An improved formula for Wigner function and spin polarization in a decoupling relativistic fluid at local thermodynamic equilibrium

Abstract: We present an upgraded formula for Wigner function and spin polarization of fermions emitted by a relativistic fluid at local thermodynamic equilibrium at the decoupling which improves the one obtained in refs. [1, 2] and used in numerical simulations of relativistic nuclear collisions. By using a new expansion method, applicable to decoupling hypersurfaces with arbitrary geometry, we reproduce the known term proportional to thermal vorticity and obtain an upgraded form of the spin-shear term which captures the dependence on the geometry. The new method also includes additional contributions whose physical nature is to be assessed. The new expression also naturally excludes contributions from space-time gradients in the normal direction of the hypersurface, providing a theoretical justification for the isothermal condition previously imposed a priori. This framework can be extended to particles with arbitrary spin.