Abstract
Relativistic hydrodynamic equations for particles with spin one-half are used to determine the space-time evolution of the spin polarization in a boost-invariant and transversely homogeneous background. The hydrodynamic approach uses the forms of the energy-momentum and spin tensors based on de Groot, van Leeuwen, and van Weert formalism. Our calculations illustrate how the formalism of hydrodynamics with spin can be used to determine physical observables related to the spin polarization and how the latter can be compared with the experimental data.
Highlights
The recent measurements of the spin polarization of hyperons in relativistic heavy-ion collisions [1,2] suggest that the space-time evolution of spin polarization should be included in the hydrodynamic description of such processes
Since at the moment no solutions of such a scheme are known, the purpose of this paper is to explore the simplest, boost-invariant expansion geometry known as the Bjorken expansion [41] and to look for the consequences of the hydrodynamic scheme introduced in this way
In this work we have presented the first numerical results describing the space-time evolution of the spin polarization tensor in a hydrodynamic boost-invariant background
Summary
The recent measurements of the spin polarization of hyperons in relativistic heavy-ion collisions [1,2] suggest that the space-time evolution of spin polarization should be included in the hydrodynamic description of such processes. [36] that the GLW forms are connected with the canonical expressions (given through the Noether theorem) via the so-called pseudogauge transformation [8,14,40] In view of this fact, we have decided to consider here the case where the hydrodynamics with spin is formulated with the GLW forms of the energy-momentum and spin tensors. The study presented in this work can be used as a practical illustration as well as a check of the theoretical scheme defined above The latter consists of four distinct steps: (i) solving the standard perfect-fluid hydrodynamic equations without spin, (ii) determination of the spin evolution in the hydrodynamic background, (iii) determination of the PauliLubanski (PL) vector on the freeze-out hypersurface, and, (iv) calculation of the spin polarization of particles in their rest frame.
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