Parton self-energies for general momentum-space anisotropy

Abstract

We introduce an efficient general method for calculating the self-energies, collective modes, and dispersion relations of quarks and gluons in a momentum-anisotropic high-temperature quark-gluon plasma. The method introduced is applicable to the most general classes of deformed anisotropic momentum distributions and the resulting self-energies are expressed in terms of a series of hypergeometric basis functions which are valid in the entire complex phase-velocity plane. Comparing to direct numerical integration of the self-energies, the proposed method is orders of magnitude faster and provides results with similar or better accuracy. To extend previous studies and demonstrate the application of the proposed method, we present numerical results for the parton self-energies and dispersion relations of partonic collective excitations for the case of an ellipsoidal momentum-space anisotropy. Finally, we also present, for the first time, the gluon unstable mode growth rate for the case of an ellipsoidal momentum-space anisotropy.

Photon production and elliptic flow from a momentum-anisotropic quark-gluon plasma

“…This is an extension of previous results of photon production including only longitudinal momentum anisotropy [51] and in line with our previous study of dilepton emission [87]. To calculate soft contributions to the photon rate, we utilized our previous results for quark self-energy in anisotropic QGP [81] advancing in the direction of including more information about collective excitations of the strongly interacting matter in phenomenological studies. In addition, the efficient method introduced in [81] for self-energy calculations in an anisotropic medium was essential in meeting the challenge of demanding numerical calculation of the photon rate with two extra parameters ξ 2 and ϕ q compared to the previous spheroidally anisotropic case.…”

“…On the contrary, calculation of the quark self-energy (7) for an ellipsoidal anisotropy was shown [84] to be more tedious than the spheroidal case [85]. In a previous paper [81], we introduced an efficient method to calculate the integral (7) for general forms of anisotropic momentum distributions which makes it possible to obtain the results for the photon rates in this paper.…”

“…In this paper, for first time we include in the LRF photon rate calculation the momentum anisotropy in the transverse direction in the form of ellipsoidal deformation of isotropic distributions. This is done using an efficient method introduced in our previous paper [81] to calculate the quark self-energies in anisotropic medium. In this paper, we further introduce a suitable ansatz to encode the numerically calculated nonequilibrium photon rate values in a compact form which facilitates its use for hydrodynamic computation of photon yield and flow.…”

Dilepton production and elliptic flow from an anisotropic quark-gluon plasma

“…On the contrary, calculation of the quark self-energy (7) for an ellipsoidal anisotropy was shown [77] to be more tedious than the spheroidal case [78]. In a previous paper [74] we introduced an efficient method to calculate the integral (7) for general forms of anisotropic momentum distributions which makes it possible to obtain the results for photon rates in this paper.…”

“…In this paper, for first time we include in LRF photon rate calculation the momentum anisotropy in transverse direction in the form of ellipsoidal deformation of isotropic distributions. This is done using an efficient method, introduced in our previous paper [74], to calculate the quark self-energies in anisotropic medium. In this paper we further introduce a suitable ansatz to encode the numerically calculated nonequi-librium photon rate values in a compact form which facilitates its use for hydrodynamic computation of photon yield and flow.…”