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Register a new userNew proposal of numerical modelling of Bose-Einstein correlations: Bose-Einstein correlations from within
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We describe an attempt to numerically model Bose-Einstein correlations (BEC) from within, i.e., by using them as the most fundamental ingredient of a Monte Carlo event generator (MC) rather than considering them as a kind of (more or less important, depending on the actual situation) afterburner, which inevitably changes the original physical content of the MC code used to model multiparticle production process.
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Notwithstanding the visible maturity of the subject of Bose-Einstein Correlations (BEC), as witnessed nowadays, we would like to bring to ones attention two points, which apparently did not received attention they deserve: the problem of the choice of the form of $C_2(Q)$ correlation function when effects of partial coherence of the hadronizing source are to be included and the feasibility to model effects of Bose-Einstein statistics, in particular the BEC, by direct numerical simulations.
We are presenting here the new formulae for Bose-Einstein correlations (BEC) which contain effects of final state interactions (FSI) of both strong (in $s$-wave) and electromagnetic origin. We demonstrate the importance of FSI in BEC by analysing data for $e^+e^-$ annihilation and for heavy collisions. The inclusion of FSI results in the practical elimination (at least in $e^+e^-$ data) of the so called degree of coherence parameter $lambda$ (which becomes equal unity) and the long range parameter $gamma$ (which is now equal zero).
A wavepacket model for a system of free pions, which takes into account the full permutation symmetry of the wavefunction and which is suitable for any phase space parametrization is developed. The properties of the resulting mixed ensembles and the two-particle correlation function are discussed. A physical interpretation of the chaoticity lambda as localizat of the pions in the source is presented. Two techniques to generate test-particles, which satisfy the probability densities of the wavepacket state, are studied: 1. A Monte Carlo procedure in momentum space based on the standard Metropolis technique. 2. A molecular dynamic procedure using Bohms quantum theory of motion. In order to reduce the numerical complexity, the separation of the wavefunction into momentum space clusters is discussed. In this context th influence of an unauthorized factorization of the state, i. e. the omissio of interference terms, is investigated. It is shown that the correlation radius remains almost uneffected, but the chaoticity parameter decreases substantially. A similar effect is observed in systems with high multiplic where the omission of higher order corrections in the analysis of two-part correlations causes a reduction of the chaoticity and the radius. The approximative treatment of the Coulomb interaction between pions and source is investigated. The results suggest that Coulomb effects on the co radii are not symmetric for pion pairs of different charges. For negative the radius, integrated over the whole momentum spectrum, increases substan while for positive pions the radius remains almost unchanged.
We present an analytical formula for the Bose-Einstein correlations (BEC) which includes effects of both Coulomb and strong final stateinteractions (FSI). It was obtained by using Coulomb wave function together with the scattering partial wave amplitude of the strong interactions describing data on the $s$-wave phase shift. We have proved numerically that this method is equivalent to solving Schr{o}dinger equation with Coulomb and the $s$-wave strong interaction potentials. As an application we have analysed, using our formula which includes the degree of coherence and the long range correlation, the data for $e^+e^-$ annihilations. We have found that the degree of coherence present in our formula approaches approximately unity whereas the long range correlation parameter becomes approximately zero. These results suggest that the physical meanings of the fractional degree of coherence and the long range correlation observed in various other analyses can most probably be attributed to FSI.
We applied an improved Coulomb correction method developed by us recently to data on identical KK-pairs production in S + Pb and p + Pb reactions at 200 GeV/c obtained by NA44 Collaboration. To analyse the whole range of the momentum transfers measured the method of seamless fitting has been proposed and used together with the asymptotic expansion formula for the Coulomb wave function. We found that such Coulomb corrections lead sometimes to different than previously reported (by NA44 Collaboration) interaction region and strongly influence the long range correlations.
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