Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma

We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse-momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the matter. Our results for the quark self-energy set the stage for the calculation of the effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon spectra and collective flow.

Figure 1

The real and imaginary parts of ${\overline{\mathrm{\Sigma }}}_0$, ${\overline{\mathrm{\Sigma }}}_x$, ${\overline{\mathrm{\Sigma }}}_y$, and ${\overline{\mathrm{\Sigma }}}_z$ as a function of $\omega /k$ for ${\xi }_1=10$, ${\theta }_k=\pi /3$, ${\varphi }_k=\pi /6$, and ${\xi }_2=\{-0.2,0,1,3\}$.

Figure 2

The real and imaginary parts of ${\overline{\mathrm{\Sigma }}}_0$, ${\overline{\mathrm{\Sigma }}}_x$, ${\overline{\mathrm{\Sigma }}}_y$, and ${\overline{\mathrm{\Sigma }}}_z$ as a function of $\omega /k$ for ${\xi }_1=10$, ${\xi }_2=3$, ${\theta }_k=\pi /3$, and ${\varphi }_k=\{0,\pi /6,\pi /4,\pi /3\}$.

Figure 3

The real and imaginary parts of ${\overline{\mathrm{\Sigma }}}_0$, ${\overline{\mathrm{\Sigma }}}_x$, ${\overline{\mathrm{\Sigma }}}_y$, and ${\overline{\mathrm{\Sigma }}}_z$ as a function of ${\varphi }_k$ for ${\xi }_1=10$, ${\xi }_2=3$, ${\theta }_k=\pi /3$, and $\omega /k=\{0.1,0.5,0.7,1.5\}$.