Dissipative spin hydrodynamics in Bjorken flow and thermal dilepton production

Abstract

We investigate the boost-invariant expansion of a recently developed first-order spin hydrodynamic framework in which the spin chemical potential is treated as a leading-order hydrodynamic variable. Considering a symmetric energy-momentum tensor and a separately conserved spin tensor, we derive the coupled evolution equations for the medium temperature and the independent components of the spin chemical potential in the presence of both viscous and spin-diffusive transport coefficients. For a boost-invariant system, only the magnetic-like components of the spin chemical potential survive, and their evolution is shown to depend sensitively on the spin transport coefficients. The transverse spin components decay more rapidly due to spin dissipation, while the longitudinal component survives for a longer duration. We further demonstrate that the evolution of the spin degrees of freedom modifies the temperature profile of the expanding medium. Using the resulting temperature profiles, we calculate thermal dilepton production rates from quark-antiquark annihilation. We find that the presence of spin dynamics enhances the dilepton yield relative to standard dissipative hydrodynamics, with the magnitude of the enhancement depending on the spin transport coefficients. Our results indicate that thermal dileptons can provide an indirect probe of spin dynamics and spin transport in the quark-gluon plasma.

Figures (6)

• Figure 1: Proper time evolution of the medium temperature $T(\tau)$. The red solid line and the blue dashed-dotted line represent the temperature evolution in dissipative spin hydrodynamics. For this case, we consider $C_{\omega X}(\tau_0)=C_{\omega Y}(\tau_0)=C_{\omega Z}(\tau_0)=80$ MeV. The green dashed line and the black dotted lines represent the temperature evolution for standard dissipative hydrodynamics. This is obtained by setting $C_{\omega X}=C_{\omega Y}=C_{\omega Z}=0$. In the limit $C_{\omega X}=C_{\omega Y}=C_{\omega Z}=0$ the spin hydrodynamic framework boils down to the standard dissipative hydrodynamics.
• Figure 2: We show the evolution of different components of the spin chemical potential, i.e., $C_{\omega X}(\tau)$, $C_{\omega Y}(\tau)$, and $C_{\omega Z}(\tau)$. We observe that with proper time $C_{\omega X}(\tau)$, $C_{\omega Y}(\tau)$, and $C_{\omega Z}(\tau)$ decreases. The decrease of $C_{\omega X}(\tau)$, and $C_{\omega Y}(\tau)$ is faster as comped to $C_{\omega Z}(\tau)$, due to the spin dissipation. Note $\eta/s_0$ does not directly affect the evolution of spin chemical potential. But $\eta/s_0$ affects the temperature evolution, thereby indirectly affecting the evolution of the spin chemical potential. Due to the symmetry in the transverse plane $C_{\omega X}(\tau)=C_{\omega Y}(\tau)$.
• Figure 3: Dilepton production rate as a function of transverse momenta $p_T$. Here, the invariant mass is considered to be $M=0.4$ GeV. For the estimation of the dilepton production rate the temperature profile of the medium has been obtained for (a) Case I: dissipative spin hydrodynamics with $\eta/s_0=5/4\pi$, $\chi_s=10/4\pi$, dissipative hydrodynamics with $\eta/s_0=5/4\pi$, and (b) Case II: dissipative spin hydrodynamics with $\eta/s_0=1/4\pi$, $\chi_s=3/4\pi$, dissipative hydrodynamics with $\eta/s_0=1/4\pi$. For the spin hydrodynamic case we consider $C_{\omega X}(\tau_0)=C_{\omega Y}(\tau_0)=C_{\omega Z}(\tau_0)=80$ MeV. We compare our results with the results obtained in Ref. Singh:2018bih. The brown dashed line represents the dilepton rate from a medium with non-vanishing vorticity $\omega_0=0.7$ fm$^{-1}$ obtained in Ref. Singh:2018bih.
• Figure 4: Dilepton production rate as a function of invariant mass $M$. Here, the transverse momentum has been considered in the range $0.5\leq p_T\leq 2$ GeV. Here, four temperature profiles have also been used to obtain the rates. (a) Case I: dissipative spin hydrodynamics with $\eta/s_0=5/4\pi$, $\chi_s=10/4\pi$, dissipative hydrodynamics with $\eta/s_0=5/4\pi$, and (b) Case II: dissipative spin hydrodynamics with $\eta/s_0=1/4\pi$, $\chi_s=3/4\pi$, dissipative standard hydrodynamics with $\eta/s_0=1/4\pi$. For the spin hydrodynamic case we consider $C_{\omega X}(\tau_0)=C_{\omega Y}(\tau_0)=C_{\omega Z}(\tau_0)=80$ MeV. We compare our results with the results obtained in Ref. Singh:2018bih (brown dashed line) for a medium with non-vanishing vorticity $\omega_0=0.7$ fm$^{-1}$Singh:2018bih.
• Figure 5: Dilepton production rate as a function of transverse momenta $p_T$. Here, the invariant mass is considered to be $M=0.4$ GeV. For this plot, $T(\tau)$ has been obtained by solving spin hydrodynamic equations with $\eta/s_0=1/4\pi$, $\chi_s=3/4\pi$. The red solid line corresponds to the case where $C_{\omega X}(\tau_0)=C_{\omega Y} (\tau_0)=80$ MeV, $C_{\omega Z}(\tau_0)=0$. The green dashed line corresponds to $C_{\omega Z}(\tau_0)=80$ MeV, $C_{\omega X}(\tau_0)=C_{\omega Y} (\tau_0)=0$.