1 1 I - 1 2.9GeV/c 2.9GeV/c (c) 405 47r EVENTS (d) 405 4 TT EVENTS

4.00

X 2.00

0.00 a\ 0)

2.4 GeV/c 5184 EVENTS

-0.8 0.00 0-8 A 2 ( MM) (GeV/cZ)^

Figure 4a. Scatter plot of the chi-squared versus the missing mass squared for the five pion events at 2.4 GeV/c 6.00

4.00

CM X 2.00

000

ot cr

2.9 GeV/c 2752 EVENTS

-1.2 -0.8 -0.4 0.00 0.4 0.8 « (MM)2 (GeV/c^) Figure 4b. Scatter plot of the chi-squared versus the missing mass squared for the five pion events at 2.9 GeV/c 17

substantially biasing the five pion samples.

Final data samples

After the and beam restrictions were imposed on the four pion

category, 758 events at 2.4 GeV/c and 356 events at 2.9 GeV/c remained

for analysis. The five pion selection process eliminated most of the multi-

neutral pion background. Approximately 25% of the real five pion fits were

lost by the selection criteria. Since many of the lost events can be clas

sified as poorly measured, no systematic biases are believed to be introduced

into the five pion samples used for analysis. The final selected samples

of. 2631 events at 2.4 GeV/c and 1216 events at 2.9 GeV/c are believed to

have less than 4% background contaminations. The samples surviving the

cuts on the kit MM events consisted of 6728 events at 2.4 GeV/c and 4216

. events at 2.9 GeV/c. Table 5 gives a summary of the final selected data

samples.

Table 5- Summary of data samples used in the analysis

Category 2.4 GeV/c 2.9 GeV/c

4îr Events 758 356

5 Events 2631 1216

kit MM 6728 4216 18

III. CROSS SECTIONS

The cross section for the i reaction is obtained from the expression

(g (R Ng) (tpN^ )

The quantities in this expression are defined in the following list:

1« N. is the number of measured events of the ireaction.'

2. S, the scanning efficiency, was determined by rescanning 10,000

frames at each momentum. Only events found in the first scan

were included in the sample of events measuredo

3. is the number of events found in the first scan.

4. R is the ratio of the number of events passing reconstruction to

the number of events found in the first scan.

5. Ng, the average number of beam tracks, was determined by counting

the number of beam tracks in the fiducial volume for every tenth

frame of the film.

6. A is the atomic weight of hydrogen.

7« ' tj the average length of the interacting beam tracks in the

fiducial volume, was determined from the distributions of the vertex

position in the bubble chamber.

8. p is the density of hydrogen at the operating temperature of the

chamber. The density was calculated by comparing the mean lengths

from n /n e decays, when the it decays at rest, wi th the known range

of such muons In hydrogen as a function of density.

9* is Avagadro's number.

1 Corrections arising from the four-prong, l.vee events, where the vee was determined to be a Dalitz pair, were included in the cross section calcula tions. 19

Cross section corrections were made for four and five pion events that were lost through the missing mass tests made in the kinematic fitting procedure (Section II). One method of determining the number of these lost MM events was to plot the quantity (7^) for the fitted four pion events or .AMM ( ) for fitted five pion events and then estimate the missed events in the tails of these distributions beyond the imposed cutoff. The other procedure use was to assign pion masses to the four charged tracks of events in the unconstrained category and then determine, the percentages of 3îT/5îtj and 3#/7# phase space contributions needed to fit + ' + T the jt-Tt—jr effective mass distribution of the events receiving a missing 2 2 mass squared assignment between the wide range of -1.0 (GeV/c ) to 2 2 1.0(GeV/c ) . Both methods showed that at each energy approximately k% of the real four pion events and 23% of the real five pion events were lost through the missing mass tests used in the kinematical fitting of the four-pronged events. It was assumed that these lost events have the same mass distributions, the same angular distributions, etc» as the corresponding events which obtained fits.

The values used in calculating cr. for the four-pronged pion annihila tion channels are listed in Table 6. These reaction cross sections at 2 2.4 GeV/c and 2.9 GeV/c are given in Table 7 « The reaction cross sections for four-pronged pion annihilations as a function of incident antiproton ^The number of events measured at each momentum was primarily determined by a study of the reaction "pp -* (17)° While the cross section for this reaction rises with increasing Incident momentum, the cross sections for the four and five plon final states fall with Increasing momentum. Thus, although the cross sections for the annihilation channels is higher at 2.4 GeV/c than at 2.9 GeV/c, more pictures were measured at the lower momentum. In general, the statistics for the annihilation reactions at 2.4 GeV/c are twice those for the corresponding reactions at 2.9 GeV/c as seen in Table 1. 20

Table 6» (Quantities used for calculation of reaction cross sections

. • 2.0k .Ge.V/.c ... .2.9 .Ge\//c_.. .

N. (2« 2n ) 953 437-

Nj (2ît^ 2ît 4548 2258

Nj (2jt^ Ztc nj(\ n ^ 2) 8895 ' 5473

S 0.88 0.92

R 15,965/17,613 9,393/10,246

58,^77 37,189

8.81 8.75

A 1.008 gm/atomi c wei ght

I 15.61 + 0.37 in. 15.24 + 0.25 in.

0.0658 + 0. 0005 gm/ctn^ .23 6.025 X 10 atoms/atomic weight

Table 7» Cross sections for four-pronged pp annihilations into pions at 2.4 and 2.9 GeV/c

Reaction 2.4 GeV/c 2.9 GeV/c

pp =4 2it 2j( 1. 49 ± 0.1 1 mb 1. 05 + 0. 13 mb — — o pp ^ 2jt 2jt n 7.13 ± 0.56 mb 5.42 ± 0.52 mb

PP 2it 23t n«° (n > 1) 13.9 ± 0.7 mb 13.1 + 0.8 mb 21 momentum are shown in Figure 5» The four and five pion reaction cross sections at 2,4 and 2.9 GeV/c are in good agreement with the decreasing slope of other experimental data points. From the large scatter of points for pp -, 2:t^2it n3(°(n > 1) cross sections as a function of p momentum,

(Figure 5c) no energy dependence is apparent for these reactions. 22

' pp-^ir*ir*-ir-ir- 4 MSU (preliminary) 4 BNL " - 4 OTHER J3 4 E t ANL (preliminary) i 4 ISU

s g

_L P MOMENTUM (LAB) . GeV/c

I I 16 pp—'v*ir*ir-v-ii* (b) ^ MSU (preliminary) 14 4 BNL " " 4 OTHER 12 t ANL (preliminary) f ISU ^ 10 i I i} i e 1 i ( V

2 3 p MOMENTUM (LAB) GeV/c

20 ' pp-'V*Tr*7r-n- nv'{n >1 ) ^ MSU(pr«llnilnor)r) ^ ANL(prcllnitory) 16 (c) 4 BHL If ISU 4 OTHER i a il |.4 • N,2 8O g 10 if 2 3 MOMENTUM (LAB) GeV/c — + - - - — + + -- 0 — + + + -0 Figure 5* pp _» ît ît ît 3t , pp _^îr 3t ot :iT 3t , and pp -«.^r jt jt jt nit (n > 1) cross sections as a function of incident "p beam momentum 23

IV. EFFECTIVE MASS DISTRIBUTIONS

A. General Method of Analysis

All effective mass combinations for the final selected data samples have been examined. The effective (invariant) mass squared of a combination of N particles is defined by

A N « N ,4 « = ( S Ej) - ( Z P.) (6) ' N : ;=1 '

-* th where E. is the total energy and P. is the momentum of the I particle.

Any effective mass distribution which indicated one or more possible resonances was fitted by an equation of the form

A. = [1 + S Cjf ] C(PS„) .

Aj^ is the value of the function of the bin. PSj^ is the phase space th contribution of the k bin. The number of resonances is designated by n. C;(r./2) The factor ^ 2 's the Breit-Wigner form with Pj the full width (m^-m. ) _ th at half maximum and m. trie central value of the mass of the I resonance.

ti^ is the effective mass at the midpoint of the k^^ bin and Cj gives the

amplitude of the Iresonance. C is a normalization factor.

The minimization of chl-squared was the method used to fit the function

A to the effective mass distribution. The chi-squared function is defined

here as

M (8, Aj

where N is the number of bin in the distribution. The quantity NNj Is the

number of events in the jbin and A. is the value of the calculated J 24

function at.the midpoint of the jbin. The chi-squared was minimized by varying the parameters C.^ r.j and M.G was recalculated at each II I step in the fitting procedure to normalize the calculated function to the experimental distribution. In order to determine the confidence level of a fit, the chi-squared values, which are dependent on the number of bins, were converted to chi-squared probabilities.

In the following sections, any deviations from phase space predictions are discussed if they are in the region of a known resonance even though the statistics may be limited or if the structure, in a region where there are no reported resonances, is consistent at both momenta. The bin widths have been determined by the event statistics associated with each final state. Since the combinatorial background is large in most final states, reflections should not be a serious problem and have been ignored in thé analysis. All distributions which differ only by charge conjugation are shown combined.

B. Resonance Production in the Four Pion Channel

I. General features

The jt , at-, and 2jr^ jr"*^ invariant mass distributions that are shown in Figures 6 to 8 are calculated from the 758 selected four pion events at 2.4 GeV/c and the 356 selected events at 2.9 GeV/c. If there are no apparent resonance contributions in a mass spectrum, a single solid line superimposed on the histogram represents the predictions of

Lorentz invariant phase space normalized to the total number of events. If resonances are present in a distribution, a dashed curve represents phase space predictions, while a solid curve gives the contribution from an 25

160 2.4 GeV/c 4 X 758 COMB.

w 120

0 0.0 0.4 0.8 1.2 . 1.6 2.0 2.4 GeV/c EFFECTIVE MASSCTr+ir")

2.9 GeV/c 80 4 X 356 COMB.

CO 60 JU.

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 GeV/c EFFECTIVE MASSCTT+TT") Figure 6. The effective mass distributions of the it ir combinations for events from the samples 26

2.4 GeV/c 80 2 X 789 COMB.

« 60

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 GeV/c' EFFECTIVE MASS

40 2.9 GeV/c 2 X 356 COMB. in

< 20

10 L.

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 GeV/c' EFFECTIVE MASS(7r*7r*)

Figure 7* The effective mass distributions of the ir— jr— combinations from the 4ir samples 27

CM 2.4 6eV/c 4x758 COMB. «160

m 80

o 40

0 04 0.8 2.0 2.4 EFFECTIVE MASS (27r± ttt)

2.9 6eV/c '80 4 X 356 COMB. to

240

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 GeV/c EFFECTIVE MASS(2'?r*7r*)

Figure 8. The effective mass distributions of the combinations from the kjt samples 28

incoherent sum of phase space plus Breit-Wigner curves.

2. Dipion effective mass distributions

As seen in the ir jt dipion mass spectra (Figure 6), there is copious

p°(7&5) and f°(1260) resonance production in the four pion channel at both momentao At 2.4 GeV/c^ there is an indication of a narrow peak in the

S (1060) region and an accumulation of events in the g°(l650) region.

When a p°f°g° fit was attempted to the jt spectrum at 2.4 GeV/c, a

g° central mass value of 1677 + 14 MeV/c^ was obtained with a corresponding

width of 124 + 22 MeV/c ; however, the fitted p width of ISO + 15 MeV/c

and the f° width of 209 + 16 MeV/c^ are larger than the accepted values given

in Table 8. In general, as additional resonance contributions are included

in the fitting procedure, the width parameters tend to increase, but the

central mass values remain approximately constant. The best fit to the

data was obtained by assuming the presence of the f°, and a peak in

the 1060 region but neglecting the possible existence of the g°. Since

the fitted contribution in the 1060 region was not statistically significant,

the fit displayed on the jc^ jc distribution at 2.4 GeV/c shows only p°

and f^ contributions where the f^ width is fixed at the value obtained in O ^1% the three resonance p , S , f fit. With more limited statistics at 2.9

GeV/c, the only apparent resonance contributions come from p° and f°

production® Evidence has been reported for S" production at 2»5 GeV/c (8).

The fitted values for the masses and widths plus the cross sections for

p° and f° resonance production are displayed in Table 8. 29

Table 8. Masses, widths, and cross sections for p° and f° resonance production in the four pion annihilation channel at 2,4 and 2.9 GeV/c

Mass (MeV/c^) Width (MeV/c^) Momentum Resonance Exp. Accepted Expo Accepted Cross Section (mb. Val ue Val ue Val ue Val ue

o p 749+16 765+10 126+25 125+20 0.73 ± 0.09 2.4 f° 1255+24 1264+10 180+38 145+25 0.77+ 0.11

o p 725+11 765+10 122+23 125+20 0.56 + 0. 08 2.9 f° 1243+21 1264+10 198+42 145+25 0.58 + 0.10

The deviations from the accepted mass values can be explained in part

from the knowledge that for a broad resonance, the energy dependence of the width causes a skewing of the peak (22). Such energy dependent correction .

factors were not incorporated into the fitting procedure. Other pp

annihilation experiments have reported a wide range of central values

for known resonance production (1-15)« The errors given in Table 8 for

the resonance widths are largely determined from the broadening effect of

two Breit-Wigner curves on the fitted widths of both assumed resonances.

In the IT- effective mass distributions (Figure 7) the deviations

from the phase space predictions were not considered significant enough for

an extensive analysis.

3. Three pion effective mass distributions

Inspection of the M(it^ distribution of the four pion events

at 2.4 GeV/c, displayed in Figure 8a, reveals an accumulation of events 30

in both the A^C^^OO MeV/c^) and 1700 MeV/c^ regions.^ From the best fit to the assumption of a single resonance in the Ag region, the mass parameter 2 was determined to be 1326 + 18 MeV/c and the corresponding width was 2 73+6 MeV/c . When a second resonance contribution was assumed for the 2 1700 region, a value of I698 + 17 MeV/c was assigned to its mass parameter 2 and a broad width of 280 + 23 MeV/c . The inclusion of a resonance 2 contribution at I7OO MeV/c into the fitting of the three pion distribution 2 increased the resonance width in the A^ region to 97 + 14 KeV/c , but the 2 ^ probability was not significantly improved. Only the assumed single resonance contribution on the Ag region is shown in the fit to the three pion distribution shown in Figure 8a.

Further evidence for Ag production was found in the pit mass distribu

tion at 2,4 GeV/c and structure in the fir spectrum at the same momentum

indicates a two meson decay mode of the I7OO signal found in the three

pion effective mass plot. The p° mass distribution (Figure 9a) is derived

from a p° band chosen as the region within one half width of the fitted

resonance mass value. In defining the rho region as above, a higher signal

to combinatorial background ratio is obtained than if the real p° events in

the tail of the Breit-Wigner curves were included. Assuming Ag production,

a phase space plus Breit-Wigner fit to the pîf- distribution yielded a central 2 2 resonance mass value of I297 + 15 MeV/c but a narrow width of 23 + 7 MeV/c .

Events which also had a K combination in the f° region were then removed

from the pjt—mass spectra and a fit to the resulting distribution, shown

A cross section of 0.59 + 0.12 mb has been reported at 1.2 GeV/c (2) for A2 production in the four pion channel. No evidence for A2 production in the four pion channel has been found in experiments with incident antiproton momentum above 2.9 GeV/c (11, 12, 13, 16). 31

2.4 GeV/o O40 854 COMB.

g 2.0

0 0.4 0.8 I. 1.6 2.0 2.4 2.8 GeV/c EFFECTIVE MASS(/)®7r^)

Figure 9a. The effective mass distribution of the p°ic^ combinations for events from the 4jc sample at 2.4 GeV/c

w 1 I r 2.4GeV/c IO 586 COMB. g 32 10 q (b) M 24 % M I.S o o O 8 <3 / z JL 0.4 0.8 1.2 1.6 2.0 2.4 2.8 EFFECTIVE MASS 6eV/c2 o + Figure 9b. The effective mass distribution of the p Ttr- combinations for events in the sample at 2.4 GeV/c after removing events which had a combination in the f° region 32

2 în Figure 9b, obtained a central mass value of 1319 + 22 MeV/c with a 2 corresponding resonance width of 209 + 23 MeV/c .

After slicing on the f° region,again defined by the region within one half width of the fitted mass value, a plot of the f° mass spectrum

(Figure 10a) indicates deviations from the phase space predictions in the

1700 region. The stronger signal occurs in the f^ effective mass plot which is shown as the dashed histogram in Figure 10a. When the fjt mass distribution was fit with a single Breit-Wigner plus phase space predictions, the best fit was obtained with a mass parameter of 1697 ±

16 MeV/c^ and a width of 105 + 33 MeV/c^.

• A fit to the assumption of a single resonance in the combined fjt^ 2 distribution placed the resonance mass parameter at 1704+22 MeV/c and

the width at 137 + 29 MeV/c^. When events which also had a #

combination in the rho band were removed from the fir^ distribution, as 2 shown In Figure 10b, the remaining signal in the 1700 MeV/c region was 2 fitted with a resonance mass parameter 1736 + 19 MeV/c and a much narrower 2 width of 32 + 9 MeV/c . It is possible that the signal in the I7OO region 2 is associated with the jt^Clô'fO) resonance having a width of 93 + 20 MeV/c .

The jr^(l6U0) has a fit decay mode and reportedly may consist of several

resonances.

With the more limited statistics at 2.9 GeV/c, the only significant

deviations from the phase space predictions in the three pion effective 2 2 mass spectrum (Figure 8b) occur in the 1950 MeV/c and 2100 MeV/c regions.

It should be noted that at both momentum, there are deviations from the

phase space predictions in the three pion distributions at about 1950 MeV/c'

but the shape of this structure is not consistent. The p° distribution 33

2.4 GeV/c 900 COMB. 80 —

S 60

0.8 1.2 1.6 2.0 2.4 2.8 32 EFFECTIVE MASS(fV-) GeV/c^

O 4" Figure 10a. The effective mass distribution of the f s— combinations for events from the kjt sample at 2.4 GeV/c

2.4 GeV/c % (b) 632 COMB. o 40 9 I 930 g

i m 20 o o

§'° z

I ± 8.00 1.2 1.6 2.0 2.4 2.8 32 EFFECTIVE MASS (f*7r±) GeV/cZ rO + Figure 10b. The effective mass distribution of the f jt— combinations for events in the kit sample at 2.4 GeV/c after removing events which had a combination in the p° region 34

(Figure lia) at 2,9 GeV/c shows no enhancement in the Ag region and the fit spectrum (Figure lib) has no statistically significant accumulation of 2 events above phase space» The pjt enhancement found about 2.10 GeV/c at 2 2o9 GeV/c could indicate a decay mode of the 2100 MeV/c signal in the three pion distribution, however, there are no corresponding effects at

2.4 GeV/c. The frequencies and cross sections for the above production modes are given in Table 10» The enhancement found in the fjr effective mass distribution at 2.4 GeV/c is designated by M(1700).

4o Associated production in the four pion channel

The frequencies of associated production of p°f°, and f°f° in the

•I* — four pion channel were determined from scatterplots of the mass of a # # combination versus the mass of the opposite it combination. Thus, the

illustration shown for four pion events at 2o4 GeV/c (Figure 12) has two

scatterpoints per event. Resonance bands are shown as parallel lines on the

plot and intersection of two bands comprises an associated production region»

Background subtractions were made from narrow mass bands just outside the

region of intersection. The resonance bands used to determine the associated

production at.2.4 GeV/c and 2.9 GeV/c together with the regions designated

as background are given in Table 9. The frequencies for p° p° p°f°, and f°f° associated resonance production are given in Table 10.

Table 9* Mass regions used for investigating associative production in the four pion annihilation channel at 2.4 and 2.9 GeV/c Momentum Resonance Resonance Region Background Region Background Region (GeV/c) (MeV/c^) Below Resonance Above Resonance (MeV/c^) (MeV/cZ) 690-840 600-690 840-930 2.4 fo 1170-1350 1080-1170 1350-1440 o 660-8I0 560-660 810-910 2.9 fO 1110-1360 960-1110 1360-1510 35

2.9 GeV/c (a) 415 COMB.

I 6

0 0.4 0.8 1.2 2.0 2.4 2.8 GeV/c EFFECTIVE MASSip^yr^)

Figure 11a. The effective mass distribution of the p°ji^ combinations for events from the sample at 2.9 GeV/c

O 2.9 GeV/c 461 COMB.

±16 8 8 d z

0 0.8 1.2 1.6 2.0 2.4 2.8 3.2 2 EFFECTIVE MASS if°ir± ) GeV/c'

Figure lib. The effective mass distribution of the f°jt^ combinations for events from the sample at 2. g GeV/c 2.4 GeV/c h-n Sample 758 Events /\y

•1,8 . • 2.25 GeV/c2

•|» » mm Figure 12. Scatter plot of an « combination versus the opposite, st jt combination effective mass distributions- The parallel solid lines indicate resonance bands. The kinematic limits are shown by the, triangular perimeter 37

5* Summary of the production modes in the four pion annihilation channel

The frequencies and cross sections for production modes in the four

pion final state are listed in Table 10, The high percentage of events

having a three meson intermediate state is consistent with the quark

rearrangement model (23). For annihilations, this model proposes that the

three spin - 1/2 quarks making up the nucléon and the three spin - 1/2

"antiquarks making up the antinucleon rearrange themselves into three quark-

antiquark pairs, without exchanging spin, isospin or hypercharge. The

final state, thus, contains three non-strange mesons.

Table 10» Production modes in the four pion final state at 2.4 and 2.9 ...... ^™ .

Reaction GsV/c 2.9 GaV/c Frequency Cross Section (mb) Frequency Cross Section (mb)

PP •4 0.38 ± Oo 07 Oo 57 ± 0.10 0o47 ± 0o08 0.49 ± 0.08

pp 0.42 + 0. 09 0.62 + 0.13 0.49 ± 0.10 0o52 + O.H

pp P°P° Oo 015 +, 0. 01 Oo 02 + Oo 01 0.01 + OoOl 0.01 + OoOl . o

—• Q pp 0.03 ± 0o02 0.04 + Oo 03 0.04 ± Oo 03 Oo 04 + Oo 03

fOfO pp < 0.01 < 0.015 < OoOl < 0.01

pp —$ Ag* 0.06 + 0.04 Oo 09 + Oo 06 < 0.02 < Oo 03

M (1700) at 0. 07 + Oo 05 Oo 10 + 0.08 < 0.02 pp —• < 0o03

pp —» 2a+2a- <0.10 <0.15 .. < OolO < 0.10

The energy dependences of the reactions, pp , f°jr^jt , p°f°,

and p°p° are shown in Figure 13• As the incident antiproton momentum is

increased beyond 1.1 GeV/c, two body resonance production steadily decreases. 38

4 OTH ER

2 3 P MOMENTUM (LAB) 6eV/c

•pp-^-fTT+TT- 1 1 ^MSU 0.8 - {OTHER (b) S ^ ISU •^0.6 z o ^0.4 I : u — T (0

§0.2 -i H cc i o 1 , 1 " I 2 3 p MOMENTUM (LAB ) GeV/c

1.0 • PP- -pof o pp. •P'P' 2 0.8 {{MSU ^iJlSU e U LIVERPOOL, OSLO, g 0.6 FftDUA

OT 0.4 (c) L;l. 't

JL A A I 2 3 4 F MOMENTUM (LAB) GeV/c -Figure 13. PP -» p°3t^3r ^ PP -» , pp -• and pp -* p°p° cross sections as a function of incident p beam momentum 39

but the three meson production rate tends to increase up to 3=0 GeV/c. At

3.6 GeV/c (12), 80 + 20% of the dipion resonances are reported to be

produced in association. Although no cross sections are given at 3.6

GeV/Cj the authors' estimates of the frequencies for associated production

in the four pion channel are given in the following list:

PP -» p°p°, 7 ± 8 %

pp ^ f°f°, ~ 28 + 30 %

PP - p°f° 5 ± 6% . C. Resonance Production in the Five Pion Channel •

1. General features

The two and three pion invariant mass distributions for the final

selected five pion samples of 2631 events at 2.4 GeV/c and 1216 events at

. 2o9 GeV/c are displayed in Figure 14 through Figure 18. Substantial amounts

of p", p—, and resonance production are found at both momenta. There

are also indications for f° production in the jt spectra. The fitted

mass and width parameters together with production cross sections for the

above resonances are listed in Table 11.

Table 11. Masses, widths, and cross sections for resonance production in the five pion annihilation channel at 2.4 and 2.9 GeV/c

Momentum Resonance Mass (MeV/c^) Width (MeV/c^) Cross Secti on (mb. ) (GeV/c) o 2.4 P 749 + 6 116 + 21 2.83 + 0.68 + P~ 767 ± 7 187 + 29 3.08 + 0.40 f° fixed (1260) fixed (140) 0.90 + 0.56 o m fixed (783) 22+10 0.43 + 0.10 o 2.9 p 774 + 8 110 + 13 1.53 + 0.28 + P~ 745 + 28 158 + 16 1.83 ± 0.36 f° 1241 + 4 91 ± 17 0.42 +0.13 (0° fixed (783) 22+7 0.32 + 0.11 40

2.4 6eV/c CVI 4x2631 COMB. r% 400

^ 300 V)

< 200

o 100

0.0 0.4 0.8 1.2 1.6 2.0 2.4 EFFECTIVE MASS {7r+ TT" ) 6eV/c %

2.9 GeV/c 4x1216 COMB. o 200

to 150

100

o 50

0.0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 EFFECTIVE MASS {ir* tt') GeV/c^

Figure 14. The effective mass distributions of the sâ" it" combinations for events from the 5jr samples 41

2.4 GeV/c 4 x 2631 COMB.

0 400

Ù) 300 z o

z 200

u. 100

0 0.0 0.4 0.8 1.2 l.( 2.0 2.4 EFFECTIVE MASS {•tri-tr")

2.96eV/c 4x1216 COMB.

® 200

150

<100

0 0.0 0.4 0.8 2.0 2.4 EFFECTIVE MASS (7r± tt")

Figure 15» The effective mass distributions of the it- combinations for events from the 5jr samples 42

2.4 6eV/c 2x2631 EVENTS

^ 200

q 150

50 u_

0.0 0.4 0.8 1.2 1,5 2.0 2.4 EFFECTIVE MASS(7r± ir±) GeV/c

2.9GeV/c «160 2x1216 COMB.

<120

z 80

0.00 0.5 1.0 1.5 2.0 2.5 3.0 EFFECTIVE MASS ^TTtTTi) GeV/c

Figure l6o The effective mass distributions of the jr- ir- combinations for events from the 5:t samples 43

2.4 GeV/c 4 X 2631 COMB. tvi 320 o

<240

<160

u 80 u.

0.0 0.4 0.8 1.2 1.5 2.0 24 EFFECTIVE MASS {tt* GeV/c

160

<120

z 80

0 0.4 0.8 1.2 1.6 2.0 2.4 , EFFECTIVE MASS (tt+TT-TT®) GeV/c'

Figure 17« The effective mass distributions of the sT jt® combinations for events from the 5jt samples 44

2.4 GeV/c 4x2631 COMB.

> 320

3 240

b 160

o 80 u.

0 0.4 0.8 1.2 2.0 2.4 EFFECTIVE MASS (2-jr±7rî) GeV/c^

2.96eV/c 4x1216 COMB.

^ "60

^ 120 CO

fe 40

0 0.4 0.8 1.2 16 2.0 2.4 EFFECTIVE MASS (2 u ± TTT) 6eV/c^ + jZ Figure 18. The effective mass distributions of the jt combinations for events from the samples 45

2. Dipion effective mass distributions

The contribution of f° resonance production at 2.4 GeV/c was difficult to determine because the fitting procedure attempted to incorporate contri butions from structure below the f mass region. The amount of f° production at the lower momentum was estimated by fixing the mass and width parameters at the accepted values and allowing only the resonance amplitude to vary.

At both momenta, the assumption of an f signal in the 3t distribution

(Figure 14) increased the fitted width of the p° resonance by about 20 2 MeV/c . The errors calculated for the corresponding resonance cross sections are mainly due to uncertainties in the widths.

As a result of poorer mass resolution arising from the inclusion of a neutral particle in the spectra, the p— resonance width can be expected to be broader than the corresponding p° contributions in the it spectra. A fit to the tc invariant mass distribution at 2.4 GeV/c 2 2 resulted in a p mass of 756 + 6 MeV/c and a width of 187 ± 18 MeV/c .

A similar fit to the ît° distribution at 2.4 GeV/c determined the p^ 2 9 mass at 778 + 9 MeV/c but with a broad width of approximately 240 MeV/c . + o A fit to the composite it- jt distribution yielded a mass value of 7^7 + 10

MeV/c and a resonance width of 216 + 23 MeV/c . This composite width is 2 2 ^ more than 50 MeV/c larger than the 120-160 MeV/c p— width range reported by other bubble chamber experiments. In order to obtain a reasonable estimate of the combined p— contribution, the mass and width parameters of the

single resonance fit to the jt° distribution were fixed at the values obtained for the p fit to the ir jt° spectrum. By fixing the p— mass 2 2 parameter at 756 MeV/c and the width at 187 MeV/c , essentially all real

p^ production is included in the fitting procedure. 46

In the or- :r— mass plots shown in Figure 16, the deviations in the distributions near the peak of the Lorentz invariant phase space predictions at both momenta are not believed significant enough to warrant serious investigation.

3® Three pion effective mass distributions

The jr*^ jt it° distributions shown in Figure 17 were fitted with the assumption of both and resonance production in the five pion final state.^ Since the accepted value for thedf width is a narrow 12.6+ 1.1 2 MeV/c J estimates of the mass resolution in the experiment can be made

from the fitted width of the tu°• The procedure is to assume the is

produced with essentially zero width and use the fitted width as an estimate 2 of the resolution. After fixing the mass parameter at 783 MeV/c , the

10° widths were determined to be 22 + 13 MeV/c^ at 2.4 GeV/c and 22 + 7

MeV/c^ at 2.9 GeV/c. These estimates of the u)° width were taken into account

when determining the error for other resonance widths. The resonance fit

to the region at 2.4 GeV/c (Figure 17a) resulted in a mass parameter of

1269 £ 8 MeV/c^ and a width of 60 + 14 MeV/c^« The best fit for the Ag 2 region at 2.9 GeV/c (Figure 17b) set the resonance mass at 1344 + 11 MeV/c 2 and the width at 50 + 17 MeV/c « The structure in the Ag region at 2»9

GeV/c has marginal statistics and the fit was attempted only to obtain an

upper limit for Ag production^ + + Since the phase space predictions to the 2jr- it distribution at 2.4 2 GeV/c (Figure 18a) are not a good representation of the 1000-1400 MeV/c

region, both Aj— and Ag— resonance production were assumed in fitting the _ _ Evidence for A^ or A2 production in the five pion annihilation channel has been reported at 1.2 GeV/c (3), at 1.2 to 1.6 GeV/c (4), and at 2.5 GeV/co No A] or A2 production is reported above 2.9 GeV/c (11, 12, 14, 16). 47 distribution. In order to obtain reasonable fits and estimates of resonance production, it was necessary to fix both resonance widths at the standard values. Fixing the resonance widths, the two resonance fit to the

23t— distribution results in a central mass values of 1081 + 11 MeV/c^ 2 in the Aj region and 1302 + 9 MeV/c in the A^ region. No apparent resonance

structure is seen in the 23t— mass distribution at 2.9 GeV/c (Figure 18b); •f* however, the lit distribution alone shown in Figure l8b as a dashed

curve indicates Aj and A^ production. The 2t^ ir mass distribution was

fitted to obtain upper limits for A production.^

The pit invariant mass distributions were investigated for further

indication of A resonance production in the five pion annihilation channel.

The p° mass plot at 2.4 GeV/c, displayed in Figure 19a, has only

marginal statistics for either A^— or A^— production. In order to obtain a

reasonable fit to the p° it- distribution assuming Aj and A^ production,

the width had to be fixed at the accepted value. The varied mass and

width parameters were fitted to the values given in Table 11. Evidence O 4" for both A| and A^ production is seen in the p it- distribution at 2.9 GeV/c

as shown in Figure 19a. In agreement with the assumed A contributions in

the three pion distribution at 2.9 GeV/c, the A^ and Ag contributions in the

p°jA plot originate from the p® jt^ distribution. A fit to the p^ 3t^

distribution at 2.9 GeV/c resulted in the mass and width parameters for A|

and Ag production given in Table 12. Factors such as mass resolution, high

Combinatorial background, and the small cross section for Ag production

prevent one from investigating any splitting of the A^ meson in this experi

ment.

Estimates of the amounts of A] and A2 resonance production in the five pion channel are given in Table I3. 48

2.4 6eV/c ^ 160 2 998 COMB. o

i 120

Î5 80

o 40

04 0.8 1.2 1.6 2.0 2.4 2.8 EFFECTIVE MASS (/)»7r±) 6eV/c2

2.9 GeV/c 80 1315 COMB.

^ 40

O 20

0.4 0.8 1.2 1.6 2.0 2.4 2.8 EFFECTIVE MASS Ip" iri ) GeV/c %

Figure 19» The effective mass distributions of the p°jt^ combinations for events from the 5:r samples 49

Table 12. Mass and width parameters for A production in the p° ïA distributions at 2.4 and 2.9 GeV/c

Mass (MeV/c^) Width (MeV/c^) Momentum Resonance Exp. Value Accepted Valus Exp. Value Accepted Value (GeV/c) .

2.4 1036 + 19 1070 + 20 83 ± 13 80 + 35

A2 1320 + 17 1297 + 10 Fixed 91 + 10

2.9 A, 1086 +15 1070 + 20 41 ± 12 80 + 35

I308 + 14 1297 + 10 63 + 20 91 + 10 *2

The p— distributions at both momenta (Figure 20) give indication o + + of only Ag production. After fixing the Ag widths a fit to the p— it

distribution àt 2.4 GeV/c resulted in a central mass values of 1275 +35

MeV/c^. Fitting the p— distribution at 2.9 GeV/c (Figure 20b) with the

assumption of Ag resonance production yielded a central resonance mass 2 2 value of 1252 + 28 MeV/c and a corresponding width of 94 + 18 MeV/c .

For completeness, the fn mass spectra in the 5it channel channel are

shown in Figure 21. It is not believed that any particular significance

can be assigned to the deviations from the phase space predictions at the

peak of each distribution.

4. Four pion effective mass distributions

In a pp experiment performed by the Iowa State group at 2.7 GeV/c (12),

evidence was reported for the existence of an 1=0 meson state of I6IO

MeV/c mass end width of 155 + 85 MeV/c . This 2.5 to 3 standard deviation

effect was based on a sample of 320 selected five pion events. In the

present data, the 2it^ 2jt effective mass distributions, which consist of

2631 events at 2.4 GeV/c (Figure 22a) and 1216 events at 2.9 GeV/c 50

2.4GeV/c 5432 COMB.

<160

0.4 08 1.2 1.6 2.0 2.4 2.8 EFFECTIVE MASS (p±rr + ) GeV/c^

2.9 GeV/c 2056 COMB. ai6o lO

80 m o

2.0 2.8 EFFECTIVE MASS(/)±7r+)

Figure 20. The effective mass distributions of the p— it combinations for events from the samples 51

>160 2.4 6eV/c 1287 COMB.

i 120 V.

E 80

o 40

1.2 1.4 1.6 1.8 2.0 2.2 2.4 EFFECTIVE MASS(f°Tr±) GeV/c'

2.9GeV/c 80 694 COMB.

$40

1.4 1.6 1.8 2.0 2.4 EFFECTIVE MASS (frrt)

Figure 21o The effective mass distributions of the f°jt— combinations for events from the Sît samples 52

2.46eV/c « 160 2631 EVENTS

< 120 to

UJ 80 u. o

40-

0.0 OA 08 1.2 1.6 2.0 2.4 EFFECTIVE MASS (2Tr+ 27r-) GeV/c^

2.9 GeV/c %80 1216 EVENTS in

w 40

00 0.5 1.0 1.5 20 25 3.0 EFFECTIVE MASS (ZTr*ZTr~) GeV/c^ + - Figure 22. The effective mass distributions of the 2jt jr combination for events from the 5it samples 53

(Figure 22b)^. -show no significant deviations from phase space predictions

in the 1600 region. The conclusion is that there is no statistically sig

nificant evidence in the present data for a four pion decay of a meson of 2 ' mass 1600-1650 MeV/c « Attempts to fit the enhancements seen in the peaks of both distributions did not lead to any consistent results.

The 2ic~ 3r° (Figure 23) distributions in general follow the predic

tions of Lorentz invariant phase space. Although there is a small accumula

tion of events in the 1200 region at 2.4 and 2.9 GeV/c, there is no definite

indication of B(1220 -» ujJt) production in the gross distributions. This is

not surprising when one assumes that B production frequency would only be

a fraction of the 0.05 production frequency found at both momenta. The + (ijjt— mass spectrum plotted for incident antiproton momentum of 2.4 GeV/c as

shown in Figure 24a indicates an enhancement above the phase space predic

tions in the 1220 region. The dashed curve in Figure 24a is a plot of the

(OJt distribution in which the enhancement is more prominent. The best fit

to the wn— distribution assuming B production placed the central mass 2 value at 1212 + 4 MeV/c and determined the fitted width to be 15 + 10 2 MeV/c « The resulting mass value is in good agreement with the 1221 + 16 2 MeV/c value of the B meson determined from other experiments. The fitted

resonance width in the B region is much smaller than the accepted width 2 M of 123 + 16 MeV/c . A fit to the 1200 region in the distribution resulted 2 2 In a central mass value of 1210 + 7 MeV/c and a width of 13+9 MeV/c .

Considering the limited statistics in the B region, it is not surprising

that the fitted widths are not in agreement with accepted values. At 2.9

GeV/c, the distribution (Figure 24b), which contains even fewer events

than the similar distribution at 2.4 GeV/c^ has a cluster of events centered 54

2.4GeV/c 4x2631 COMB.

400

; 300

H 200

o 100

0 0.0 0.4 08 2.0 EFFECTIVE MASS (2%r± TTîTr")

(b) 2.9GeV/fc 4x1216 COMB. S 200 in

^ 150

k 50

0 0.0 0.5 1.0 1.5 2.0 2.5 30 EFFECTIVE MASS (27r± tt ttt») GeV/c^

Figure 23. The effective mass distribution of the 2]r it° combinations for events from the Sit samples 55

2.4 GeV/c O 40 776 COMB.

W 30

Z 20

10 L-J" •1.

0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 GeV/c EFFECTIVE

32 - (b) 2.9 GeV/c 317 COMB.

%:24

< 16

O 28

0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 GeV/C EFFECTIVE MASSCWOtt*)

Figure 24. The effective mass distributions of the ir combinations for events from the 5^ samples 56

at a mass of 1310 MeV/c . This statistically small accumulation of events is at too high a mass value to be associated with B meson production. The estimated frequencies and cross sections for B production are given in

Table 14.

A search for possible p 3t :it effects in the five pion channel proved unsuccessful for the distributions essentially followed the predictions of phase space. Similarly no evidence was found for consistent structure in the pp invariant mass plots.

5. Associated production in the five pion channel

Evidence for associated production of p°p°j p°p~^ m°f° and m°p° was found in the five pion final state at both momenta. The frequencies for such coincidence resonance production were determined by the scatterplot technique (see Part B). The resonance bands and corresponding background regions used in the analysis are listed in Table 13.

Table 13» Mass regions used for investigating associative production in the five pion annihilation channel at 2.4 and 2.9 GeV/c

Momentum Resonance Resonance Region Background Region Background Region (GeV/c) (MeV/c^) Below Resonance Above Resonance (MeV/c ) (MeV/c^)

2.4 p 660-810 570-660 810-900 p— 660-840 570-660 840-930 u)° 750-840 . 690-750 840-900 f° 1170-1350 1080-1170 1350-1440

2.9 p® 665-840 560-665 840-945 p— 665-840 560-665 840-945 w 735-840 665-735 840-910 f° 1120-1295 1015-1120 1295-1400

The frequencies for associated production in the five pion annihilation 57

channel at 2.4 and 2.9 GeV/c are given in Table 14.

6. Summary of production modes In the five pion annihilation channel

The frequencies and cross sections for the production modes in the five pion channel at 2.4 and 2.9 GeV/c are listed in Table 14. In contrast to the four pion channel where a three meson intermediate state occurs in over •

75% of the reactions, five pion reactions are produced via three mesons with frequencies of 0.42 + 0.10 at 2.4 GeV/c and 0.29 + 0.06 at 2.9 QeV/c. At both momenta, the state is the most frequently produced three meson intermediate state. The ir"'^jt state is produced in about 20% of the five pion reactions at each momentum. Although there are large errors associated with the values for direct five pion production, this process appears to increase at the higher momentum.

The energy dependences of the reactions pp -» p—p°ît^, p°p°]r°

0)°p° and u)°f° are shown In Figure 25. The p~p°Jt^ cross section (Figure 25a) decreases with Increasing momentum, but the energy dependence of the p*^p°3r° cannot be determined from the data in Figure 2$bo Omega production at 2o4 and 2.9 GeV/c is lower than would be predicted from an interpolation of other data points. It Is difficult to determine whether or not this lack of production results from a bias introduced from the missing mass criteria that was used In the kinematic fitting procedure (see Section II)o

The u)°p° and production at 2.4 and 2.9 GeV/c appear to decrease

sharply as compared to the 1-2 GeV/c momentum range.

Do Effective Mass Distributions of the 4jcMM Events

The , 3t^ MM, and zi MM effective mass distributions for the 4aMM

events subject to the restrictions discussed In Section 11 are shown in 58

Table 14. Production modes in the five pion final state of 2.4 and 2,9 GeV/c 2,4 GeV/c 2.9 GeV/c Production Mode . Frequency Cross Section (mb) Frequency Cross Section (mb) — o + - o PP -• p It 3t 3t 0.06 + 0.08 0.42 + 0.55 0. 06 + 0. 06 0.33 ± 0.33

+ ^ + - p—Jt It # 0.20 + 0.07 1.44 + 0.49 0.21 + 0.06 1.11 + 0. 34

_o + - o f 3t 3t ît 0.12 + 0.07 0.83 + 0.53 0. 05 + 0. 02 0.28 + 0.12

0 + - fU ît ît 0.05 + 0.01 0.40 +0.11 0. 06 + 0. 01 0.32 + 0.07

0 o o p p IT 0.02 + 0. 01 0.15 + 0.07 0.025+0.015 0.14 + 0.08

pW < 0.01 < 0.07 0.012+0. 012 0.07 + 0.07

0.17 ± 0.05 1.20 + 0.34 0.09 + 0.04 0.50 + 0.20

pW < .01 < .01 < 0.01 < 0.05

b o (U p 0. 00^0.004 0.06 + 0.03 0. 010+0. 006 0.05 + Oo 03

0.01q+0.007 0.07 + 0.05 0.012+0. 007 0.07 + 0.04

A,W 0. 06 + 0.04 0.43 + 0.32 0. 02 + 0.02 0.14 + 0.13

A, Vît" < 0.02 < 0.14 < 0.02 <0.10

AgTît^t"^ 0.05 + 0.04 0.42 + 0,27 0.04 + 0.02 0.23 + 0. 17

AgVît- 0.06 + 0.04 0.44 +0.29 0.04 + 0.03 0.22 + 0.17

B^ît? 0.008+4.005 0.06 + 0.04 < 0.005 < 0.02

+ - + - o ît ît ît ît It 0.17 + 0.14 1.2 + 1.0 0.37 + 0.11 • 2.0 + 0.6 59a

p-p~ Tr +

4 OTHER

pp-^ P°P°Tr°

_2 3 P MOMENTUM (LAB) GeV/c — + o + J — Figure 25- PP -H- p-p 3t , and pp -» p° p cross sections as a function of incident beam momentum 59b

T 4 T pp TT+TT- (aHw®evenîs) MSU (preliminary) (c) 3 <1 ISU j: BNL (preliminary) 2 3 \ OTHER 5

pp — xi (d) E 1.0

•rf g H 05 LU <0 OT 0 e CO O tu O (e) pp -4'W O f o 1.5

1.0 ïiMiII 0.5

L 2 3 4 p MOMENTUM (LAB) GeV/c

Figure 25 (continued), pp -> jc , pp -> and pp -» u)°f^ cross sections as a function of incident "p beam momentum 60

Figure 26 and Figure 27, There are indications of p° production in the

ît spectra (Figure 26) at both momenta. The estimated cross sections for p° production in the reactions pp -* njt° (n > 1) are 1.1 + 0.4 mb at 2.4 GeV/c and 0.8 + 0.5 mb at 2.9 GeV/c. No apparent resonance structure is seen in the jt— MM and jt MM distributions (Figure 2?), but they are displayed for completeness. 61

T Io 2.4 GeV/c § 9 1200 4 X 6728 COMB.

COz o P 800 < z OQ S o 400 o u. o d z 0.0 0.5 1.0 1.5 2.0 GeV/c"^ EFFECTIVE MASS{7-V")

1 1 1 Io m g (b) 2-9 GeV/c 1200 d 4 X 4216 COMB. •V. (0 z F 800 - - < J \ P° z m S 1 o 400 o Lu o d 1 1 1 z 0.0 0.5 10.0 15.0 GeV/c^ EFFECTIVE MASSCTT+TT")

Figure 26o The effective mass, distributions of the jr combinations for events from the 4#MM samples 62

2.4 6eV/c ? 1200 4 X 6728 COMB.

800

o 400 u.

0.0 0.5 10.0 15.0 20.0 GeV/c^ EFFECTIVE MASS (Tri WM)

2.9 GeV/c q 600 4 X 4216 COMB.

hf 400

S 200

0.0 0.5 1.0 2.0 GeV/c EFFECTIVE MASS(7r±MM)

Figure 27. The effective mass distributions of the jr-MM combinations for events from the ^jtMM samples 63

2.4 GeV/c O 1200 .4 X 6728 COMB.

800

400

z 0.0 5.0 10.0 15.0 2 0.0 25.0 GeV/C EFFECTIVE MASS(irV-MM) N

2.9 GeV/c

600 4 X 4216 COMB.

200 u.

0.0 5.0 10.0 15.0 20.0 25.0 GeV/c EFFECTIVE MASS(7rV"MM)

Figure 27 (continued)oThe effective mass distributions of the rt jc MM combinations for events from the 4#MM samples 64

• Vo ANGULAR DISTRIBUTIONS

Four types of angular distributions are presented in this section.

The production angle of pions in the center-of-mass system and the correla

tion between the momentum vectors of dipions in the center-of-mass system for events in the selected 4^, Sjt, and 4jtMM samples are investigated at each momentum. Also, the center of mass production angles of resonance particles and their decay angular distributions in their own rest frame are studied after background substract ions have been performed,

Ac Production Angles of Pions

If the 3t direction is taken with respect to the antiproton direction

in the center of mass system and the with respect to the proton direction,

charge conjugation invariance of the pp interaction requires that the

cos 0^^ distribution be the same as the cos distribution (24). The center of mass angular distributions for the charged pions of the 43t, Sitj and 43tMM

events are shown in Figure 28 through Figure 32, Since these plots clearly

indicate that the it (jt^) tends to be emitted in the direction of the incoming

p(p), in all calculations the cos distributions were reflected about o — 6 = 90 and combined with the cos jt distributions. The distributions for

cos are given Figure 30c and Figure 31c. As a consequence of the

fact that the ît° is its own antiparticle, the cos distribution is

expected to be symmetric about cos G = 0 (24). The angular distributions

of the missing mass in the 4#MM events are given in Figure 33® The back

ward asymmetry in the missing mass distributions allows an estimate of the

contamination in the 43tMM events. Measurements of any asymmetric character

of the angular distributions are obtained from the forward-backward (F/B) 65

160 2.4 GeV/c 47r EVENTS

2 X 758 PIONS

-1.0 -0.6 0.2 0.2 0.6 1.0 COS e-ir*

160 2.4 GeV/c 47r EVENTS in 2 X 758 PIONS

-1.0 -0.6 -0.2 0.2 0.6 1.0 COS e-TT-

Figure 28» Distributions of the production angles of charged pions in the center-of-mass system for events in the h-K sample at 2o4 GeV/c 66

2.9 6eV/c 80 r~ (a) 4TT EVENTS (O z 2 X 356 PIONS o EGO u. o Ltl w40 (D S 3 ^20

I _L —I.O —0.6 -0.2 0.2 0.6 1.0 COS 6ir*

T T 2.9 GeV/c (b) 4 TT EVENTS 80 2 X 356 PIONS

g 60- I 0. (JL o u 40 m J1 S=) z 20 IP

-1.0 -0.6 -02 0.2 0.6 1.0 COSBv-

Figure 29, Distributions of the production angles of charged pions in the center-of-mass system for events in the sample at 2.9 6eV/c 67

400 2.4 GeV/c (a) Sir EVENTS 320 2 (2631 PIONS

160

0 H.O -0.6 -0.2 0.2 0.6 1.0 COSTT*

400 2.4 GeV/c (b) Sir EVENTS 2 * 2631 PIONS 1320 °-240 ë mz 160 i 80

0 -1.0 -0.6 -0.2 OZ 0.6 1.0 COS

T 1 1 r 200 f » 2.4 GoV/c VCj Sir EVENTS 2631 PIONS , «'60 1 O (E m 80 z • 40

- 0 J L. -1.0 -0.6 -0.2 0.2 0.6 1.0 COS SttO gure 30a, 30b. Distributions of the production angles of charged pions in the center-of-mass system for events in the Sit sample at 2o 4 GeV/c Figure 30c.Distribution of the production angles of the neutral pions i the center-of-mass systems for events in the Sit s an pie at 2.9 GeV/c 68

2.9 GeV/c STT EVENTS 2 * 1216 PIONS

S: 120

H.O -O.G -0.2 0.2 0.6 10 COS 0ir*

2.9 GoV/c STT EVENTS 2 % 1216 PIONS

Ol20

-1.0 -Oj6 -0.2 0.2 • 0.6 1.0 COS 6r-

100 . . 2.9 G«V/e (C J Sir EVENTS 1216 PIONS

0S a ë g 10

120

-1.0 -0.6 -0.2 0.2 0.6 1.0 COS Sir® Figure 31a, 31b. Distributions of the production angles of charged pions in the center-of-mass system for events in the 5ît sample at 2.9 GeV/c Figure 31c. Distribution of the production angles of the neutral pions in the center-of-mass system for events in the sample'at 2.9 GeV/c 69

1—I—r 1 I r , ^ 2.4 GeV/c 2.4 GeV/c (a) 4TrMMEVENTS (b) 47rMM EVENTS 13455 COMB. 13456 COMB. [01200 §1200 g O CL 0. U. ll_ 800 ° 800 q: K w ID CO 03 S S 3 3 Z 400 Z 400

I _L I -1.0 -0.5 0.0 0.5 1.0 -1.0-0.5 0.0 0.5 1.0 COS e-rr* COS e-TT-

2.9 GeV/c 2.9 GeV/c (c) 4TrMM EVENTS (d)47rMM EVENTS 8432 COMB. 8432 COMB. 600 Z 600

0: 400 400

200

1.0 -0.5 0.0 0.5 1.0 1.0 -0.5 0.0 0.5 1.0 COS e-TT* COS ÔTT" Figure 32« Distributions of the production anc, • of charged pions in the center-of-mass system for events in the 4#MM samples 70

2.4 GeV/c 6728(4TrMM)E\/ENT£

600

400

200

0 0.5 0.0 0.5 1.0 COS

1 1 1 2.9 GeV/c 42l6(47rMM)EVENTS 240\

160

1 1 1 -1.0-0.5 0.0 0.5 1.0 COS

Figure 33» Distributions of the production angles of the neutral pions in the center-of-mass system for events in the samples 71

and polar-equîtorial (P/E)ratios [F is the number of pions with cos > 0;

B is the number With cos € < 0; P is the number with I cos € I > 0.5 ; E jt ' It' ; is the number with Icos 6^1 < 0.5.3« The F/B and P/E ratios for the

various angular distributions are given in Table 15-

Table 15» Forward-backward (F/B) and polar-equatorial (P/E) ratios for pion production angles in the center-of-mass system

Final State Momentum Charged Pions • Neutral Pions (6eV/c) F/B . P/E F/B P/E

2/ 2/ 2.4 i .20 + 0.06. 1.371 0.07

2/2KV 1,20 +0.04 1,23 + 0.04 0.94 + 0.06 1. 04 10.06

2jr 2jt nK° ns2 1, 06 + 0.03 1.12 + 0.03 0.91 + 0.05 1.21 + 0. 05

•L - 2jt 2it 2.9 1.44 +0.10 1.68 + 0.11

2it it° 1.14+0.05 1.27 + 0.06 1.03 + 0.08 1, 00 10.09

2jt^ 2jt njt° ns2 1. 07 + 0.03 1.15 ± 0.03 0.85i 0.05 1.25 + 0.06

The.table clearly indicates that the anisotropy in the charged pions

decreases with increasing multiplicity. In agreement with other experiments

(7j llj 15) the anisotropy is,in general, greater at 2,9 GeV/c than at

2,4 GeV/co

The asymmetry observed in the angular distributions can be understood

in terms of the Koba-Takeda model (25). In this model, the nucléon is

comprised of a neutral core with an approximate radius of 2/3 I2m^c

and an outer pion cloud. The net charge of the pion cloud gives the charge

of the nucléon. In the pp annihilations, the core-core interaction sprays

out pions more or less uniformly, but the cloud pions tend to maintain the 72 motion which they had with their respective nucléons» This motion results in a forward peaking of the negative pions and a backward peaking of the positive pion with respect to the antiproton directiono

The increase of the anisotropy with decreased multiplicity and with increased antiproton momentum suggests that the asymmetry is a function of the pion momentum. In an extention of the Koba-Takeda model made by

Stajano (26) and in a statistical model by Pilkuhn (2?), the pion-angular asymmetry is predicted to be dependent on the momentum of the pion in the center of mass-systemo

The F/B and P/E ratios as a function of pion momentum in the center- of-mass system are shown in Figure 34 through Figure 36 for the charged pions in the SjTj and %MM selected samples. As predicted, the asymmetry is particularly characteristic of the faster pions in the center- of-mass system and P/E ratio increases with pion momentum at a faster rate

than the corresponding F/B ratio.

The multi-Regge model (28, 29) is another attempt to explain the

anisotropy in the charged pion distributions. In this model, the multi-

Regge exchange graphs which are applicable only to events in which all the

final particle pairs emerge with high invariant mass, are supplemented by

the assumption that non-resonance production with low invariant mass follows

phase space predictions. The increase of the F/B and P/E ratio with

increased incident antiproton momentum is attributed to the increasing

probability of pion production according to Regge exchange since there is

an increase of energy available per particle pair.

B. Pion Correlation Angles

The distributions of the center of mass angle between pairs of pions 73

_F I I 1 r B 2.4 GeV/c 24GeV/c h -477 EVENTS 4 TT EVENTS

1 1 150 450 750 1050 150 450 750 1050 F T T 1 _P T T B 2.9 GeV/c E 2.9 GeV/c 3 - 47r EVENTS 3(-47r.EVENTS

1 i

1 1 I 1 X 1 150 450 750 1050 150 450 750 1050 PION MOMENTUM (MeV/c)

Figure 34* Forward-backward and polar-equatorial asymmetry ratios as functions of pion momentum in the center-of-mass for events in the 4jr samples 74

1 1 1 1 1 1 1 F p B 2.4 GeV/c 2.4 GeV/c _5 7r EVENTS E 3 3 _ 5 TT EVENTS

(a) (b)

•

2 — — 2 — — 1 I I 1 • ' 1 - I

1 1 1 1 1 1 1 150 480 750 1000 150 450 750 1050 F 1 1 1 1 P 1 1 1 B 2.9 6eV/c E 2.9 GeV/c 3 - 5 TT EVENTS 3 - 5 TT EVENTS

2 — 2 —

r 1 Î 5 1 -j ^ 1

. _I1 I1 I1 I1 II1 I1 I1 II 150 450 750 1050 150 450 750 1050 PION MOMENTUM (MeV/c)

Figure 35» Forward-backward and polar-equatorial asymmetry ratios as functions of pion momentum in the center-of-mass for events in the Sît samples 75

E P 2.4 GeV/c 2.4 GeV/c B E _ 4 TT MM EVENTS _ 4 7rMM EVENTS 3

(a) (b)

- i I - 5

100 300 500 700 100 300 500 700 F 1 i T" P T B 2.9 GeV/c E 2.9 GeV/c 47r MM EVENTS 4 7rMM EVENTS 3

- I I - J

1 ± 100 300 500 700 100 300 500 700 PION MOMENTUM (MeV/c)

Figure 36. Forward-backward and polar-equatorial asymmetry ratios as function? of pion momentum in the center-of-mass for events in the UjtMM samples 76

of various charge (correlation angle) as shown for the and 4#MM selected events in Figure 37 through Figure 41. The smooth curves super imposed on the distributions are the predictions of Lorentz-invariant phase space. For similarly charged pions, small opening angles are preferredo

For unlike charged pions,large opening angles are preferred» This effect in the pion correlation angles can be interpreted in terms of Bose statis

tics (30),

To measure the deviations from phase space predictions, the parameter

7 defined by

Number of pion pairs with opening angle > 90° Number of pion pairs with opening angle < 90°

was calculated for the dipion distributionso The results of these calcula

tions are tabulated in Table 16.

Table 16. Correlation functions for dipion pairs in the pioh annihilation channel s

Reaction Momentum 7 + + y y îT- jr- jti phase space

2/2jt" 2.4 GeV/c 2.15 + 0.14 2.41 + 0.11 2.20

1.48 + 0.05 1.99 + 0.05 1.79 + 0.05 I.78

2#*2a n3t° n^ 1.34 + 0.03 1.66 + 0.03 1.58

2jt 2it 2.9 GeV/c 2.33 + 0.23 2.26 + 0.16 2.20

2#*2# It® 1.70 + 0.09 1.84 + 0.07 1.80 + 0.07 1.78

2ît'^lu n3t° nsZ 1.40 + 0.04 1.62 + 0.03 1.58 2.4 GeV/c 2.4 GeV/c 200 47r EVENTSJ 400 47r EVENTS. l5l6(7r±7ri)PAIRS 3032 (7r"''7r")F%IRS

(a) (b) 160 320 CO CO cc OÇ < < CL S 120 240 •vi U. U. O 0 û: tr LU ^ 80 m 160 =) 1 z 40- 80

I _L _L J_ -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 COS e COS 9

Figure 37. Distributions of the pion correlation angles in the center-of-mass system for events in the kji sample at 2.4 GeV/c 2.9 GeV/c 2.9 GcV/c 200 - 47r EVENTS - 100 h 47r EVENTS 4 l424(7r+7r~)PAIRS 7l2{7ri7ri)PAIRS

160 i (a) (b) CO to g C£ < 120 0- 60 u. 00 U. o O c: LU 80 g 40 m S •3 3 z Z 40 20

-1.0 -0.3 0.0 0.5 1.0 -1.0-0.5 0.0 0.5 1.0 cos e COS 9 Figure 380 Distributions of the pion correlation angles in the center-of-mass system for events in the % sample at 2.9 GeV/c —1—!—r— 1 1 1 2.4 GeV/c 2.4 GeV/c 2.4 GeV/c 57r EVENTS 57r EVENTS Sir EVENTS 1000 :ii0524(7rV;FaiRS 1000 _I0524(7r±7rO)5%fRS 400 |52S2(7ri7ri)PAIRS

800 800 V) W œ

200 - 200 80

I JL I _L JL I — 1.0 —0.5 0.0 0.5 1.0 -1.0-0.5 0.0 0.5 1.0 -1.0-0.5 0.0 0.5 1.0 COS e COS e COS 9 Figure 39» Distributions of the pion corrélation angles in the center-of-mass system for events in the 5it sample at 2.4 GeV/c 2.9 6eV/c 2.9 GeV/c 2.9 GeV/c 57r EVENTS _ 200 5 TT EVENTS _ 400 Sir EVENTS _ 400 4864(7r+7r~)PAIRS 4864 (7ri7r®)PAIRS 2432(77^ TT^) PAIRS

ISO 320 to 320

^ 240 U.240 t 120

UJ 2 160 2 160

80 80 40

0 1.0 -0.5 0.0 0.5 1.0 1.0 COS B

Figure 40. Distributions of the pion correlation angles in the center-of-mass system for events in the 5ît sample at 2»9 GeV/c 81

—I—I—I— 2.4 GeV/c 2.4 GeV/c 477-MM EVENTS 47rMM EVENTS 269l2(Tr+7r-)C0MB. l3456(7r±7r±)C0MB. ^2400 200 - a: g (b) U. s O u_ 1600 o 800 û: UJ cc CO LU 2 m 3 2 3 Z 800 400-

J L J L -1.0 -0.5 0.0 05 1.0 -1.0 -0.5 0.0 0:5 1.0 COS e COS B

1—r T 2.9 GeV/c 2.9 GeV/c 47rMM EVENTS 47rMM EVENTS (O .,l6864(Tr+7r-)PAIR3 8432(7r±7r±)PAlRS g 1200

I J L -I.O -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 COS e COS e

Figure 41» Distribution of the pion correlation angles in the center-oF-mass system for events in the 4aMM samples 82

The deviations from the values expected according to the Lorentz invariant phase space predictions are, in general, smaller at 2,S GeV/c than at 2.4 GeV/c. This trend, which has been reported at other antiproton momenta (3> 7, 11), is consistent with the Goldhaber model (30).

Co Angular Distributions of Resonance Production

The center of mass production angles for the various resonance particles and their decay angular distributions are presented in this section. Back ground events were subtracted using particle combinations in control regions outside the resonance region. In the annihilation channels, there is no clearly preferable choice for the quantization axis. The decay angular distributions were calculated with respect to the normal to the production pi ane in the rest frame of the resonance in order to determi ne if the resonance spins lie preferentially in the production plane,^ A list of the resonance particles whose angular distributions are studied in this section together with their designated resonance and background regions is shown in Table 17» li Production angles of resonances

The center-of-mass production angular distributions taken with respect to the antiproton direction are shown for resonances in the four and five pion annihilation channels in Figure 42. Charge conjugation invariance implies that the p°f°and (o° production angular distributions should be symmetric about cos € = 0. The p° production angular distribution at

2.4 GeV/c for the four and five pion events and the f° distribution in the

^In the four pion annihilation events at 5»7 GeV/c, the p° mesons were, produced with their spin lying preferentially in the production plane. Table 17» Mass regions used for investigating resonance angular distribu tions at 2.4 and 2.g GeV/c "

Resonance ^ Background Background . Channel Momentum Resonance Region (MeV/c ) Region-Below Region-Above Resonance Resonance (MeV/c^) - (MeV/c^)

o 4jr 2.4 P 690-840 480-630 900-1050

1170-1350 960-1110 1410-1560

.1200-1400 1000-1200 1400-1600 *2 M (1700) 1600-1800 1400-1600 1800-2000 o hjt 2.9 P 660-810 460-610 860-1010

1110-1360 910-1060 .1410-1560 o 2.4 p 660-810 480-630 840-990 + p~ 660-840 420-600 870-1050 o (0 750-810 630-720 840-930

G 53T 2.9 P 700-840 525-665 875-1015 + P- 665-840 455-630 875-1050 o (U 770-805 595-735 805-945 _1 , f 60 2.4 GeV/c 2.4 GeV/c 4 TT EVENTS 47r EVENTS (a) (b) 50 226 /o'COMBINATION: 215 f°COMBINATIONS - 40

I10

z 2.9 GeV/c 2.9 GeV/c I i30 (c) 4 TT EVENTS (d) 47r EVENTS 8 105/J"COMBINATIONS I34f° COMBINATIONS u-25 o £20 !•=

10 51=

0 _L I I ±1 -0.8 -0,4 00 0.4 0.8 -0.8 -0.4 0.0 0.4 0.8 COS d COS e

Figure 42. Production angles of resonances . a),c) Distributions of the cosine of the production angle in the center-of-mass system of p° combinations from events in the 4m samples b),d) Distributions of the cosine of the production angle in the center-of-mass system of f° combinations from events in the 4]t samples -1 I I 1 1— 2.4 GeV/c 2.4 6eV/c 150 577- EVENTS 5 ^EVENTS 180 732^0" COMBINATIONS 582 p' COMBINATIONS 125 150 100 (e) (f) 120

CO 90 z 75 o 60 Î5 50 u. z m 25 30 0 2.9 GeV/c 2.9 GeV/c 5 TT EVENTS . 5 TT EVENTS 120 220/9» COMBINATIONS 253 yO-COMBINATIONS m 50 90 60

30 0

-30 0.0 -60 Figure 42 (Continued)^oontinueu/» COS e COS e e),g) Distributions of the cosine of the production angle in the center-of-mass system of

pO UWIMUcombinations I I io c 1 VI1^ fromt I v^iii eventscvcNLO IIIin theLUC 53t samples fhh) Distributions of the cosine of the production angle in the center-of-mass system of «2 combinations from events' in the 53t samples 2.4 GeV/c 2.4GCV/C 47r EVENTS 0) 4 TT EVENTS 45 COMBINATIONS 55 M(1700)COMBINATIONS

P-5

S 50 2.4GDV/C r, V 2.9 GeV/c 57r EVENTS ' ' 57rEVENTS 20 u. 40- 120a)"C0MBlNATI0NS 43a;» COMBINATIONS fS30 § 20

—10 — AO 0.4 0.8 -0.8 -0.4 0.0 0.4 0.8 COS0 COS# Figure 43 (Continued) » i),j) Distributions of the cosine of the production angles in the center-of-mass system of Ao and M(1700) combinations from events at the hjt sample at 2.4 GeV/c k),1) Distributions of the cosine of the production angles in the center-of-mass system of (i,° combinations from events in the 5ît samples 85

four pion samples at both momenta are consistent with charge conjugation invariance. The distributions at 2,4 GeV/c in both the four and five pion events show a forward and backward peaking. The p° production angular distributions at 2.9 GeV/c have an accumulation of events in the forward direction only. The (j)° production angular distributions at both momenta show a small forward peaking.

For charged resonances, the positively charged resonance distributions were reflected about cos 6=0. Thus, from the forward peaking of the p~ distributions at 2.4 and 2.9 GeV/c, there is indication that the p (p^) is produced preferentially in the direction of the antiproton (proton). + . The A—2 production angular distributions for four pion events at 2.4 GeV/c show a forward accumulation of events. The F/B ratio for these events is

2.8 + lo7o The anomaly at about 750 MeV/c in the F/B ratio of charged pions as a function of pion momentum in the center-of mass system for events in the 4jt sample at 2,4 GeV/c (Figure 34) can in part be attributed to the class of events where the pion is produced in association with an Ag meson.

Two-body A—production comprises about 6% of the 4jt sample at 2.4

GeV/c (Table 10). Within the errors, the M(1700) production angular

distribution is consistent with isotropy.

2. Decay angular distributions

Information about the polarization of a resonance can be obtained

from the angular distributions of its decay products. For example, the

decay correlation W^S, ep) for the p° meson (having spin one and decaying

into spinlëss pions) is given by .... • = ^[pooôsê + ^('-Poo)sinê - Re p,_, sinfo cos 2.tp]

where G and tp are defined in the p° rest frame with the z-axis taken as the 86

normal to the production plane and the y axis taken as the Incident beam direction (31)o The p's are the decay density matrix elements with being the product of p° amplitudes with spin projections n and n'. Thus p^^ Is the probability for the p° meson to decay with its spin aligned

In the production plane* integration over cp gives

W^ (e). = |tpoo cos^e +l (1 - Poo) sin^O]

Thus If the polarization is along the normal, is zero and W^(G) Is 2 proportional to sin 0. A corresponding (cos G) distribution would be peaked at 6 = 90» If the p° decays with its spin aligned in the production plane, then p^^ Is equal to one and Wj(€)is proportional to cos 0. For a spin two particle (J=2) decaying into two spinless particles,the decay correlation as a function of G, Is given by

W^CG) = 2'• fô P22 2 cos^G

+ ç(3 cos^G - 1)^ Poo + 2 sin^G cos^G p_,_,

+ 16 s,n G p_2_2] where again the z-axis Is taken as the normal to the production plane.

Thus, if the f'^(-»3tir, J=2) decays with its spin aligned in the production plane, then p^^ equals one and all other density matrix elements are zero, 2 4 In this case,WgfG) Is proportional to 1 - 6 cos G + 9 cos G and a (cos G)

distribution would show a forward and backward peaking. If the f° decays k with Its spin aligned along the normal, then Wg(G) is proportional to sin G

and the W2(cos G) distribution would be peaked at 0=90 degrees. No correlation

functions were calculated for the more complicated -+ pit or^MO700)-> fît

decays. 87

The decay angular distributions shown in Figure 43 were calculated with respect to the normal to the production plane in the rest frame of the resonance. For p and f° decays, the distributions are of the cosine of the angle between a it coming from the resonance decay and the normal to the production plane» The cosine of the angle between the normal to the decay plane and the normal to the production plane was calculated for wT,

A, M(1700), decays. As shown in Figure 42^ except for the p° combinations in the 4jt sample at 2.4 GeV/c, the p° mesons have a tendency to be produced with their spins lying preferentially in the production plane. The f° decays in the 4jt sample at 2.9 GeV/c shows a preference for the f° to be produced with its spin along the normal to the production plane. As would be expected for a J = 0 resonance, the decay distributions are consistent with isotropy. The p— decay angular distributions indicate that the p— is produced without a preferred polarization. 60 - 2.4 GeV/c 24 GeV/c 47r EVENTS 47rEVENTS 50 — 226/?" COMBINATIONS 215 f'COMBINATIONS 40 30

CO 20 î=IO

2.9 6eV/c 2.9GeV/c 4 TT EVENTS R25 4 TT EVENTS lOSyo» COMBINATIONS l34f®C0MBINf^TI0NS 30 O20 25 • 20

-0.8 -0.4 0.0 0.4 0.8 -0.8 -0.4 0.0 0.4 0.8 COS g COS#

Figure 43. Decay angular distributions ^ a), c) Distribution of the cosine of the angle between the it coming from the p -decay and the normal to the production plane in the rest frame of the p°-meson for events in the h% samples + „ b), d) Distributions of the cosine of the angle between the « coming from the f -decay and the normal to the production plane in the rest frame of the fO-meson for events in the 4jt samples V

(e) 2.4 GeV/c ' (f) 2.4 GeV/c 120 5TTEVENTS 5 TT EVENTS 125 732p° COMBINATIONS 582 bMBlNATIONS 100 100

80 75 (/) 60 50 p 40 25 < z m 20 0 S 8 u. fq) 2.9 GeV/c y (h) 2.9 GeV/c f 0 50 ^9-' 5-rrEVENTS I 5TTEVENTS 100 cc j220p" COMBINATIONS 253^*C0MBINATI0NS s 40 80 2 1 30 60 20 40 10 20

0.0 Figure 43 (Continued). COS 0 COS e ; â), g) Distribution of the cosine of the angles between the « coming from the p • decay and the normal to the production plane in the rest frame of the p°-meson for events in the Sît samples _ f), h) Distribution of the cosine of the angle between the i: (it") coming from the p^cp" )- decay and the normal to the production plane in the rest frame of the (p")-meson for events in the 5ît samples 2.4 GeV/c 2.4GeV/c 4 TT EVENTS 47rEVENTS 45 A COMBINATIONS INATIONS

2.4 GeV/c 2.9GeV/c o SttEVENTS 43 W COMBINATIONS

-0.8 -04 0.0 04 0.8 -0.8 -0.4 0.0 Figure 43 (Continued). COS 6 COS 6 i), j) Distributions of the cosine of the angle between the normal to the decay plane of A? (M(1700)) meson and the normal to the production plane in the rest frame of the P>2 (M(1700)) meson for events in the kjt sample at 2.4 GeV/c ^ k), 1) Distributions of the cosine of the normal to the decay plane of the tu meson and the normal to the production plane in the rest of the u)° for events in the Sît samples 89

• VI. CONCLUSION.

The cross sections for four and five pion annihilations at 2o4 and 2.9

GeV/c, which are listed in Table 7, were found to compare favorably with the corresponding cross sections at other energies (Figure 5)« The cross section for the reactions pp jt (n > 1) (Table 7) is somewhat lower at 2»9 GeV/c, than at 2,4 GeV/c; however, the energy dependence, of this cross section over the 1-4 GeV/c range is not immediately apparent.

Copious and f*^ resonance production was found in the four pion channel at both momenta. The four pion final states were found to be pri marily produced via the pp -» and pp -> f^ir^jt production modes. The frequency for associated resonance production in the four pion channel at each momentum was less than 0.10. As seen from Figure 13, the cross section for two-body production processes in the four pion channel de creases as the incident antiproton momentum is increased from 1 to 3 GeV/c, but the cross section for three-body production increases over this range.

Evidence for Ag production and a fit enhancement at a mass of approximately 2 1700 MeV/c was found in the four pion channel at 2.4 GeV/c.

Abundant p°, p—, and (d° resonance production was found in the five pion channel at each momentum. The cross sections at both 2.4 and 2.9

GeV/c are smaller than would be predicted from experimental data at other energies (Figure 27a).

Many types of production modes were found in the five pion channel at both momenta. The most frequently produced three meson intermediate state was the p—p'^ît^ state. The production mode was found to occur in about 20% of the five pion reactions at each momentum. The frequencies for Aj and Ag production were small at both momenta. Indica 90

tions of B meson production was seen in the co°3t^ distribution at 2.4 GeV/c

(Figure 24)«

The production angular distribution for charged pions in the center-of- mass system showed a tendency for the it to be produced in the direction of the antiproton (proton)o This forward-backward asymmetry decreased with increased multiplicity and increased at the higher momentum. The distributions of the center of mass angle between pairs of pions of various charge showed that similarly charged pions prefer small opening angles and unlike charged pions prefer large opening angles. The decay angular distri bution showed that the p° is preferentially produced with its spin in the production plane, but in the 4:rt sample the f° at 2.9 GeV/c is produced with its spin preferentially along the normal to the production plane. 91

VII.. BIBLIOGRAPHY

1« Go Kalbfleishj Ro Strand, and V. Vanderburg, PhySo Letters, 29B, 259 (1969)0

2. Ro Ao Donald, Do N» Edwards, R. So Moore, E. J. Co Read, So Rencrof, Ao Go Frodesen, To Jacobsen, S. Sire, 0. Skjeggestad, Po Saetre, Ho T;5fte, A. Bettinz, So Limentani, L. Peruzzo, R. Santangelo, and So SartorI, Nucl. Physo _B^ 174 (1968)0

3» R- Ao Donald, Do No Edwards, Ro So Moore, Eo J. C. Read, S. Rencroft. To Buran, A. Go Frodesen, So Sire, Po Saetre, A. Bettini, S. Limentani, Lo Peruzzo, Ro Santangelo, and So Sartori, Nucl. PhySo Bl1, 551 (I969)*

4o Wo Ao Cooper, Lo Go Hyman, Jo Loken, W. Manner, and L. Voyvodic, Physo Revo Letters 2J0, 1059 (1968)0

5" V/o Ao Cooper, Lo Go Hyman, J» Loken, V/o Manner,. and Lo Voyvodic, (Abstract) Bull. Am. Physo Soco J3^ 1441 (1968)0

60 Ro Jo Sprafka, Po So Eastman, Zo M. Ma, Bo Yo Oh, Do L. Parker and Go Ao Smith, (Abstract) Bullo Amo Phys. Soco 637 (1969)»

7» Bo Co Magiic. Go R. Kalbfleisch, and M. Lo Stevenson, Phys. Rev, Letters J, 137 (1961 )o

8. Jo Clayton, P. Mason, Ho Muirhead, 0. Waldren, R. Rigopoulos, P. Tsi1imigras, and A. Vayaki - Serafimidou. The annihilation process pp =4 2jt"'' 2jt~ at 2.5 GeV/c. Unpublished preliminary report presented at the Lund International Conference on Elementary Particles, Lund, Sweden, June, 1969. Department of Physics, University of Liverpool, Liverpool, England.

9» Jo Clayton, P. Mason, H. Muirhead, Ko Whiteley, R. Rigopoulos, P. ^ Tsilimigras, Ao Vayaki - Serafimidou, The annihilation process"pp^2)t 2jt if at 2,5 GeV/co Unpublished preliminary report presented at the Lund International Conference,on Elementary Particles, Lund, Sweden^ June, 1969» Department of Physics, University of Liverpool, Liverpool,England.

10. Wo J. Kernan, D. E. Lyon, and H. B. Crawley, Phys. Rev. Letters J_5, 803 (1965)0

11. To Ferbel, A, Firestone, J. Sandweiss, Ho D. Taft, Mo Gail loud, T. Wo Morris, W. Jo Willis, A. H. Bachman, Po Banmel, and R. M. Lea, Phys. Revo 1096 (1966)0

12. Jo Debray, Jo Laberrigue, G. Pichon, M. Rumpf, Co De La Vaissiere, and . To Po Yiou, General characteristics of pp ^ 2%+ 2a"(#0) annihilations at 3o6 GeV/co Unpublished preliminary report presented at the Lund International Conference on Elementary Particles, Lund, Sweden, June, .1969» Institute de Physique Nucléaire," Paris, France. 92

13» Ao Accensi, \I„ A1 les-Borel 11, B. French, Frisk, Jo M. Howie, Wo Krischer, L» Michejda, W. G. Moorhead, Bo W. Powell, P. Seyboth, and Po Villemoes, Phys. Letters ^0, 557 (l966)o

Ko Bockmann, Bo Nell en, Eo Paul, B. Vfagini, I o Borecka, J, Diaz, Do Heeren, V. Liebermeister, E. Lohrmann, Eo Ranbol d, P. Soding, So Wolft, Jo Kidd, Lo Mandelli, L. Mosca, Vo Pelosi, S. Ratli, and L. Tallone, Nuovo Cimento 42A, 954 (1966). o 15» Vo A1 les-Borel 1i. Bo French, A. Frisk, Lo Michejda, and E. Paul, Nuovo Cimento 50A, 776 (1967)0

16. To Ferbel, A. Firestone, Jo Johnson, Jo Sandweiss, and H. D. Taft, Nuovo Cimento 38, 12 (1965)»

17» Ro Ao Jespersen, Two- and Three-Pioii Production Without Annihilation in Antiproton-Proton Interactions at 2.4 and 2.9 GeV/c, Unpublished Ph.Do Thesis, Iowa State University, (1969)°

I80 W. J. Higby and Ao Ho Klein, UoS.AoEoC. Ames Laboratory On-Line Control System for Bubble Chamber Film Measuring, Report to be published. Department of Physics, Iowa State University, Ames, Iowa (ca» 1970).

19» Jo Po Berge, Fo To Solmitz, and Ho Do Taft, Rev. Scio Instro 32, 538 (1961)0

20. Wo Jo Kernan, W. J. Higby, and I. H. Boessenroth, United States Atomic Energy Commission Report IS-IO72 [Iowa State University, Ames, Iowa] (1964). o 21. L. So Schroeder, W. Jo Kernan, G. Po Fisher, A. J. Eide, J. Von Krogh, Lo Marshall Ltbby, and R. Sears, "pp Annihilations to K and it Mesons at 2»7 GeV/c, Paper to be published in Physo ReVo (cao 1969)0

22o Jo Do Jackson, Nuova Cimento 34» 1644 (1964).

23o Ho Ro Rubinstein and Ho Stern, Phys. Letters 21, 447 (1966)0

24o Ao Pais, Phys. Rev. Letters 3, 242 (1959)»

25. Z. Koba and G. Tokeda, Progr. Theoret. Phys. (Kyoto) 269 (1958)o

260 Ao Stajano, Nuovo Cimento 2^ 197 (1963)»

27o Ho Pilkuhn, Arkiv Fysik 23, 259 (1962).

28. Ho Chan, Jo Loskiewicz, and Wo V/o M. Allison, Nuovo Cimento 57A, 93 (1968)0

29. Go Ranft, Rutherford Preprint RPP/H/43 Aug. I9680 93

G. Goldhaber, S. Goldhaber, W. Lee, and A» Pais, Phys. Rev. 120, 300 (I960).

Dalitz, R. H. The Production and Decay of Resonant States. Scuola InternazionàTe di Fisica ((Enrico Fertnî>), Proc. XXXII 1: 70-188. 1966. 94

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation to Professor

William J. Kernan for his poignant suggestions, amicable discussions, and flexible policies in directing this dissertation»

Much credit is due Dr. H» Bert Crawley for his enthusiastic and unselfish aid in completing the final stages of this. work.

A special note of thanks is due Dr« Lee So Schroeder for his many helpful suggestions and encouragement throughout the course of this study.

Appreciation is expressed to Professor Robert 0. Haxby for his personal interest and for his help in proofreading, to Dr. Robert Ao Leacock for his pungent suggestions. Dr. Terry L. Schalk and Dr. J. Ivan Rhode for pro gramming assistance, and Dro Richard A. Jesperson for aid in the kinematical processing of events.

Acknowledgment is given to the programming staff headed by Mr. W. J.

Higby and to the scanning and measuring staff directed by Mrs. Betty Pepper.

The cooperation of John Linderblood and Chris Hanson of the Iowa State

Computing Center is gratefully appreciatedo

The author wishes to thank Carol Beavers for performing several of the arduous calculations needed for the final analysis.

Finally, the author wishes to thank all others who have given him encouragement throughout his graduate studies.