Interpolation of hard and soft dilepton rates

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 ≪ (πT ) 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, which is theoretically consistent in both regimes and free from double counting. The final numerical results are presented in a tabulated form, suitable for insertion into hydrodynamical codes.

The thermal dilepton rate at NLO at small and large invariant mass

“…[4], which become unreliable away from the light cone. The dashed line is the merge of the small- [4] and large-M results [6], according to the procedure of [7,4]. Since no large-M calculation is available for the spacelike region, no dashed line is shown there.…”

“…The dashed line is the ratio of the NLO merged results [4] shown in dashes in Fig. 5 over the LO merged results [7], which do not include the small-M NLO results described in Sec. 2.…”

“…This large-M calculation does not require HTL resummation; hence, it diverges logarithmically for small M. Conversely, the small-M calculation described before behaves like W < ∼ g 2 (M 2 +T 2 ) at large M, whereas an OPE analysis [16] shows that no T 2 -proportional term can exist for M T . These drawbacks of the two calculations can be overcome by merging them in a single one which has the right behaviour both at small and large M. This can be done [7,4] by taking the collinear part of the small M calculation and expanding it for large M: the first and second term in that expansion correspond to terms that are already included in the large M calculation. Thus, if the collinear part of the small M calculation is added to the large-M one, minus these two terms, the result is the sought after merged calculation.…”

“…Thus, if the collinear part of the small M calculation is added to the large-M one, minus these two terms, the result is the sought after merged calculation. In [7] it was presented with the LO collinear part and in [4] the small-M NLO corrections were added, leading to a merged result that is NLO-correct for M ∼ gT , M ∼ √ gT and M ∼ T .…”

“…In this contribution we will then first illustrate a recent perturbative calculation of the thermal dilepton rate at small M (and for k ∼ T ) to NLO [4], extending the previous work on real photons [5], aiming also at understanding whether the rate, as a function of M, is smooth enough in going from M = 0 to finite M, so that the ersatz photon rate measurements are meaningful. We will afterwards show the results of an NLO calculation at larger M [6] and then show how the small-and large-M computations can be merged [7,4], resulting in a rate that is reliably NLO for most invariant masses. Another motivation for these NLO calculation is to assess the reliability of the pQCD rates, widely employed in phenomenological analyses, when extrapolated to α s ∼ 0.3 where the coupling g is not small.…”