Bremsstrahlung and photon production in thermal QCD

TL;DR

This paper addresses photon and lepton-pair production in a thermal QCD plasma using hard thermal loop (HTL) resummation. It shows that bremsstrahlung, though arising at two loops, contributes at the same order as one-loop processes for soft static and hard real photons, and identifies a new two-loop mechanism that dominates ultra-hard real photons, significantly increasing the production rates over previous one-loop estimates. The analysis covers soft and hard photon regimes, derives explicit expressions for the imaginary part of the photon polarization tensor, and compares with prior one-loop results and semiclassical approaches, revealing the critical role of two-loop bremsstrahlung and related processes in shaping photon emission from the quark-gluon plasma. The findings have important implications for interpreting electromagnetic signals from heavy-ion collisions, highlighting the necessity of including two-loop effects to obtain accurate photon yield predictions in a thermal medium.

Abstract

In this paper, we extend the study of bremsstrahlung photon production in a quark-gluon plasma to the cases of soft static photons and hard real photons. The general framework of this study is the effective perturbative expansion based on the resummation of hard thermal loops. Despite the fact that bremsstrahlung only comes at two loops, we find that in both cases it generates contributions of the same order of magnitude as those already calculated by several other groups at one loop. Furthermore, a new process contained in the two-loop diagrams dominate the emission of a very hard real photon. In all cases, the rate of real or virtual photon production in the plasma is appreciably increased compared to the one-loop predictions.

Figures (8)

• Figure 1: Two-loop contributions involving bremsstrahlung processes. A black dot denotes an effective propagator or vertex. Crosses are HTL counterterms.
• Figure 2: Simplified two-loop contributions involving bremsstrahlung processes. The circled vertices correspond to the framework of the cutting rules.
• Figure 3: Allowed domains in the $(l_o,l)$ plane for $p_o=\pm p$. The area shaded in dark gray is excluded by the delta functions. The region shaded in light gray is above the light--cone (dotted lines). The solid curves are the transverse and longitudinal dispersion curves of the thermalized gluon. The vertical dotted line is the separation between $\epsilon(p_o)\epsilon(r_o+l_o)=+1$ and $\epsilon(p_o)\epsilon(r_o+l_o)=-1$. The value of the thermal mass has been exaggerated in order to make the figure more readable.
• Figure 4: Physical processes included in the diagrams of Fig. \ref{['fig:2loopsimple']}, in the region $L^2<0$. Region I: $p_o<0$, $r_o+l_o<0$: bremsstrahlung with an antiquark. Region II: $p_o<0$, $r_o+l_o>0$: $q\bar{q}$ annihilation with scattering. Region III: $p_o>0$, $r_o+l_o>0$: bremsstrahlung with a quark. The particle on which the quark is scattered can also be a gluon.
• Figure 5: Comparison of numerical estimates of the complete matrix element with the simple theoretical expression obtained in Eq. (\ref{['eq:staticfinal']}). Both plots show the ratio "Numerical/Theoretical". On the left plot, $q_o/T$ is fixed at $10^{-4}$ and we look at the variations with $m_{\rm g}/T$ ( i.e. with $g$). On the right plot, $m_{\rm g}/T$ is fixed at $10^{-2}$ and the photon energy varies from ultra-soft energies to hard ones.