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Description
The quark-gluon plasmas produced in non-central relativistic heavy-ion collisions can have large vorticities, leading to spin polarization in a manner analogous to the Barnett effect. Such spin polarization has been observed in $\Lambda$ hyperons [1], spurring rapid development in the area of spin physics in heavy-ion collisions. However, tension remains between experimental data and theories that assume no dynamics for spin. Building on the success of hydrodynamics in describing the evolution of the quark-gluon plasma, relativistic theories of spin hydrodynamics have been developed to assess whether spin dynamics is relevant to heavy-ion phenomenology. These theories treat spin as a dynamical degree of freedom that evolves through the conservation of total angular momentum. Despite significant progress in relativistic spin hydrodynamics, our understanding of relativistic causality and the stability of thermal equilibria--both of which are crucial for numerical simulations--remains limited. As a step toward addressing this issue in a unified framework, we demonstrate that non-dissipative relativistic spin fluids fit naturally into the framework of so-called divergence-type hydrodynamic theories [2], which have desirable mathematical properties. In particular, a perfect spin fluid can be fully specified by a scalar generating function. This formulation makes it straightforward to assess whether a given theory is compatible with causality and stability. When the generating function is based on a generalized Boltzmann distribution, we show that the theory is both causal and stable and is therefore suitable for numerical implementation. Furthermore, it reproduces existing results when expanded up to second order in $\hbar$. Finally, retaining all orders in $\hbar$, we calculate the relevant components of the stress-energy and spin tensors, such as spin-induced pressure anistropy.
[1] L. Adamczyk et al., Nature 548, 62 (2017)
[2] R. Geroch and L. Lindblom, Phys. Rev. D 41, 1855 (1990)
| Category | Theory |
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