Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes

Abstract

We derive two-loop scattering amplitudes for bottom-quark pair production in association with a Higgs boson at the LHC, focusing on terms proportional to the top-quark Yukawa coupling. We treat the bottom quark as a massless parton and employ both the leading-colour and heavy-top-quark approximations. The finite remainder of the two-loop amplitude is expressed in terms of one-mass pentagon functions, and the corresponding rational coefficients are reconstructed analytically from evaluations over finite fields. The scattering processes considered in this work also constitute a subset of Higgs+2-jet production at the LHC in the heavy-top-quark approximation.

Figures (5)

• Figure 1: Representative Feynman diagrams illustrating the three $b\bar{b}H$ cross-section components defined in \ref{['eq:SigmaBBHdecomposition']} at leading order in 4FS, grouped according to their dependence on the bottom- and top-Yukawa couplings.
• Figure 2: Representative Feynman diagrams illustrating the $y_t$-dependent cross-section components defined in \ref{['eq:SigmaBBHdecomposition']} at leading order in 4FS within the HTL framework.
• Figure 3: Sample two-loop Feynman diagrams contributing to leading colour $0\to\bar{b}bggH$ partial amplitudes. Solid lines denote massless quarks (bottom quarks in red), while dashed lines indicate the Higgs boson.
• Figure 4: Sample two-loop Feynman diagrams contributing to leading colour $0\to\bar{b}b\bar{q}qH$ partial amplitudes. Solid lines denote massless quarks (bottom quarks in red), while dashed lines indicate the Higgs boson.
• Figure 5: The four panels show the distribution of the estimated numerical precision for four partonic channels ($gg\to\bar{b}bH$, $\bar{q}q\to\bar{b}bH$, $\bar{b}b\to\bar{b}bH$ and $bb\to bbH$) based on 100k phase space points (the same for each channel). The blue line represents evaluations using double precision for the transcendental and rational parts. All points with fewer than 4 digits (indicated by the blue area) were re-evaluated with higher floating-point precision () for the rational part, shown as the orange line. Finally, all points that, even then, failed to achieve 4-digit precision (indicated by the orange area) were re-evaluated, also using floats for the pentagon functions (the green line).