Damping Rate of Quasiparticles in Degenerate Ultrarelativistic Plasmas

We compute the damping rate of a fermion in a dense relativistic plasma at zero temperature. Just above the Fermi sea, the damping rate is dominated by the exchange of soft magnetic photons (or gluons in QCD) and is proportional to (E − μ), where E is the fermion energy and μ the chemical potential. We also compute the contribution of soft electric photons and of hard photons. As in the nonrelativistic case, the contribution of longitudinal photons is proportional to (E − μ), and is thus non leading in the relativistic case. PACS No: 11.10.Wx, 12.20.-m, 12.20.Ds, 52.60.+h ECM-UB-PF-96/15, INLN 96/19 September/1996 The properties of quasiparticles in ultrarelativistic (UR) plasmas have attracted much attention in a recent past [1]. A crucial property of a quasiparticle is its decay (or damping) rate: a quasiparticle which propagates in a plasma is not stable, as it undergoes collisions with the other particles of the plasma, and the very concept of a quasiparticle makes sense only if its damping rate is small enough. The damping rate of an electron propagating in a nonrelativistic (NR) plasma was computed almost forty years ago by Quinn and Ferrell [2], [3]. At first sight, this damping rate is infinite, due to the singular behavior of the Rutherford cross-section at small angles. However Quinn and Ferrell were able to obtain a finite result because the Coulomb interaction is screened in a plasma (Debye screening), and in the case of a degenerate plasma, they showed that the damping rate is proportional to (εp − εF ), where εp = p/2m is the NR kinetic energy and εF the Fermi energy, when εp is slightly larger than εF . The damping rate remains finite for a non zero temperature T : only the value of the Debye screening length is modified. It is interesting to extend the calculation of the damping rate to the case of relativistic plasmas: one may have in mind either electromagnetic (QED) plasmas, such as found in white dwarves or in the core of nascent neutron stars, or chromodynamic (QCD) plasmas such as the quark-gluon plasma which is believed to be formed for large enough values of the temperature T and/or the chemical potential μ. The NR results are not easily transposed to the relativistic case, because the exchange of magnetic (or transverse) photons in QED or of magnetic gluons in QCD becomes important, while in the NR case it is suppressed by powers of (v/c) with respect to the exchange of electric (or longitudinal) gauge bosons, and is usually neglected. These magnetic photons, or gluons, give rise to severe infrared (IR) divergences which are not easily cured, because there is no static magnetic screening analogous to Debye screening in the electric case, but only a weaker dynamical screening [4]. In many cases, this dynamical screening is sufficient to remove the IR divergences [5], [6] but it has been known for some time that it cannot solve easily the IR problem of the damping rate [7], at least for non zero T . In a recent paper [8], Blaizot and Iancu were nevertheless able to derive a finite result in the T 6= 0, μ = 0 case, by using a non perturbative approach to resum the leading divergencies. However they also discovered that the decay law is no longer exponential. In this Letter, we address the problem of computing the damping rate of quasiparticles in degenerate UR plasmas. For the sake of definiteness, we treat the case of a QED plasma,