Charged-particle decay at finite temperature

Radiative corrections to the decay rate of charged fermions caused by the presence of a thermal bath of photons are calculated in the limit when temperatures are below the masses of all charged particles involved. The cancellation of finite-temperature infrared divergences in the decay rate is described in detail. Temperature-dependent radiative corrections to a two-body decay of a hypothetical charged fermion and to electroweak decays of a muon $\mu \to e{\nu }_{\mu }{\overline{\nu }}_e$ are given. We touch upon possible implications of these results for charged particles in the early Universe.

Figure 1

The diagram for the decay $\psi \to \chi \varphi$. Note that we shall distinguish between the $\psi$ and $\chi$ particles in the diagrams below by representing them with thick and thin solid lines, respectively.

Figure 2

The two diagrams via which absorption of a photon can lead to induced $\psi$ decay (or $\chi$ and $\varphi$ production).

Figure 3

The diagrams for radiative $\psi$-decays. Note that the topologies of the diagrams are identical to those for absorption in Fig. 2, with the exception of the photon line placement. This results in the relation given in Eq. (8).

Figure 4

The $T$-dependent part of the photon propagator.

Figure 5

The diagram contributing to the $T$-dependent part of the $\mathcal{O}(\alpha )$ correction to the vertex.

Figure 6

The diagram contributing to the $T$-dependent part of the fermion self-energy.