Photon emission from a momentum-anisotropic quark-gluon plasma

We compute the photon emission rate from a quark-gluon plasma with an anisotropic particle momentum distribution induced by a nonvanishing local shear pressure tensor. Our calculation includes photon production through Compton scattering and quark-antiquark annihilation at leading order in ${\alpha }_s$, with all off-equilibrium corrections to leading order in the momentum anisotropy. For fermions we prove that the Kubo-Martin-Schwinger relation holds in the hard loop regime for any particle momentum distribution function that is reflection symmetric. This supports the equivalence, for 2-to-2 scattering processes, of the diagrammatic and kinetic approaches to calculating the photon emission rate. We compare the viscous rates from these two approaches at weak and realistic coupling strengths and provide parametrizations of the equilibrium and viscous photon emission rates for phenomenological studies in relativistic heavy-ion collisions.

Figure 1

Off-diagonal component ${\Sigma }^{12}\left(P\right)$ of the one-loop quark self-energy.

Figure 2

(12)-component of one-loop photon self-energy with one HTL-resummed quark propagator.

Figure 3

Compton scattering and pair annihilation. Compton scattering can involve gluons scattering off quarks (shown) or antiquarks (not shown).

Figure 4

Cutoff dependence of the normalized equilibrium rate ${\tilde{\Gamma }}_0$ (a) and (c), and viscous correction coefficient ${\tilde{\Gamma }}_1$ (b) and (d) from the diagrammatic approach at $k/T=10$, for two values of the strong coupling constant, $g_s=0.01$ (a) and (b), and $g_s=2.0$ (c) and (d). Horizontal dotted lines indicate the value from the amy parametrization [1] in (a) and (c) and from Ref. [7] in (b) and (d). Vertical dotted lines indicate the positions of the minima of the numerical curves and of $q_{\mathrm{cut}}/T=\sqrt{g_s}$, respectively. See text for discussion.

Figure 5

Same as Fig. 4, but for softer photons at $k/T=1$.

Figure 6

The temperature-scaled equilibrium photon emission rate ${\tilde{\Gamma }}_0$ as a function of $k/T$ for relatively weak [$g_s=0.1$, (a)] and moderately strong coupling [$g_s=2$, (b)]. Results are shown for the diagrammatic approach, the kinetic approach, amy's parametrization [1], and for Ref. [7] as labeled. In the lower panels we show the ratio between these rates and the one from the diagrammatic approach on a linear scale. The gray band is a lower bound on the uncertainty of higher order corrections in $g_s$ to the diagrammatic and kinetic approaches.

Figure 7

Similar to Fig. 6 but for the viscous correction coefficient ${\tilde{\Gamma }}_1$.

Figure 8

The viscous correction coefficient ${\tilde{\Gamma }}_1$ (a) and its ratio ${\tilde{\Gamma }}_1/{\tilde{\Gamma }}_0$ to the thermal equilibrium emission rate (b) as functions of $k/T$ at $g_s=2.0$ for two values $\lambda ,\lambda =1$ and 2 (see text for details). The slope parameters in (b) were obtained by a linear fit of the log-log plot for $k/T>5$.