Spin polarization as a probe of the QCD critical point

Abstract: Spin polarization is a novel method for probing the rotational properties of the quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions. In this work, we investigate the effective transport and thermodynamic coefficients in non-central O+O light-ion collisions, considering a parton distribution function that incorporates the spin polarization induced by thermal vorticity during the collision. Using a kinetic theory approach, we find that while the speed of sound squared ($c_s^2$) remains largely unaffected by spin polarization, the specific shear viscosity ($\eta/s$), specific bulk viscosity ($\zeta/s$), and mean free path ($\lambda$) are significantly modified. Notably, when spin polarization is taken into account, both $c_s^2 $ and $\zeta/s$ exhibit a non-monotonic dependence on collision energy, with an inflection point around $\sqrt{s_{NN}} = 27 $~GeV, corresponding to an average parton chemical potential of $\langle\mu_p\rangle = 0.021 $~GeV. This non-monotonic behavior suggests that incorporating spin polarization into theoretical calculations could provide an effective probe for locating the critical point of the QCD phase transition.