Hybrid model with viscous relativistic hydrodynamics: a role of constraints on the shear-stress tensor

We present the hybrid model connecting parton–hadron–string dynamic (PHSD) and a hydrodynamic taking into account shear viscosity within Israel–Stewart approach. The numerical scheme, initialization, particlization procedure are discussed in detail. performance of code is tested on pion proton rapidity transverse mass distributions calculated for Au + Pb+Pb collisions at AGS–SPS energies. influence switch time from transport to hydro models, viscous parameter, freeze-out discussed. Since applicability hydrodynamics assumes perturbative character stress tensor, $$\pi ^{\mu \nu }$$ , which should not exceed ideal energy–momentum $$T_{\mathrm{id}}^{\mu hydrodynamical codes usually rescale tensor if inequality $$\Vert \pi }\Vert \ll \Vert T_{\mathrm{id}}^{\mu $$ fulfilled some sense. There several conditions used literature we analyze detail different values cut-off parameter observables. show that form corresponding condition plays an important role sensitivity calculations – ratio entropy density, $$\eta /s$$ . It shown constraints vHLLE MUSIC models give same results With these constraints, momentum spectra most sensitive change ratio. demonstrate do guarantee each element smaller than As alternative, strict used. When applied it reduces parameter. performed global fits protons. was also found as function collision energy monotonically increases $$E_{\mathrm{lab}}=6\,A\text {GeV}$$ up $$E_{\mathrm{lab}}=40\,A\text saturates higher SPS observe difficult reproduce simultaneously distribution our with choice equation state without phase transition.