Accelerating solutions of perfect fluid hydrodynamics for initial energy density and life-time measurements in heavy ion collisions

Abstract

A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density and life-time of high energy heavy ion collisions. Accelerating solutions are also given for spherical expansions in arbitrary number of spatial dimensions.

Initial Energy Density of √s = 7 and 8 TeV p–p Collisions at the LHC

“…For λ > 1, we obtain several classes of accelerating solutions, described in Refs. [26][27][28]41]. For example, 1+1 dimensional hydrodynamical solutions are obtained for any real value of λ, for the special EoS of κ = 1.…”

“…It is important to observe that in order to describe the majority of experimental data, besides rapidity distributions, pseudorapidity distributions (with pseudorapidity defined as η = 0.5 ln ((p + p z )/(p − p z ))) have to be calculated as well [26][27][28]41]. This can be done by using an average transverse momentum (p t ) value and making a transformation from pseudorapidity η to rapidity y.…”

“…The size of this slab is estimated by the radius R of the colliding hadrons or nuclei, them the initial volume is dV = (R 2 π)τ 0 dη 0 , with τ 0 dη S0 being the longitudinal size, while dη S0 is the space-time rapidity width at τ 0 , as detailed in Refs. [26][27][28]41]. The energy contained in this volume is dE = E dN , where dN is the number of particles and E is their average energy near y = 0.…”

“…In Refs. [26][27][28]41] we performed fits to BRAHMS pseudo-rapidity distributions from Ref. [48], and these fits indicate that corr ≈ 10 GeV/fm 3 in √ s NN = 200 GeV Au+Au collisions at RHIC.…”

“…Besides these efforts, there is also an interest in models where exact, explicit and parametric solutions of the hydrodynamical equations are used, and where the initial state may be inferred directly from matching the parameters of the solution to the data. Several famous hydrodynamical solutions were developed to describe high energy collisions [22][23][24], but also advanced relativistic solutions were found in the last decade [25][26][27][28][29][30][31][32], when a revival of this sub-field was seen.…”