Abstract
We compute the two-loop mixed QCD-Electroweak (QCD-EW) corrections to the production of a Higgs boson and a gluon in gluon fusion through a loop of light quarks. The relevant four-point functions with internal massive propagators are expressed as multiple polylogarithms with algebraic arguments. We perform the calculation by integration over Feynman parameters and, independently, by the method of differential equations. We compute the two independent helicity amplitudes for the process and we find that they are both finite. Moreover, we observe a weight drop when all gluons have the same helicity. We also provide a simplified expression for the all-plus helicity amplitude, which is optimised for fast and reliable numerical evaluation in the physical region.
Highlights
Prohibitively complicated still today, primarily due to the complexity of the relevant threeloop massive scattering amplitudes
In this paper we described the first calculation of the two-loop mixed QCD-EW corrections to the production of a Higgs boson and a gluon in gluon fusion through a loop of massless quarks, with full dependence on the Higgs and on the vector boson masses
The amplitudes presented here are the last missing building blocks required to compute the NLO mixed QCD-EW corrections to Higgs production in gluon fusion, overcoming the shortcoming of the various approximations that have been used to estimate these corrections in the past
Summary
We stress that in this decomposition no parity-violating terms appear This can be justified by noticing that, if we only consider massless quarks, the axial contribution drops when summing over degenerate isospin doublets. We indicate the helicity of the gluon of momentum pj by λj and write for a generic helicity amplitude and for a given vector boson V. where Aμνρ(s, t, u, m2V ) was defined in eq (2.3). To eq (2.6), we can explicitly extract the LO EW and QCD couplings from the amplitudes and write for the perturbative expansion of the helicity coefficients. Such that, again, the full QCD-EW contributions are obtained by summing the corresponding helicity amplitudes with V = Z, W
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