A Lattice Calculation of Thermal Dilepton Rates

TL;DR

This study addresses thermal dilepton production in the quark–gluon plasma by computing vector current correlators in quenched QCD using clover-improved Wilson fermions. The authors relate the Euclidean correlator $G_V(\tau, T)$ to the vector spectral function $\sigma_V(\omega, T)$ via $G_V(\tau,\vec p,T)=\int_0^{\infty} d\omega\, \sigma_V(\omega,\vec p,T)\, K(\tau,\omega)$ with the finite-temperature kernel and reconstruct $\sigma_V$ from lattice data using the Maximum Entropy Method with a lattice-aware kernel $K_L(\tau,\omega,N_\tau)$. They find that, at $T=1.5T_c$ and $3T_c$, the vector correlator deviates by less than 15% from the free result and that $\sigma_V$ differs from the free form by at most a factor of two for $\omega/T \gtrsim 4$, while exhibiting a sharp low-energy cutoff around $\omega/T \sim 3$–$5$, corresponding to a thermal mass threshold of roughly $(2-3)T$. These findings imply no infrared divergence in the dilepton rate and predict a suppressed thermal yield at low energies, providing robust lattice constraints on dilepton production models relevant to SPS, RHIC, and LHC heavy-ion collisions.

Abstract

Using clover improved Wilson fermions we calculate thermal vector meson correlation functions above the deconfinement phase transition of quenched QCD. At temperatures 1.5 Tc and 3Tc they are found to differ by less than 15% from that of a freely propagating quark anti-quark pair. This puts severe constraints on the dilepton production rate and in particular rules out a strong divergence of the dilepton rate at low energies. The vector spectral function, which has been reconstructed using the Maximum Entropy Method, yields an enhancement of the dilepton rate over the Born rate of at most a factor two in the energy interval 4 < E/T < 8 and suggests that the spectrum is cut-off at low energies by a thermal mass threshold of about (2-3)T.

Figures (2)

• Figure 1:
• Figure 2: Reconstructed vector spectral function $\sigma_V$ in units of $\omega^2$ at zero momentum (a) and the resulting zero momentum differential dilepton rate (b) at $T/T_c = 1.5$ (doted line) and 3 (dashed line). The solid lines give the free spectral function (a) and the resulting Born rate (b). The insertion in (a) shows the error band on the spectral function at $3T_c$ obtained from a jackknife analysis and errors on the average value of $\sigma_V(\omega, T)/\omega^2$ in four energy bins (see text).