Calculations of three-pion correlations from a final-state rescattering model: comparisons with experiment.

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Nuclear Physics A661 (1999) 431c--434c www.elsevier.nl/Iocate/npe

Calculations of three-pion correlations from a final-state rescattering model: comparisons with experiment. T. J. Humanic a aDepartment of Physics, The Ohio State University, Columbus, OH 43210 A simple rescattering model is used to predict three-pion correlation functions in CERN SPS-energy S + P b and P b + P b collisions. Gaussian pion source parameters are extracted from these calculations as well as the three-pion phase factor, cos¢. The three-pion phase factor is found to be close to unity for both systems and for all regions of rapidity and transverse momentum investigated. Comparisons are made with recent experimental results from NA44. 1. I n t r o d u c t i o n A recently published study[l] uses a final-state rescattering model coupled with a threepion symmetrization method to predict the three-pion correlation functions and source distribution phase variables [2] for SPS S+Pb and P b + P b collisions. Also recently, the CERN NA44 experiment has published a three-pion analysis for 200 GeV/nucleon S + P b collisions[3]. In addition, NA44 has reported a preliminary analysis of 158 GeV/nucleon P b + P b data for three-pion correlations at this conference[4]. The present paper compares the three-pion phase variables from the rescattering model with those extracted by NA44. It should be noted that this rescattering model coupled with a two-pion symmetrization has already been shown to qualitatively agree with the trends of published two-pion correlation data for these systems[5-7] as illustrated in Figure 1. Thus, these calculation should represent realistic expectations for the anticipated experimental three-pion results assuming that no exotic processes are taking place in these collisions which might produce, for example, coherent pion emission. 2. C a l c u l a t i o n a l M e t h o d A brief description of the calculational method used is given below. A more detailed description of this calculation may be found elsewhere[I]. Rescattering is simulated with a semi-classical Monte Carlo calculation which assumes strong binary collisions between hadrons. The Monte Carlo calculation is carried out in three stages: 1) initialization and hadronization, 2) rescattering and freeze out, and 3) calculation of two-pion and threepion observables. All calculations are made to simulate CERN-energy S + P b and P b + P b collisions in order to compare with CERN experiments. The two-pion and three-pion observables are calculated from the freeze out space-time positions of the pions from the rescattering stage. For the present work, one-dimensional 0375-9474/99/$ see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0375-9474(99)00490-X

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T.J Humanic/Nuclear Physics A661 (1999) 431c-434c

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two-pion and three-pion correlation functions are formed in terms of the variables Qin,, and Q3, respectively, where, Q~,~ = [Qn[ = IPl -/'21

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and where Pi (i = 1, 2, 3) is the momentum four-vector of the i th pion. Pairs and triplets of pions are weighted by symmetrization terms and binned appropriately to form the two-pion and three-pion correlation functions. The two-pion and three-pion correlation functions, C2 and Ca respectively, are calculated as C~(Q~,,~) = a2(Q~n,)/~2(Q~,~)

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where ~2(aa) represents the binned weighted pion pairs(triples) and fl~(fla) represents the binned unweighted pion pairs(triples). Binnings of 10 MeV are used throughout to match

T.J Humanic/Nuclear Physics A661 (1999) 431c-434c

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those normally used by experiments. Heinz and Zhang[2] have derived an expression for calculating a pion source phase factor, cos ~b, from a knowledge of 6'2 and C3 which is cos¢ = [C3(Qa) - 1 ] - [C2(Qn) - 1 ] - [C2(Q23) - 1 ] - [C~(Qal) - 1] 2~/C2(Q12) - l~C~(Q2a) - 1~/C2(Q31) - 1

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For a totally incoherent symmetric pion source, cos ¢ = 1, whereas for a source which is only partially coherent and/or asymmetric, then cos¢ < 112]. For simplicity, in order to express cos ¢ in terms of Q3 alone, the quantity can be defined which is the average of cos ¢ over the two-body Qij's for a given Q3 bin. This quantity is calculated in the present paper. 3. R e s u l t s and D i s c u s s i o n

Comparisons between calculated and measured values of the quantity (cos ~b> are given below for the systems S+Pb and Pb+Pb in Figures 2 and 3, respectively. Figure 2 shows the quantity (cos ¢) for S+Pb plotted versus Q3 calculated in two different ways using Eq. (5): 1) using the two-pion and three-pion correlation functions directly from the rescattering calculations (filled circles), and 2) using fitted gaussian parameters from the rescattering model to represent the two-pion and three-pion correlation functions (open triangles). The experimental results from NA44 are also shown (open squares). The range plotted in Qa gives the region most sensitive to three-pion effects. As can be seen

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TJ. Humanic/Nuclear Physics A661 (1999) 431c-434c

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from the direct calculation from the rescattering model, (cos ¢) is close to unity for all values of Q3 plotted, with an average value of 1.06 4- 0.04, as would be expected for a totally incoherent symmetric pion source[2]. Thus for this system and acceptance the rescattering process does not distort the phase information carried by (cos ¢). However, the rescattering results are seen to be too high compared with NA44, indicating that some feature(s) of the data is not included in the model. Figure 3 show plots of
T . J . Humanic, Phys. Rev. C 60, 014901 (1999). U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997). H. Boggild et al., NA44 Collaboration, Phys. Lett. B 455, 77 (1999). J. Schmidt-Sorensen et al., NA44 Collaboration, in these Proceedings. T. J. Humanic, Phys. Rev. C 50, 2525 (1994). T. J. Humanic, Phys. Rev. C 53, 901 (1996). T . J . Humanic, Phys. Rev. C 57, 866 (1998). I.G. Bearden et al., NA44 Collaboration, Phys. Rev. C 58, 1656 (1998) and references therein; D. Reichhold et al., NA44 Collaboration, in these Proceedings.