Relaxation time for the alignment between quark spin and angular velocity in a rotating QCD medium

We compute the relaxation times for massive quarks and antiquarks to align their spins with the angular velocity in a rigidly rotating medium at finite temperature and baryon density. The rotation effects are implemented using a fermion propagator immersed in a cylindrical rotating environment. The relaxation time is computed as the inverse of the interaction rate to produce an asymmetry between the quark (antiquark) spin components along and opposite to the angular velocity. For conditions resembling heavy-ion collisions, the relaxation times for quarks are smaller than for antiquarks. For semicentral collisions, the relaxation time for quarks is within the possible lifetime of the QGP for all collision energies. However, for antiquarks, this happens only for collision energies $\sqrt{s_{NN}}\gtrsim 50\mathrm{GeV}$. The results are quantified in terms of the intrinsic quark and antiquark polarizations, namely, the probability to build the spin asymmetry as a function of time. Our results show that these intrinsic polarizations tend to 1 with time at different rates given by the relaxation times with quarks reaching a sizable asymmetry at a faster pace. These are key results to further elucidate the mechanisms of hyperon polarization in relativistic heavy-ion collisions.

Figure 1

One-loop quark self-energy diagram that defines the kinematics. The gluon line with a blob represents the effective gluon propagator at finite density and temperature. The open circle on the fermion propagator represents the effect of the rotating environment.

Figure 2

Feynman diagram representing a process whereby an initially nonrotating quark is dragged by the medium and aligns its spin either parallel or antiparallel to the angular velocity by means of its interactions with medium particles mediated by soft thermal gluons.

Figure 3

Interaction rates ${\mathrm{\Gamma }}^{\pm }$ for positive ($+$) and negative ($-$) spin projections for quarks as functions of the angular velocity $\mathrm{\Omega }$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ and chemical potential $\mu =100\mathrm{MeV}$ for a temperature $T=150\mathrm{MeV}$. Shown is also the interaction rate $\mathrm{\Gamma }$ obtained as the phase space integrated difference ${\mathrm{\Gamma }}^{+}(p_0)-{\mathrm{\Gamma }}^{-}(p_0)$.

Figure 4

Interaction rates ${\overline{\mathrm{\Gamma }}}^{\pm }$ for positive ($+$) and negative ($-$) spin projections for antiquarks as functions of the angular velocity $\mathrm{\Omega }$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ and chemical potential $\overline{\mu }=100\mathrm{MeV}$ for a temperature $T=150\mathrm{MeV}$. Shown is also the interaction rate $\overline{\mathrm{\Gamma }}$ obtained as the phase space integrated difference ${\overline{\mathrm{\Gamma }}}^{+}(p_0)-{\overline{\mathrm{\Gamma }}}^{-}(p_0)$.

Figure 5

Relaxation time $\tau$ for quarks as a function of the temperature $T$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ for $\sqrt{s_{NN}}=200\mathrm{GeV}$, which corresponds to a angular velocity $\mathrm{\Omega }=0.052{\mathrm{fm}}^{-1}$ with $\mu =0$, 100 MeV.

Figure 6

Relaxation time $\tau$ for quarks as a function of the temperature $T$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ for $\sqrt{s_{NN}}=10\mathrm{GeV}$, which corresponds to a angular velocity $\mathrm{\Omega }=0.071{\mathrm{fm}}^{-1}$ with $\mu =0$, 100 MeV.

Figure 7

Relaxation time $\overline{\tau }$ for antiquarks as a function of the temperature $T$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ for $\sqrt{s_{NN}}=200\mathrm{GeV}$, which corresponds to a angular velocity $\mathrm{\Omega }=0.052{\mathrm{fm}}^{-1}$ with $\overline{\mu }=0$, 100 MeV.

Figure 8

Relaxation time $\overline{\tau }$ for antiquarks as a function of the temperature $T$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ for $\sqrt{s_{NN}}=10\mathrm{GeV}$, which corresponds to a angular velocity $\mathrm{\Omega }=0.071{\mathrm{fm}}^{-1}$ with $\overline{\mu }=0$, 100 MeV.

Figure 9

Top: relaxation time $\tau$ for quarks as a function of $\sqrt{s_{NN}}$ for semicentral collisions at impact parameters $b=5$, 8, and 10 fm. Bottom: relaxation time $\overline{\tau }$ for antiquarks as a function of $\sqrt{s_{NN}}$ for semicentral collisions at impact parameters $b=5$, 8, and 10 fm.

Figure 10

Intrinsic polarization for quarks ($z$) and antiquarks ($\overline{z}$) as functions of time $t$ for semicentral collisions at an impact parameter $b=10\mathrm{fm}$ for $\sqrt{s_{NN}}=4\mathrm{GeV}$.