Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium

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.

39 pages, 1 figure, published version, minor corrections made

References in corpus (28)

• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Global quark polarization in non-central $A+A$ collisions
• Polarization and Vorticity in the Quark Gluon Plasma
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Spin-thermal shear coupling in a relativistic fluid
• New physics from the polarised light of the cosmic microwave background
• Spin Hydrodynamics and Symmetric Energy-Momentum Tensors -- A current induced by the spin vorticity --
• Hydrodynamics of spin currents
• Spin polarization induced by the hydrodynamic gradients
• Anomalous chiral transports and spin polarization in heavy-ion collisions
• A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions
• Spin alignment of vector mesons in heavy-ion collisions
• Covariant Spin Kinetic Theory I: Collisionless Limit
• Local spin alignment of vector mesons in relativistic heavy-ion collisions
• Relativistic Viscous Hydrodynamics with Angular Momentum
• Spin alignment of vector mesons by glasma fields
• Vorticity and Spin Polarization in Heavy Ion Collisions: Transport Models
• Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity
• Polarization in relativistic fluids: a quantum field theoretical derivation
• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Spin Polarization Formula for Dirac Fermions at Local Equilibrium
• Polarization phenomenon in heavy-ion collisions
• Spin alignment of vector mesons by second-order hydrodynamic gradients
• Spin polarization and correlation of quarks from glasma
• Quantum kinetic theory for spin transport of quarks with background chromo-electromagnetic fields
• Spin alignment of vector mesons from quark dynamics in a rotating medium
• The spin alignment of vector mesons with light front quarks
• Spin alignment of $K^{\ast }$ induced by strange-baryon density inhomogeneity

Cited by in corpus (2)

• Production of $K^{+}{K}^{-}$ Pairs Through Decay of $\varphi$ Meson
• An improved formula for Wigner function and spin polarization in a decoupling relativistic fluid at local thermodynamic equilibrium