Two-loop mixed QCD-EW corrections to gg → Hg

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.

One-loop Feynman integrals for 2 → 3 scattering involving many scales including internal masses

“…One of the expected challenges when considering such integrals is the introduction of many square roots in the alphabet of the resulting canonical differential equations. It remains a non-trivial exercise to find a universal way to handle these roots and achieve a result in terms of Goncharov polylogarithms, however several ideas have been put forward in recent times [41][42][43][44]. One should also keep in mind that even if a so-called dlog form of the differential equations is achieved, it does not guarantee that its solution will be in terms of Goncharov polylogarithms [52].…”

“…In order to achieve a result in such a form we need to find a way to deal JHEP10(2021)041 with these square roots. Several ideas have been put forward recently that are able to circumvent this problem and provide solutions in terms of Goncharov polylogarithms [41][42][43][44] for specific cases, however a universal method to treat the problem of square roots appearing in the alphabet of canonical differential equations for multiscale families of Feynman integrals is still missing.…”

One-loop Feynman integrals for $2\to3$ scattering involving many scales including internal masses

“…One of the expected challenges when considering such integrals is the introduction of many square roots in the alphabet of the resulting canonical differential equations. It remains a nontrivial exercise to find a universal way to handle these roots and achieve a result in terms of Goncharov polylogarithms, however several ideas have been put forward in recent times [41][42][43][44]. One should also keep in mind that even if a so-called dlog form of the differential equations is achieved, it does not guarantee that its solution will be in terms of Goncharov polylogarithms [52].…”

“…In order to achieve a result in such a form we need to find a way to deal with these square roots. Several ideas have been put forward recently that are able to circumvent this problem and provide solutions in terms of Goncharov polylogarithms [41][42][43][44] for specific cases, however a universal method to treat the problem of square roots appearing in the alphabet of canonical differential equations for multiscale families of Feynman integrals is still missing.…”

Calculational Techniques in Particle Theory

“…A revolution in direct integration methods, based for example on the well known Feynman-Schwinger parametrisation, has happened with the establishment of the criterion of linear reducibility [67] for Feynman integrals and the development of algorithms to exploit it to compute Feynman integrals in terms of MPLs [68]. Many important calculations have been performed thanks to this insight, recent examples are various form factor integrals up to four loops [69] and 2 → 2 scattering amplitudes with masses [70].…”