Speaker
Description
Heavy-ion collisions have been an excellent tool for studying the nature of the strong force. In non-central heavy-ion collisions, a large amount of angular momentum is generated during the collision process. This angular momentum can induce a non-zero vorticity in the medium, leading to the spin polarization of the produced hadrons. Experimental evidence for such vortical structures has been observed in relativistic heavy-ion collisions [1]. Various theoretical approaches, including spin hydrodynamics, have been developed to describe this polarization phenomenon [2-4].
The hydrodynamic evolution of such a relativistic spin-fluid should ensure conservation of total angular momentum tensor ($\partial_{\lambda}J^{\lambda\alpha\beta}=0$), along with the conservation of energy-momentum tensor ($\partial_{\mu}T^{\mu\nu}=0$) and baryon current ($\partial_{\mu}J^{\mu}=0$). Spin hydrodynamics promotes total angular momentum to a hydrodynamic variable with its own conservation laws and gradient expansions.
\begin{align}
& J^{\lambda\alpha\beta}=\mathcal{O}(1)+\mathcal{O}(\partial)+\mathcal{O}(\partial^2)+...
\end{align}
We investigate the solution of spin hydrodynamic equations for a boost invariant system by taking the spin chemical potential as a leading-order ($\mathcal{O}(1)$) hydrodynamic variable. For a symmetric energy–momentum tensor and an independently conserved spin tensor, we derive the coupled evolution equations governing the temperature evolution of the medium and the independent components of the spin chemical potential, including dissipation from both viscous and spin diffusive currents. We also consider a spin dependent equation-of-state to solve the spin hydrodynamic equations.
We solve the spin hydrodynamic equations, including dissipative effects, for a longitudinally expanding boost-invariant system. We find that for Bjorken flow only the magnetic-like components of the spin chemical potential affect the proper time evolution of the system. We find that the spin transport coefficients crucially determine the proper time evolution of the spin chemical potential, i.e., the evolution of the spin tensor.
Due to dissipative effects, the longitudinal component of spin chemical potential survives for a longer duration, whereas transverse components decay more rapidly. We also find that a non-vanishing spin chemical potential and spin diffusion affect the system's temperature evolution. Using the temperature evolution in the dissipative spin-hydrodynamic framework, we estimate the thermal dilepton production rate from quark-antiquark annihilation. Thermal dileptons are considered an excellent probe of medium temperature, and capture the crucial information of the system evolution.
We find that the inclusion of spin dynamics enhances the dilepton production yield, and the magnitude of the enhancement depends on the spin transport coefficients. Various research groups are working on the development of numerical tools for dissipative spin hydrodynamics, and these results can serve as a test for such numerical simulations.
References
[1] STAR Collaboration, B. I. Abelev et al., “Global polarization measurement in Au+Au collisions,” Phys. Rev. C 76 (2007) 024915, arXiv:0705.1691 [nucl-ex]. [Erratum: Phys.Rev.C 95, 039906 (2017)].
[2] S. Bhadury, W. Florkowski, A. Jaiswal, A. Kumar, and R. Ryblewski, “Dissipative Spin Dynamics in Relativistic Matter,” Phys. Rev. D 103 no.1, (2021) 014030, arXiv:2008.10976 [nucl-th].
[3] R. Takahashi, M. Matsuo, M. Ono, K. Harii, H. Chudo, S. Okayasu, J. Ieda, S. Takahashi, S. Maekawa, and E. Saitoh, “Spin hydrodynamic generation,” Nature Physics 12 no. 1, (2016) 52–56.
[4] W. Florkowski, B. Friman, A. Jaiswal, R. Ryblewski, and E. Speranza, “Relativistic hydrodynamics with spin,” Nucl. Phys. A982 (2019) 523–526, arXiv:1807.04946 [nucl-th].