Abstract
We compute the contribution of three-loop mixed QCD-electroweak corrections ($\alpha_S^2\alpha^2$) to the $gg \to H$ scattering amplitude. We employ the method of differential equations to compute the relevant integrals and express them in terms of Goncharov polylogarithms.
Highlights
It is an open question if the scalar boson discovered by ATLAS and CMS Collaborations in 2012 is the Higgs boson of the Standard Model
If the Standard Model is not a complete theory, new physics at scale Λ that couples to the Higgs boson is expected to modify its couplings to matter and gauge particles by an amount δg=g ∼ Oðv2=Λ2Þ where v 1⁄4 246 GeV is the scale of electroweak symmetry breaking
Once the canonical basis is found and integrals are normalized in such a way that the finite ε-limit exists limε→0Fðε; yÞ 1⁄4 F0, it becomes straightforward to obtain the solution to the system of differential equations as series expansion in the dimensional regularization parameter ε
Summary
It is an open question if the scalar boson discovered by ATLAS and CMS Collaborations in 2012 is the Higgs boson of the Standard Model. The theoretical uncertainty in the gg → H cross section originates from (see [1,2]) the Oð2%Þ residual scale uncertainty in pure QCD contributions, the Oð1%Þ uncertainty caused by unknown mass effects of b and c quarks in higher orders of QCD perturbation theory, and the Oð1%Þ uncertainty in QCD-EW contributions The latter uncertainty is peculiar since computation of QCD corrections to mixed QCD-. The leading-order QCD-EW OðαSα2Þ contribution is known for arbitrary values of the Higgs and electroweak gauge boson masses [4,5,6,7], the next-to-leading-order (NLO) QCD corrections to it have only been computed in the unphysical limit mH ≪ mW;Z [3]. To compute the three-loop mixed QCD-EW contribution to the gg → H amplitude, we use the method of differential equations [8,9,10] to calculate the relevant master integrals (MIs). We provide the analytic results for leading- and next-to-leadingorder QCD-EW contributions to gg → H amplitude in the ancillary file
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