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Description
We present the calculation of the irreducible components of the spin polarization of massive spin-3/2 particles emitted by a decoupling relativistic fluid at local thermodynamic equilibrium [A. Vignoli, F. Becattini, in preparation]. The local equilibrium calculation is performed within the framework of quantum statistical field theory using linear response theory at first order in the space-time derivatives of the fluid four-temperature vector, and exploits the free Rarita-Schwinger field and the related covariant Wigner operator to describe massive spin-3/2 particles. The formula obtained for the vector polarization scales with respect to the spin-1/2 formula as expected from global equilibrium calculations. The rank-2 tensor component of polarization vanishes at first order in the four-temperature derivatives, as occurs for the tensor component of massive spin-1 particles. As a central result, we provide the formula for the rank-3 tensor component of polarization at first order in the derivatives of the four-temperature. The formulas for the polarization of massive spin-3/2 particles derived in the present work can be employed to provide predictions for upcoming high-precision measurements of the polarization of $\Omega^-$ hyperons produced in relativistic heavy-ion collisions.
