Abstract
The kinetic freeze-out for the hydrodynamical description of relativistic heavy ion collisions is discussed using a background-fluctuation splitting of the hydrodynamical fields. For a single event, the particle spectrum, or its logarithm, can be written as the sum of background part that is symmetric with respect to azimuthal rotations and longitudinal boosts and a part containing the contribution of fluctuations or deviations from the background. Using a complete orthonormal basis to characterize the initial state allows one to write the double differential harmonic flow coefficients determined by the two-particle correlation method as matrix expressions involving the initial fluid correlations. We discuss the use of these expressions for a mode-by-mode analysis of fluctuating initial conditions in heavy ion collisions.
Highlights
We have developed an approach [23] that allows for a differential study of the effects of such fluctuations in the fluid-dynamic fields. It is based on a mode-by-mode decomposition of fluctuations in single events, on a functional characterization of initial conditions for event classes, and on a background-fluctuation splitting for the hydrodynamical evolution
To quantify the effect of event-by-event fluctuations on the one-particle spectrum, we plot in Fig. 4 the ratio S(mT,pT )/S0(mT,pT ) as defined by Eq (43) for an ensemble of central collisions with initial conditions taken from a Glauber Monte Carlo model as discussed in Ref. [23]
We have discussed here the kinetic freeze-out for heavyion collisions using a background-fluctuation splitting for the hydrodynamical fields
Summary
Fluid-dynamic models of relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC) and at the CERN Large Hadron Collider (LHC) provide an overall good description of transverse momentum spectra and harmonicflow coefficients up to about pT 2–3 GeV [1,2,3,4,5,6,7,8,9,10,11,12,13]; for reviews, see Refs. [14,15,16]. We have developed an approach [23] that allows for a differential study of the effects of such fluctuations in the fluid-dynamic fields It is based on a mode-by-mode decomposition of fluctuations in single events, on a functional characterization of initial conditions for event classes, and on a background-fluctuation splitting for the hydrodynamical evolution. The CooperFrye freeze-out prescription [24] is based on the assumptions that freeze-out occurs sufficiently rapidly to approximate it along a sharp three-dimensional freeze-out hypersurface f , and that the occupation numbers on f are given by free thermal single-particle distribution functions.. Irrespective of whether they arise from eventwise fluctuations or from collisions at finite impact parameter, are encoded in fluctuating modes that are frozen out on the azimuthally symmetric hypersurface f Appendix A compiles some analytic expressions for rapidity and azimuthal integrals and we discuss the difference between a freeze-out at constant background temperature and one at constant total temperature in Appendix B
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