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.

We calculate γ l (0), the damping rate for longitudinal on-shell gluons with zero momentum in hot QCD using the hard-thermal-loop (htl) scheme. We find it to be divergent in the infrared, which means that in this scheme γ l (0) is different from γ t (0), the corresponding damping rate for transverse gluons which is known to be finite. This result suggests that the htl scheme is infrared sensitive and thus may need to be improved upon in this sector. We discuss this issue after we present our calculation. pacs: 11.10.Wx 12.38.-t 12.38.Bx 12.38.Mh keywords: hard thermal loops. soft gluon damping. ENSK-TP-10Besides their importance regarding the stability of the quark-gluon plasma, gluon damping rates have been crucial in better understanding QCD at high temperature T . In early works, it has been noticed that in this regime, the determination of the dispersion laws for quarks and gluons beyond lowest order using standard perturbation theory is gaugedependent [1]. This problem has been emphasized in further works in which the gluon damping rates have been calculated to one-loop order in various gauges and schemes and different results have been obtained [2]. It was then realized that the problem was related to the way the expansion in powers of g, the perturbative QCD coupling constant, was performed: at high T (the hard scale), when the external momenta are soft, i.e., of magnitude gT, the standard loop expansion is not anymore an expansion in powers of g [3]. It was subsequently developed an effective perturbative expansion in the framework of a resummation scheme of the so-called hard thermal loops (htl) [4]. Using this scheme, the transverse-gluon damping rate γ t (0) with zero momentum was shown to be Coulomb-and-covariant-gaugeinvariant and determined in the strict Coulomb gauge to be finite and positive [5]. Later, a