A potential infrared problem with the damping rates for gluons with soft momentum in hot QCD

Abstract

We calculate the damping rate γ l for longitudinal gluons with zero momentum in finite high temperature QCD and show that some of its contributing terms are infrared divergent. This is in contrast with the expectation that this damping rate is to be equal to the corresponding one γ t for transverse gluons which is known to be finite. Our calculation was motivated by the fact that similar divergent terms occur when we calculated in a previous work γ t to order p 2 , p being the momentum of the gluon. After we present our results, we briefly discuss them.

Advances in perturbative thermal field theory

“…However, as will be discussed further below, the limit k → 0 involves infrared problems, and there are even explicit calculations [322,323] that claim to find obstructions to this equality, which are however contradicted by the recent work of [324].…”

Gluon Energy at Next-to-Leading Order in Hot QCD Using the Real-Time Formalism

“…This was first indicated in [4], where the direct and explicit attempt to calculate the damping rate for non-moving longitudinal gluons showed that it is infrared divergent. The infrared sensitivity occurs in other quantities too [5,6].…”

NLO dispersion laws for slow-moving quarks in HTL QCD

“…In a line of works, we have used this formalism and looked into the infrared behavior of fully-HTL-dressed one-loop-order damping rates of slow-moving longitudinal [55,56] and transverse gluons [57], quarks [58][59][60], fermions 2 [61][62][63] and photons [64] in QED, and quasiparticles [65] in scalar QED. 3 In this logic, the natural step forward is to try to calculate the NLO energies of the quasiparticles.…”