Landau-Pomeranchuk-Migdal resummation for dilepton production

TL;DR

This work computes the leading-order dilepton production rate in a quark-gluon plasma for small invariant mass $Q^2 \sim g_s^2 T^2$ and large energy $q^0 \gtrsim T$ by performing Landau-Pomeranchuk-Migdal (LPM) resummation of multiple scatterings. It extends the HTL-based ladder resummation from real photons to off-shell photons, including longitudinal polarization, and reformulates the resulting integral equations in impact-parameter space as solvable differential equations. The main result is a smooth, threshold-free dilepton spectrum where the LPM effects significantly enhance the rate in the low-to-intermediate mass range; the rate exhibits a scaling with $\alpha_s$ and $T$ and is dominated by transverse polarization except near $Q^2/q_0^2 \approx 1$. This provides a practical, LO framework for dilepton yields in heavy-ion collisions, with insights complementary to lattice results and potential applications to RHIC/LHC phenomenology.

Abstract

We consider the thermal emission rate of dileptons from a QCD plasma in the small invariant mass ($Q^2 \sim \gs^2 T^2$) but large energy ($q^0 \gsim T$) range. We derive an integral equation which resums multiple scatterings to include the LPM effect; it is valid at leading order in the coupling. Then we recast it as a differential equation and show a simple algorithm for its solution. We present results for dilepton rates at phenomenologically interesting energies and invariant masses.

Figures (7)

• Figure 1: Typical diagram which must be resummed to determine $\, {\rm Im} \: \Pi_\mu^\mu$. The gluon lines are soft and HTL-resummed, the solid (quark) lines are hard, approximately on-shell, and resummed to include the dominant imaginary part.
• Figure 2: The sum of all the multiple scattering diagrams compared to the single scattering contribution only. In this plot $\alpha_{\rm s}=0.3$ and $q_0/T=50$.
• Figure 3: All the contributions to ${\rm Im}\,\Pi_{_{\rm R}}$ up to ${\cal O}(\alpha_{\rm s})$. In this plot $\alpha_{\rm s}=0.3$ and $q_0/T=50$.
• Figure 4: ${\rm Im}\,\Pi_{_{R}}$ as a function of the photon invariant mass for two values of the strong coupling constant. The dotted lines are the corresponding Born terms. The circles illustrate the scaling law of Eq. (\ref{['eq:scaling']}). The value of $q_0/T$ is set to $30$ in this plot.
• Figure 5: Dependence of the dilepton rate on the mass of the pair. In this plot $T=1$ GeV, $q_0=5$ GeV, $N_{_{F}}=2$ and $\alpha_{\rm s}=0.3$.