Abstract
We calculate the contributions to the two-loop scattering amplitudes h → gg, h → ggg and hto qoverline{q}g that arise from a modified trilinear Higgs coupling λ. Analytic expressions are obtained by performing an asymptotic expansion near the limit of infinitely heavy top quark. The calculated amplitudes are necessary to study the impact of the mathcal{O}left(lambda right) corrections to the transverse momentum distributions (pT,h) in single-Higgs production at hadron colliders for low and moderate values of pT,h.
Highlights
Where H denotes the usual Higgs doublet
At the differential level the loop-induced effects involvingc6 are at present known for vector boson fusion (VBF), V h [3, 4] as well as tth [3] and thj [5] production, while they have not been calculated in the case of the gluon-fusion channel
The computation of the two-loop amplitudes is simplified by performing an asymptotic expansion near the limit of infinitely heavy top quark
Summary
We discuss the parametrisation of the h → gg, h → ggg and h → qqg scattering amplitudes in terms of invariant form factors. Using Lorentz symmetry and gauge invariance, one can show that the amplitude tensor Aμν that appears in (2.1) can be expressed in terms of a single form factor F in the following way. The two form factors entering (2.13) can be extracted by applying the following projection operators [13, 15]. With the tensor structures Tmμ given in (2.14) After applying these projectors one has to calculate sums over quark, anti-quark and gluon polarisations. For this purpose we employ u(p1)u(p1) = p/1 , pol. Note that it is allowed to use an unphysical result for the sum over the gluon polarisation since the Dirac structures introduced in (2.14) are independently transversal
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