Abstract
We provide two two-loop amplitudes relevant for precision Higgs physics. The first is the two-loop amplitude for Higgs boson production through gluon fusion with exact dependence on the top quark mass up to squared order in the dimensional regulator ε. The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit. Both amplitudes are computed by finding canonical bases of master integrals, which we evaluate explicitly in terms of harmonic polylogarithms. We obtain the bare, renormalized and IR-subtracted amplitude and provide the results in terms of building blocks suitable for changing renormalization schemes.
Highlights
The infinite top mass approximation has a ∼ 6% effect on the cross section, estimated from the NLO [8] prediction, which is applied to the state-of-the-art N3LO through a multiplicative correction factor
The second result we provide is the two-loop amplitude for the decay of a Higgs boson into a pair of massive bottom quarks through the Higgs-to-gluon coupling in the infinite top mass limit
While this work highlighted that more refined approaches such as the FTapprox description can provide a reasonable description within 10% up to high energies, the projected ∼ 5% uncertainty of future HL-LHC transverse momentum spectrum measurements [12, 13] warrants turning our sights toward a better control of mass effects in Higgs physics predictions
Summary
The bare amplitude ABH→bb of the process H → b(p1) ̄b(p2) can be written to all orders as. At face value, computing M0B is impractical as there are two different mass parameters for external and internal bottom quarks We will avoid this issue by renormalizing the bottom quark mass at the Lagrangian level, yielding both a propagator with the renormalized mass and a counter-propagator with the mass counterterm. MyBb,0 features no bottomquark propagator, so that only MyBt, is affected by the procedure This effect is very easy to track since MyBt, is generated by a single Feynman diagram with a single bottom quark propagator: the effect of mass renormalization in a scheme where mBb = mb + δm is summarized in diagrammatic form as follows. We provide all contributions to the bare amplitudes My0x,n as well as the renormalized and IR-subtracted amplitudes Myfti,n(1,2) in the supplementary material, such that results for a different choice of a renormalization scheme can be obtained (see section 2.2). We provide all necessary master integrals for this process up to weight 6, such that higher orders in the dimensional regulator are accessible for future computations
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