Transverse momentum dependence of Hanbury-Brown–Twiss correlation radii

Abstract

The transverse momentum dependence of Hanbury-Brown/Twiss (HBT) interferometry radii for 2-body correlation functions provides experimental access to the collective dynamics in heavy-ion collisions. We present an analytical approximation scheme for these HBT radii which combines the recently derived model-independent expressions with an approximate determination of the saddle point of the emission function. The method is illustrated for a longitudinally boost-invariant hydrodynamical model of a heavy ion collision with freeze-out on a sharp hypersurface. The analytical approximation converges rapidly to the width of the numerically computed correlation function and reproduces correctly its exact transverse momentum dependence. However, higher order corrections within our approximation scheme are essential, and the previously published lowest order results with simple m ⊥ scaling behaviour are quantitatively and qualitatively unreliable.

An inconsistency in the simulation of Bose-Einstein correlations

“…This becomes clear if one looks at the formalism used for analytical models of the emission function, where the ad hoc prescription (1) is not needed. In these, the evaluation of the Bose-Einstein correlation function is based on the coherent state formalism arising from quantum field theory, using [36], [12] …”

“…No attempt was made to reproduce any other Venus distribution. As demonstrated in [12], the flow dependence of the observables is mainly due to the size of the flow, while its functional shape plays a somewhat secondary role. The order of magnitude of the flow velocity extracted here (∼ 0.35c) can be compared to the flow parameter η f in [12].…”

“…As demonstrated in [12], the flow dependence of the observables is mainly due to the size of the flow, while its functional shape plays a somewhat secondary role. The order of magnitude of the flow velocity extracted here (∼ 0.35c) can be compared to the flow parameter η f in [12]. We have generated events for different values of the flow strength f and the result was verified to be independent of statistics.…”

“…The source parameters derived from fits to the correlation function are difficult to interpret directly as real geometric quantities, being sensitive to the transverse and longitudinal dynamical expansion of the system [6,7,8,9,10,11], which result in a momentum dependence of the extracted source radii [12,13,14] to long lived resonance decays [15,16,17,18,19], the Coulomb interaction [20,21], and final state rescattering [22]. There has been recent experimental evidence for flow effects [23,11] and one possible implication of flow is that distant points of emission in the source volume cannot emit particles with closely differing momenta, and thus do not contribute to the small relative pair momentum region [24].…”

Pion Interferometry in Au+Au Collisions at the Ags

“…The dynamical nature of colhsiona limits the Bose-Einstein Correlation measurements to the extent of spacetime "region of homogeneity" fkom which bosons of similar momenta are emitted. Thus correlation stmdks as s function of transverse momentum enable one to obtain a more complete picture of the dynamical space-time structure of the source [2]. \…”