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arXiv · 2412.19416

Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium

Zhong-Hua Zhang·Xu-Guang Huang·Francesco Becattini·Xin-Li Sheng
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Abstract

We derive expressions for the vector and tensor components of the spin polarization of massive vector bosons at local thermodynamic equilibrium up to second order in the space-time gradients of the thermodynamic fields pertaining to the canonical stress-energy tensor and spin tensor of the free Proca field. A set of Feynman rules is devised to calculate the Wigner function and the matrix-valued spin-dependent distribution (MVSD) functions order by order in space-time gradients. Due to constraints imposed by time-reversal symmetry, the leading contribution to spin alignment - defined as the 00-component of the tensor polarization - arises from second-order terms in MVSD, for which we provide an analytic formula. We discuss the physical meaning of different contributions to vector and tensor polarization. These formulae provide a prediction of a contribution to the spin alignment which can be compared with the observations in relativistic heavy-ion collisions.

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Zhong-Hua Zhang, Xu-Guang Huang, Francesco Becattini, Xin-Li Sheng. 2024-12-27. Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium. https://doi.org/10.1007/jhep07(2025)224

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