Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation

Charalampos Anastasiou,Bernhard Mistlberger,Vittorio Del Duca,Elisabetta Furlan,Armin Schweitzer,Francesco Moriello,Caterina Specchia

doi:10.1007/jhep03(2019)162

Charalampos Anastasiou, Bernhard Mistlberger + Show 5 more

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https://doi.org/10.1007/jhep03(2019)162

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Abstract

We compute the mixed QCD-electroweak corrections to the cross section for the production of a Higgs boson via gluon fusion, in the limit of a small mass of the electroweak gauge bosons. This limit is regular and we calculate it by setting the W, Z masses to zero in the Feynman rules for their propagators. Our analytic results provide an independent check, in a non-trivial limit, of a recent exact computation for the three-loop mixed QCD and electroweak virtual corrections [1] and the corresponding contribution to the cross section in the soft-virtual approximation [2]. From our calculation in the small mass approximation, we can infer the second term in the expansion of the cross section around the threshold limit with its exact dependence on the masses of the W, Z bosons. Furthermore we find that in the small mass approximation the non-factorizable contributions from the real radiation, so far unknown for full gauge boson mass dependence, are modest in comparison to the known factorizable and virtual contributions to the full mathcal{O}left({alpha}_s^3{alpha}^2right) mixed QCD and electroweak cross-section. This furnishes a new phenomenological test of estimates [3] for the mixed QCD and electroweak corrections, which were based on the hypothesis of factorization of QCD and electroweak corrections.

Highlights

JHEP03(2019)162 remarkable stability with respect to the choice of renormalisation and factorisation scale, with a typical scale variation of less than ±2%
We find that in the small mass approximation the non-factorizable contributions from the real radiation, so far unknown for full gauge boson mass dependence, are modest in comparison to the known factorizable and virtual contributions to the full O(αs3 α2) mixed QCD and electroweak cross-section
All mixed QCD-EW amplitudes factorise into a product of a Wilson coefficient and the same QCD amplitude which emerges in pure QCD corrections in HEFT

Summary

The small-mass approximation

We consider the first term of a small EW-boson mass expansion, m2V m2H , s, |t|. We neglect diagrams involving the top quark [45] This is motivated by the fact that they contribute to the two-loop electroweak correction by just a few percent of the light-quark electroweak effects [49] and we expect a similar pattern at one higher order in QCD perturbation theory. The primary analytic result of this paper is the computation of the mixed QCD-EW corrections in the approximation of a small EW-boson mass (light boson), as defined above. The overall factor (3ζ3 − 2) is the small EW-boson mass approximation, for both the W and Z bosons, of the two-loop light-quark form factor, while the non-universal part of the virtual cross section is. We note that our small mass approximation is recovered from the general formula eq (2.8) by using the results of refs. The behaviour of the factorizable soft and next-to-soft contributions of eq (2.9) are in agreement with the expectations from the next-to-leading-power corrections [66,67,68,69] to colour-singlet production from gluon-gluon fusion at NLO [70]

Phenomenological analysis

Findings

Conclusions