Thermal width of the Higgs boson in hot QCD matter

Following Caron-Huot and combining results for the thermal dependence of spectral functions at large time-like momenta, we write an explicit expression for the thermal width of the Higgs boson to $\mathcal{O}(\alpha_\mathrm{s})$ for $T \ll M_H$. It is an $\mathcal{O}( \alpha_\mathrm{s} (T/M_H)^4 )$ correction for $H\to gg$ and $H\to q\bar{q}$. We also compile corresponding results for the thermal width of the $Z$-boson, and we recall which generic structures of the field theory, accessible via the operator product expansion, fix the $T/M$-dependence of the decay of heavy particles.