Abstract
Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M^2 << (pi T)^2. In this regime an LPM resummation is needed for obtaining the correct leading-order result. We show how to construct an interpolation between the hard NLO and the leading-order LPM expression. The final numerical results are presented in a tabulated form, suitable for insertion into hydrodynamical codes.
Highlights
But large spatial momentum (k >∼ πT )
Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M 2 ≪2
We show how to construct an interpolation between the hard NLO and the leading-order LPM expression, which is theoretically consistent in both regimes and free from double counting
Summary
But large spatial momentum (k >∼ πT ) In this regime the NLO rate has a logarithmic singularity, which is regulated by Landau damping of the quarks mediating t-channel exchange [5, 6]. For M ≫ πT no resummation is needed at NLO, and the analysis can be greatly simplified by making use of Operator Product Expansion (OPE) techniques, with the results available in analytic form [10]. The goal of the present study is to present a smooth interpolation between these hard NLO expressions, and leading-order LPM resummation in the soft regime M ∼ gT , k ≫ M. After defining the observables to be considered, we briefly review the status of hard NLO computations in section 3 and of soft LPM resummation in section 4 (we introduce an efficient method for the numerical solution of the LPM equations). Choosing for convenience the z-axis to point in the direction of k, k ≡ (0, 0, k) ,
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