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

We calculate the damping rate ${\gamma }_l$ 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 ${\gamma }_t$ 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 ${\gamma }_t$ to order $p^2$, p being the momentum of the gluon. After we present our results, we briefly discuss them.