We introduce a positive-definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the nonequilibrium correction $\delta f_n$ which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and $p_T$–differential elliptic flow coefficients from the Cooper–Frye formula computed with the modified equilibrium distribution and with linearized $\delta f_n$ corrections is presented, for two different $(2+1)$–dimensional hypersurfaces corresponding to central and noncentral $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider (LHC).

中文翻译：

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Cooper-Frye 粒子化的修正平衡分布

我们引入了一个正定的单粒子分布，它适用于在中等大的粘性修正存在的情况下，在重离子碰撞的后期阶段，描述从宏观流体动力学到微观动力学描述的转变。修正的平衡分布函数可以用来自相对论粘性流体动力学或各向异性流体动力学的流体动力学输入来构建。我们测试了在给定的冻结温度和重子化学势下受剪切应力、体积压力或重子扩散流影响的固定强子共振气体的修正平衡分布的流体动力学输出。虽然它不能准确地再现净重子电流和能量-动量张量的所有分量，$\delta F_n$这通常会导致大粒子动量下的非物理负分布函数。粒子光谱的比较和${磷}_{吨}$– 来自 Cooper-Frye 公式的差分椭圆流量系数，使用修正的平衡分布和线性化计算 $\delta F_n$ 提出更正，针对两个不同的 $(2+1)$–对应于中心和非中心的维超曲面 $铅+铅$ 大型强子对撞机 (LHC) 的碰撞。