Photon Emission from Quark-Gluon Plasma: Complete Leading Order Results

TL;DR

This paper presents the first complete leading-order calculation of photon emission from a hot, weakly coupled quark-gluon plasma at zero chemical potential, incorporating both near-collinear bremsstrahlung and inelastic pair annihilation with the Landau-Pomeranchuk-Migdal (LPM) effect. It derives and solves a nontrivial integral equation to account for partial coherence in multiple scatterings, and combines these nonlogarithmic near-collinear contributions with the conventional $2\leftrightarrow 2$ processes to obtain the full rate $\nu_e(\mathbf{k})={\cal A}(k)[\ln(T/m_\infty)+C_{\rm tot}(k/T)]$, where $C_{\rm tot}$ aggregates $C_{2\leftrightarrow 2}$, $C_{\rm brem}$, and $C_{\rm annih}$. The results show that for $\alpha_s\sim 0.2$ bremsstrahlung dominates at soft photon energies ($k\lesssim 2T$) while inelastic annihilation dominates at very high energies, with $2\leftrightarrow 2$ processes remaining competitive in the intermediate range; the LPM suppression is typically modest but crucial for soft photons. The study also provides phenomenological fits for the nonlogarithmic pieces and discusses the QED analog, yielding implications for photon production in both QCD and QED plasmas. The work advances quantitative predictions for electromagnetic emission from the quark-gluon plasma relevant to heavy-ion collision phenomenology.

Abstract

We compute the photon emission rate of an equilibrated, hot QCD plasma at zero chemical potential, to leading order in both alpha_{EM} and the QCD coupling g_s(T). This requires inclusion of near-collinear bremsstrahlung and inelastic pair annihilation contributions, and correct incorporation of Landau-Pomeranchuk-Migdal suppression effects for these processes. Analogous results for a QED plasma are also included.

Figures (9)

• Figure 1: Two-to-two particle processes which generate the leading logarithmic contribution to the photo-production rate, and were originally believed to give the complete leading order contribution. Time may be viewed as running from left to right.
• Figure 2: Inelastic processes which, because of near-collinear singularities, contribute at the same order as the two-to-two particle processes. The diagrams on the left represent bremsstrahlung, and those on the right are inelastic pair annihilation. Again, time may be viewed as running from left to right.
• Figure 3: Typical ladder diagram contributing to the electromagnetic current-current correlator. All such ladder diagrams must be summed to determine the leading-order bremsstrahlung and inelastic pair annihilation rates. Resummation of self-energy insertions on all propagators is implied.
• Figure 4: Cut ladder diagram with $N$ gluon "rungs" may be interpreted as the interference between amplitudes for photon emission before and after $N$ scattering events.
• Figure 5: Contribution $C_{2\leftrightarrow 2}(k/T)$ to the constant under the log arising from $2\leftrightarrow 2$ particle processes (gluon-photon Compton scattering and quark-antiquark annihilation), as a function of $k/T$. The dotted line is the asymptotic limit, derived by KapustaBaier. The result is quite close to the asymptotic value already at $k/T = 3$; the visible but tiny difference between the curve and the asymptotic value is due to a $1/k$ tail with a very small coefficient.