Final-state interactions of the Higgs boson in quark-gluon matter

In the first version of this paper \cite{dEnterria:2018bqi}, we presented a study of the final-state interactions of the Higgs boson in the hot and dense quark-gluon systems produced in pp, pPb, and PbPb collisions at CERN LHC and FCC energies. By computing the leading-order diagrams of the Higgs-parton scattering cross sections in perturbative QCD, and by embedding the produced Higgs bosons in an expanding quark-gluon medium modeled with 2D+1 viscous hydrodynamics with various QCD equations of state, we presented estimates of the expected scalar boson yields as functions of transverse momentum $p_{\rm T}^{H}$, and produced medium space-time size. A moderate suppression of the scalar boson yields was predicted due to medium-enhanced $H\to gg,q\bar{q}$ decays, in detriment of the $H\to\gamma\gamma, 4\ell$ channels that are typically used to observe the Higgs particle. After our work appeared, J. Ghiglieri and U. Wiedemann \cite{Ghiglieri:2019lzz} have presented thermal-field-theory calculations that indicate that the $H\to gg,q\bar{q}$ partial decays widths remain basically unaffected by interactions with surrounding partons in the kinematic range of relevance of our study. Such a theoretical result, in contradiction with our estimates, has brought us to revisit our calculations and to realize of the quantitative importance of thermal virtual corrections, neglected in our first work, that are as large as the real ones and of opposite sign. Such virtual corrections significantly reduce the Higgs-parton "absorption" cross sections originally computed in Ref. \cite{dEnterria:2018bqi}, and make the Higgs boson suppression negligible in the kinematic regime considered.