Energetic dileptons from the quark-gluon plasma

Abstract

In this paper we study the production of energetic di-leptons. We calculate the rate for 2 → 2 processes. The log term is obtained analytically and the constant term is calculated numerically. When the photon mass is of the order of the thermal quark mass, the result is insensitive to the photon mass and the soft logarithmic divergence is regulated by the thermal quark mass, exactly as in the case of real photons. We also consider the production of thermal Drell-Yan dileptons (thermal quark and antiquark pairs produced by virtual photons) and calculate the rate systematically in the context of the hard thermal loop effective theory. We obtain analytic and numerical results. We compare our results with those of previous calculations.

Renormalization of the 4PI effective action using the functional renormalization group

“…2PI effective actions have been used for almost 20 years to study the thermodynamics of quantum fields [12][13][14][15][16], transport coefficients [17][18][19][20], and non-equilibrium quantum dynamics [21][22][23][24][25][26][27][28]. On the other hand, while higher order effective actions have been derived using several different methods [29][30][31][32], very little progress has been made in solving the resulting variational equations.…”

“…For the same theory, working in four dimensions, it has been shown that the 2PI approximation breaks down at large coupling -in the sense that successive orders in the loop expansion give large corrections [14,16]. In addition, it is known that leading order transport coefficients in QED and QCD cannot be obtained using a 2PI formulation [19]. Finally, there are general arguments that an L loop calculation in the nPI formalism should be done with L = n. Firstly, the n-loop nPI calculation is complete, in the sense that increasing the order of the approximation (the number of variational vertices that are included) without increasing the loop order of the truncation does not change the effective action [29].…”

Interpolation of hard and soft dilepton rates

“…[7], with minor modifications [8]), as well as a full NLO computation in a regime of "hard" invariant masses M ≫ gT [11]. We have shown that the two different regimes can be "interpolated" into a result which is theoretically consistent in both regimes and should represent a fair approximation (with uncertainties of less than ∼50%) for all spatial momenta and positive invariant masses.…”

Testing thermal photon and dilepton rates

“…Subsequently the focus shifted to the more typical hard momenta (k ∼ πT ), where a logarithmic singularity, shielded by HTL-resummation, was identified when approaching the light cone (M ≪ πT ) [12][13][14]. In addition, there are non-logarithmic terms of similar magnitude [15], originating from amongst others multiple scatterings with collinear enhancement (the so-called LPM effect [16]), whose systematic handling necessitated a major effort [17][18][19][20]. By now these resummed results have been extended up to NLO close to the light cone [21,22].…”