Boost invariant spin hydrodynamics within the first order in derivative expansion

Abstract

Recent evidence of the spin polarization of weakly decaying Lambda hyperons has opened up a newpathway for investigating nontrivial vortical structures of strongly interacting matter generated in heavy-ion experiments [1–10]. Several approaches for describing relativistic hydrodynamics for spin-polarized fluids have been developed as a result of the successes of the relativistic dissipative hydrodynamic framework in heavy-ion phenomenological research [11,12]. Different frameworks have been constructed using entropy current analysis [13–19], relativistic kinetic theory [20–38], effective Lagrangian approach [39–42], quantum statistical density operators [43–47], equilibrium partition functions [48], and holography [49,50]. To allow for future dynamic simulations of spin polarization [51–53], a consistent framework of relativistic hydrodynamics with spin degrees of freedom (spin hydrodynamics) is currently being built. In this work, we present an analysis of boost-invariant solutions of the spin hydrodynamic equations formulated by Hattori et al. in Ref. [13] and investigated later in a series of publications [14,18,19,54,55]. The approach of Ref. [13] is based on the gradient expansion and requirement of positive entropy production.