Final state interactions in two-particle interferometry

Abstract

We reconsider the influence of two-particle final state interactions (FSI) on two-particle Bose-Einstein interferometry. We concentrate in particular on the problem of particle emission at different times. Assuming chaoticity of the source, we derive a new general expression for the symmetrized two-particle cross section. We discuss the approximations needed to derive from the general result the Koonin-Pratt formula. Introducing a less stringent version of the so-called smoothness approximation we also derive a more accurate formula. It can be implemented into classical event generators and allows to calculate FSI corrected two-particle correlation functions via modified Bose-Einstein "weights".Comment: 12 pages RevTeX, 2 ps-figures included, submitted to Phys. Rev.

TWO-PARTICLECORRELATIONS INRELATIVISTICHEAVY-IONCOLLISIONS

“…Since in the absence of transverse flow the β-dependent terms in (33) and (34) vanish and the source itself depends only on M ⊥ , all three YKP radius parameters then show perfect M ⊥ -scaling: plotted as functions of M ⊥ , they coincide for pion and kaon pairs (see Figure 2, left column). This remains true if T (x) varies with x; temperature gradients in the source do not destroy the M ⊥ -scaling.…”

“…A slightly more general result which avoids the smoothness approximation was derived in [33]. For simplicity the integral in (18) is written in coordinates of the pair rest frame where K = 0.…”

“…It describes the propagation of the particle pair from an initial separation r in the pair rest frame, at the time when the second particle was emitted [33], under the influence of the mutual FSI. For identical particle pairs it must be properly symmetrized:…”

Use of cumulants to quantify uncertainties in the HBT measurements of the homogeneity regions

“…Many papers go even further and use sources which are, or can be decomposed into sources, point-like in space-time [4], [10]. A general derivation of the relation between correlation functions and emission functions, which is still [6] considered to be the most detailed, has been given by Anchishkin, Heinz and Renk [11]. Analyzing it one easily finds that the proof breaks down if the sources are not, or at least for the HBT analysis cannot be replaced by, instant sources.…”

Testing the space-time structure of event generators

“…This allows to express the two-particle correlation function in terms of the single-particle Wigner density S(x, p) of the source [8]. Neglecting final state interactions (assuming that they can be corrected for experimentally [8,9] or theoretically [10] at a later stage), it is given by [8] …”