NUMERICAL MODELLING OF QUANTUM STATISTICS IN HIGHENERGY PHYSICS

Abstract

Numerical modelling of quantum effects caused by bosonic or fermionic character of secondaries produced in high energy collisions of different sorts is at the moment still far from being established. In what follows we propose novel numerical method of modelling Bose-Einstein correlations (BEC) observed among identical (bosonic) particles produced in such reactions. We argue that the most natural approach is to work directly in the momentum space of produced secondaries in which the Bose statistics reveals itself in their tendency to bunch in a specific way in the available phase space. Fermionic particles can also be treated in similar fashion. The multiparticle production processes consist substantial part of the high energy collisions and are of considerable theoretical interest. Unfortunately their description is so far available only by means of numerical Monte Carlo codes based to some extent on modern theoretical ideas but otherwise remaining purely phenomenological [1]. They are build in such manner as to describe as close as possible the complicated final state of such reaction, cf., Fig. 1. However, using classical (positive difined) probabilities as their basic tool such MC codes cannot directly describe some observed features, which are connected with Bose-Einstein (BE) (or Fermi-Dirac (FD)) statistics of produced secondaries (in case they are identical and occupy almost the same parts of the phase space defined by the uncertainty relation, see Fig. 1). When two (or more) identical particles of the same kind are observed, their common wave function should be symmetrized (for BE statistics) or antisymmetrized (for FD statistics) what results in characteristic shapes of (two particle, for example) correlation function C2(Q = |p1 − p2|) = N(p1, p2)/[N(p1) ·N(p2)], cf., Fig. 2. Referring for details of Bose-Einstein correlations (BEC) to the literature (cf., for example, [2] and references therein) let us concentrate here directly on the problem of their proper numerical modelling, i.e., such in which the bosonic character of secondaries produced in hadronization process are going to be accounted 1 2 6 International Symposium“Frontiers of Fundamental andComputational Physics”