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 $Hto gg$ and $Hto qbar{q}$. 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.