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We show that spin polarization of a fermion in a relativistic fluid at local thermodynamic equilibrium can be generated by the symmetric derivative of the four-temperature vector, defined as thermal shear. As a consequence, besides vorticity, acceleration and temperature gradient, also the shear tensor contributes to the polarization of particles in a fluid. This contribution to the spin polarization vector, which is entirely non-dissipative, adds to the well known term proportional to thermal vorticity and may thus have important consequences for the solution of the local polarization puzzles observed in relativistic heavy ion collisions.
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Within the framework of relativistic fluctuating hydrodynamics we compute the contribution of thermal fluctuations to the effective infrared shear viscosity of a conformal fluid, focusing on quadratic (in fluctuations), second order (in velocity gradients) terms in the conservation equations. Our approach is based on the separation of hydrodynamic fields in soft and ultrasoft sectors, in which the effective shear viscosity arises due to the action of the soft modes on the evolution of the ultrasoft ones. We find that for a strongly coupled fluid with small shear viscosity--to--entropy ratio $eta/s$ the contribution of thermal fluctuations to the effective shear viscosity is small but significant. Using realistic estimates for the strongly coupled quark--gluon plasma created in heavy ion collisions, we find that for $eta/s$ close to the AdS/CFT lower bound $1/(4pi)$ the correction is positive and at most amounts to 10% in the temperature range 200--300 MeV, whereas for larger values $eta/s sim 2/(4pi)$ the correction is negligible. For weakly coupled theories the correction is very small even for $eta/s=0.08$ and can be neglected.
We use a thermal model with single freeze-out to determine longitudinal polarization of $Lambda$ hyperons emitted from a hot and rotating hadronic medium. We consider the top RHIC energies and use the model parameters determined in the previous analyses of particle spectra and elliptic flow. Using a direct connection between the spin polarization tensor and thermal vorticity, we reproduce earlier results which indicate a quadrupole structure of the longitudinal component of the polarization three-vector with an opposite sign compared to that found in the experiment. We further use only the spatial components of the thermal vorticity in the laboratory system to define polarization and show that this leads to the correct sign and magnitude of the quadrupole structure. This procedure resembles a non-relativistic connection between the polarization three-vector and vorticity employed in other works. In general, our results bring further evidence that the spin polarization dynamics in heavy-ion collisions may be not directly related to the thermal vorticity. The additional material explains the construction of the hydrodynamicaly consistent gradients of fluid velocity and temperature in thermal models with the help of the perfect-fluid equations of motion.
In this work, we briefly review the progress made in the formulation of hydrodynamics with spin with emphasis on the application to the relativistic heavy-ion collisions. In particular, we discuss the formulation of hydrodynamics with spin for perfect-fluid and the first order viscous corrections with some discussion on the calculation of spin kinetic coefficients. Finally, we apply relativistic hydrodynamics with spin to the relativistic heavy-ion collisions to calculate the spin polarization of $Lambda$-particles.
Using classical description of spin degrees of freedom, we extend recent formulation of the perfect-fluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic equations for massive particles with spin-1/2, with the collision terms treated in the relaxation time approximation. The kinetic-theory framework determines the structure of viscous and diffusive terms and allows to explicitly calculate a complete set of new kinetic coefficients that characterize dissipative spin dynamics.
A hybrid (hydrodynamics + hadronic transport) theoretical framework is assembled to model the bulk dynamics of relativistic heavy-ion collisions at energies accessible in the Beam Energy Scan (BES) program at the Relativistic Heavy-Ion Collider (RHIC) and the NA61/SHINE experiment at CERN. The systems energy-momentum tensor and net baryon current are evolved according to relativistic hydrodynamics with finite shear viscosity and non-zero net baryon diffusion. Our hydrodynamic description is matched to a hadronic transport model in the dilute region. With this fully integrated theoretical framework, we present a pilot study of the hadronic chemistry, particle spectra, and anisotropic flow. Phenomenological effects of a non-zero net-baryon current and its diffusion on hadronic observables are presented for the first time. The importance of the hadronic transport phase is also investigated.
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