Asking for an extra photon in Higgs production at the LHC and beyond

We study the inclusive production of a Higgs boson in association with a high-$p_T$ photon at the LHC, detailing the leading-order features of the main processes contributing to the $H\gamma$ final state. Requiring an extra hard photon in Higgs production upsets the cross-section hierarchy for the dominant channels. The $H\gamma$ inclusive production comes mainly from photons radiated in vector-boson fusion (VBF), which accounts for about 2/3 of the total rate, for $p_T^{\gamma,j} >30$ GeV, at leading order. On the other hand, radiating a high-$p_T$ photon in the main top-loop Higgs channel implies an extra parton in the final state, which suppresses the production rate by a further $\alpha_S$ power. As a result, the $H\gamma$ production via top loops at the LHC has rates comparable with the ones arising from either the $H t\bar t$ production or the $HW(Z)\gamma$ associated production. Then, in order of decreasing cross section, comes the single-top-plus-Higgs channel, followed in turn by the heavy-flavor fusion processes $b\bar b \to H\gamma$ and $c\bar c \to H\gamma$. The $H\gamma$ production via electroweak loops has just a minor role. At larger c.m. energies, the $H t\bar t\gamma$ channel surpasses the total contribution of top-loop processes. In particular, requiring $p_T^{\gamma,j} >30$ GeV at $\sqrt S \simeq 100$ TeV, $H t\bar t\gamma$ accounts for about $1/4$ of the inclusive $H\gamma$ production at leading order, about half of the total being due to VBF production.