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Nuclear Physics B42 (1972) 85 94. North-ftolland Publishing Company,

TRANSVERSE

AND LONGITUDINAL

MOMENTUM SPECTRA

O F P I O N S IN ~ d I N T E R A C T I O N S

A T 3.5 G e V / c *

M.A. IJAZ Department of Physics, VirginiaPolytechnic Institute and State University Blaeksburg, Virginia 24061 B.A. MUNIR and E.J.B. TERRAULT Department of Physics, Ohio University. Athens, Ohio 45 701

Received 26 January 1972

Abstract: Experimental Pt and Pl spectra of pions in 3, 4, 5 and 6 prong events in pd reactions at 3.5 GeV/c have been measured in a bubble chamber experiment. The Pt spectra are fitted with Hagedorn and Boltzmann distributions. The average value of Pt is found to be in the range of 0.35 0.40 GeV/c. The Pt spectra of annihilation pions,are fitted better with the above distributions than the spectra of pions found in production reactions. The c.m.s. Pl spectra of pions are analyzed in terms of Jacob's nova model and Feynman's scaling distribution. The Pl spectra, when analyzed after making cuts ill Pt distributions, reveal that Pl and Pt arc not independent of each other in this experiment.

1. INTRODUCTION The subject of multiple particle production at high energies has become of considerable interest in recent years. Many experimental and theoretical papers [1 5] have been devoted to the study of longitudinal (Pl) and transverse m o m e n t u m (Pt) spectra of pions produced in exclusive and inclusive reactions at accelerator energies. It is fairly well established that the average value of Pt remains constant around 350 MeV/c and is nearly independent of the nature of the colliding particles and their energy. Since average Pt stays small, a particle produced with large m o m e n t u m will have large values ofPl. A study of Pl spectra can therefore reveal some important features of the strong interaction mechanism responsible for particle production. Feynman [6] has recently suggested that at high energies the Pt and Pl of a produced particle become independent of each other and the differential cross section when studied as a function o f x = 2Pl/Ec.m. may show a scaling behavior. We have investi* Work supported in part by the National Science Foundation.

86

M.A. I/az et al., ~Jd interactions at 3. 5 (;e V/c

gated the Pl and Pt interdependence and fitted Pl spectra with an oversimplified version [7] of the scaling and Jacob's nova model distributions [8]. We have compared the spectra of pions produced in annihilation channels with the pions produced in NN, rrp and pp collisions.

..'~ EXPERIMENTAL DETAILS The experiment was performed at the Argonne National Laboratory using the 30 inch MURA deuterium bubble chamber. 90 000 pictures were taken. Most of the film has been measured and processed for three and five charged secondaries. Four and six pronged events including a visible spectator proton were also nreasured. An upper cut off of 250 MeV/c was applied on tile spectator's momentum. The momentum spectrum of tile visible protons is in agreement with the Hulthe'n wavefunction and their angular distribution is isotropic. The events were measured using film plane digitizer connected on line with an IBM 1800 computer. Data reduction was done by using Berkely TVGP, SQUAW, CHIEF and CERN version of SUMX. The following general criteria were used for accepting the fitted events. (i) SQUAW gave a fit to the hypothesis with a minimum probability of 5%. (ii) The fit chosen was compatible with ionization estimates made on the scan table. (iii) In case of more than one fit compatible with ionization estimates a 3 : 1 probability ratio was used to reject the less probable fit. Tile Pt and Pl data presented in this paper are for those pions which fitted the following reactions. ~n -7 pwr

(1)

(P) pprr rr° ,

(2)

~na+rr

(3) +

~r rr 7r , rr

rr

7r+Tr° ,

rr rr rr+r?° ,

(4) (5)

(6)

rr

7r ~

rr+~ + ,

(7)

rr

ir

rr+rr+rr ° ,

(8)

rr

r, rr rr n'+rr+~° .

(9)

Pions in reactions (1) through (3) are produced pions while the pions in reactions (4) through (9) annihilation pions.

M.A. ljaz etaL, ~d interactions at 3.5 Ge V/e

87

3. D A T A A N D A N A L Y S I S

3.1. Transverse m o m e n t u m In p l o t t i n g the Pt spectra w e have c o m b i n e d n - and n + distributions. Neutral pions were p l o t t e d separately to see if t h e y display any difference. Fig. 1 (a) repre3o0[

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88

M.A. I/az et al., pd interactions at 3.5 GeV/c

sents the same for n ° from reaction (5), and fig. l(c) represents the Pt spectra of pions produced in reactions (1) through (3). Fig. 2 shows Pt spectra of pions from reactions (7) through (9). The three distributions shown have been labelled. The distribution shown in fig. 2(c) is for a sample of data in which a cut was imposed on Pl" The object of this cut was to separate out events which could be considered analog of "beam-like" or "through-going" particles in the context of Hagedorn model [9]. ha reactions (4) through (9) ~ annihilates with a neutron to give rise to many pions and thus there is no beam-like particle in the final state. However, there is usually a fast going n - which seems to remember the path of the incoming antiproton. It is this pion which carries large values of Pl. The solid and dashed curves shown in figs. 1 and 2 are fits computed by using Hagedorn and Boltzmann distributions for the Pt spectra: N(Pt)dPt = N o P t e

-Pt/T

(Hagedorn) ,

- p t 2/c~ 2

N(Pt)dPt = NoPte

(Boltzmann);

NO is a normalization constant and T represents the Hagedorn temperature. Although Hagedorn developed the theory of statistical thermodynamics of strong interactions for the pp reactions, his expression for Pt distributions fits pion Pt spectra in many different reactions especially for high nmltiplicities [10]. Both distributions described above fit the general shape of the Pt spectra. Table 1 contains the X2 value for each data point and some other parameters. We note that the Pt spectrum of the pions produced in reactions (1) through (3) is not fitted well by the Hagedorn distribution. The reason may be that there is strong anti-isobar production [11 ] in these reactions. We also note that the Hagedorn distribution fits the data better. The value of temperature for 5 and 6 pion events is ~ 140 MeV which can be compared with the value o f ~ 130 MeV [12] obtained for 6 pion events in 7rp and pp collisions having the same c.m. energy as tile present experiment.

Table 1 x2 and fitted parameters tbr the Pt spectra. Fig.

Reaction

Particle

No. of pions

×H.D.Z

Temp. (GeV)

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spectra of pions from reactions (1), (2) and (3) fitted with Jacob's distribution.

3.2. Longitudinal momenta Figs. 3, 4, and 5 show c.m.s, longitudinal momentum (Pl) spectra of pions from reactions (1) through (9). The nature of the spectra implies that an exponential function should fit the data. Feynman's scaling hypothesis implies that for a fixed value of Pt, the mean number of particles of any kind is distributed as dPl/E, where E is the energy of the particle. Recently Jacob [8] has proposed a nova model in which either beam or target particle is diffractively excited into a state or a combination of states which decays mainly through pion emission. He obtains an expression for the differential cross section as follows:

do

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(d)

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Particle 0.9 1.4 1.5 0.5 1.1 1.2 2.0 0.8

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2 XC

0.34 0.40 0.43 0.50 0.37 0.47 0.48 0.50

+ + + + ± ± + +

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C2 ; A t 2

Table 3 x 2 a n d fitted p a r a m e t e r s o f tile e x p o n e n t i a l a n d J a c o b ' s d i s t r i b u t i o n s .

nno ~* rrlr° n+ rr rd

Particle

2

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M. A. l/az et al., ~d interactions at 3.5 Ge V/c

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(Jacob) ,

N(Pl)dP~ = Cle-c2 IPlldPl

(Exponential) ,

where a 1 contains the normalization and the structure function f(x,pt,s ) assumed to be constant; b 1 contains normalization and an exponential term exp ( - p ~ ) , whose value has been computed at an average value o f p 2. The fitted curves for Feynman and Jacob's distributions are shown in fig. 3. The fitted parameters for the three dis2 tributions are shown in table 2. We note that the scaling distribution does not fit the data. The exponential and Jacob's distribution fit most of the distributions well except for pions produced in reactions (1), (2) and (3). These reactions contain lots of anti-isobar production. We also note that when the multiplicity of an event is small, there is a marked asymmetry in the c.m.s. Pl spectra around the origin. This effect is less pronounced as we go to higher multiplicities. In figs. 6 and 7 we have plotted Pl spectra for various intervals of Pt. The exponential and Jacob's distribution fits the data. The fitted parameters are shown in table 3. The values o f parameters b 2 and c 2 increase as Pt increases. There is an apparent dependence of Pl on Pt, and it is perhaps due to this reason that the scaling distribution does not fit the Pl spectra. Fig. 8 is a plot o f (pt) versus x where x = 2Pl/Ec.m.. This also indicates that Pt and Pl are not independent o f each other.

94

M.A. ljaz et al., pd interactions at 3.5 Ge VIe

4. RESULTS AND DISCUSSION The Pt spectra of the pions produced in 3 prong and 5 prong annihilation events is best fitted by the Hagedorn model. Pions coming from the reactions where antiisobar and mesonic resonances are produced have a Pt distribution which is not fitted well by a Hagedorn or Boltzmann distribution. The Pl spectra are best fitted by a Gaussian type distribution which can be obtained from Jacob's nova model by assuming independence of Pt and Pl from each other, which is apparently not true in this experiment. It is hard to understand why the Pl spectra are fitted so well by the Jacob distributions. The Pl spectra are also fitted quite well by an exponential function with a linear Pl in the exponent. We wish to thank our colleagues, Drs. D. Huwe, J. Bishop, and J. Hsieh, for their contributions in various phases of this experiment. One of us (MAI) is thankful to Dr. R.A. Arndt and Mr. Wilson Gilliam, Jr. for their help in computer programming.

REFERENCES

[1] J.W. Elbert, et al., Phys. Rev. Letters 20 (1968) 124. [21 I. Bar-Nir, et al., Nucl. Phys. B20 (1970) 45. [3] D. Amati, et al., Nuovo Cimento 26 (1962) 896. [4] K. Imaeda, Nuovo Cimenta 48A (1967) 482. {5] K. Wilson, Cornell University, preprint (1970). [6] R.P. Feynman, Phys. Rev. Letters 23 (1969) 1415. 171 Min-Shih Chen, et al., Phys. Rev. Letters 26 (1971) 280. 181 M. Jacob and R. Slansky, preprint #2726 613, Yale University (1971). I91 R. Hagedorn, Nuovo Cimento Supp. 3 (1965) 147 and Nucl. Phys. B24, (1970) 93. 1101 M.A. Ijaz, et al., Nuovo Cimento., (to be published). [11] J.S. Hsieh and B.A. Munir, Particles and nuclei 1 (1971) 275. [12] M.A. ljaz and J.E. Campbell, Nuovo Cimento 61A (1969) 307.