Effect of spin polarization on transport and thermodynamic properties

TL;DR

The paper addresses constraining the QCD equation of state by exploiting spin polarization from thermal vorticity in noncentral collisions. It uses a kinetic-theory framework with spin-polarized distribution in O+O collisions to extract transport and thermodynamic coefficients, including $c_s^2$, $η/s$, $ζ/s$, and $λ$. The main finding is that spin polarization substantially alters $η/s$, $ζ/s$, and $λ$ while $c_s^2$ is only weakly affected, and it introduces a nonmonotonic energy dependence with an inflection near 27 GeV. This suggests spin polarization provides a new lever to constrain the QCD EoS in small systems, though the analysis neglects magnetic fields and other SP sources and uses a simplified kinetic description.

Abstract

Spin polarization provides a novel probe of the rotational properties of the quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions. We investigate the effective transport and thermodynamic coefficients in non-central O+O collisions, employing a parton distribution function that incorporates spin polarization induced by thermal vorticity. Within a kinetic theory framework, we find that the magnitude of the squared speed of sound ($c_s^2$) is only weakly modified by spin polarization, whereas the specific shear viscosity ($η/s$), specific bulk viscosity ($ζ/s$), and mean free path ($λ$) show substantial changes. When spin polarization is included, both $c_s^2$ and $ζ/s$ develop a nonmonotonic dependence on the collision energy, with an inflection point near $\sqrt{s_{NN}}=27$ GeV, corresponding to an average parton chemical potential of $\langleμ_p\rangle=0.021$ GeV. These results suggest that spin polarization may serve as a useful probe for constraining the effective equation of state of QCD matter.

Figures (10)

• Figure 1: (Color online) Comparison of SP and non-SP results: (a) squared speed of sound $c_{s}^{2}$, specific shear viscosity $\eta/s$, and specific bulk viscosity $\zeta/s$; (b) mean free path $\lambda$, shown as functions of radius for O+O collisions at $\sqrt{s_{NN}}=200$ GeV. Results correspond to proper time $\tau=0.2$ fm.
• Figure 2: (Color online) Comparison of SP and non-SP results: (a) squared speed of sound $c_{s}^{2}$, specific shear viscosity $\eta/s$, and specific bulk viscosity $\zeta/s$; (b) mean free path $\lambda$, shown as functions of temperature for O+O collisions at $\sqrt{s_{NN}}=200$ GeV. Results are integrated over proper time from $\tau=0.2$ to $5$ fm.
• Figure 3: (Color online) Comparison of SP and non-SP results for event-averaged quantities: (a) ratios $\langle \tilde{T}^{\mathrm{tot}}\rangle/\langle T^{\mathrm{tot}}\rangle$, $\langle \tilde{\varepsilon}\rangle/\langle \varepsilon\rangle$, and $\langle \tilde{P}\rangle/\langle P\rangle$; (b) ratios $\langle \tilde{P}_{\parallel}\rangle/\langle P_{\parallel}\rangle$ and $\langle \tilde{P}_{\perp}\rangle/\langle P_{\perp}\rangle$, shown as functions of energy for O+O collisions at $T=0.16$ GeV. Results are integrated over proper time from $\tau=0.2$ to 5 fm.
• Figure 4: (Color online) Comparison of SP and non-SP results for event-averaged quantities: (a) gradient of energy density $\langle d\varepsilon/dR\rangle$ and gradient of pressure $\langle dP/dR\rangle$; (b) ratios $\langle d\tilde{P}_{\parallel}/dR\rangle/\langle dP_{\parallel}/dR\rangle$ and $\langle d\tilde{P}_{\perp}/dR\rangle/\langle dP_{\perp}/dR\rangle$, shown as functions of energy for O+O collisions at $T=0.16$ GeV. Results are integrated over proper time from $\tau=0.2$ to 5 fm. The inset shows two ratios: (I) $\langle d\tilde{\varepsilon}/dR\rangle/\langle d\varepsilon/dR\rangle$ and (II) $\langle d\tilde{P}/dR\rangle/\langle dP/dR\rangle$.
• Figure 5: (Color online) Comparison of two event-averaging methods: case I and case II. (a) Squared speed of sound, comparing SP and non-SP results, shown as a function of energy for O+O collisions at $T=0.16$ GeV; (b) ratio $\tilde{c}_{s}^{2}/c_{s}^{2}$, also shown as a function of energy for O+O collisions at $T=0.16$ GeV. Results are integrated over proper time from $\tau=0.2$ to 5 fm.