Two-loop amplitudes for processes $g g \to H g, q g \to H q$ and $q \bar{q} \to H g$ at large Higgs transverse momentum

TL;DR

The authors compute two-loop QCD corrections to Higgs plus jet amplitudes in the high-$p_ op$ regime by expanding in the small parameters $\eta=-\frac{m_h^2}{4m_t^2}$ and $\kappa=-\frac{m_t^2}{s}$, while solving master integrals with differential equations. They systematically reduce Feynman diagrams to three MI families, derive renormalized form factors, and perform IR subtraction, with analytic continuation to all relevant scattering regions. Master integrals are evaluated up to weight four in Harmonic Polylogarithms, with integration constants fixed via Mellin-Barnes representations and cross-checked against numerical methods. The resulting helicity amplitudes, provided in ancillary files, enable robust NLO predictions for Higgs transverse momentum distributions at large $p_T$, aiding precision Higgs phenomenology at the LHC.

Abstract

We compute the two-loop QCD corrections to amplitudes for processes $g g \to H g, q g \to H q$ and $q \bar{q} \to H g$ in the limit when the Higgs transverse momentum is larger than the top quark mass, $p_\perp \gg m_t$. These amplitudes are important ingredients for understanding higher-order QCD effects on Higgs transverse momentum distribution at large $p_\perp$.

Figures (4)

• Figure 1: The one-loop Feynman diagrams that contribute to the quark-loop induced processes $gg\rightarrow Hg$ and $qg\rightarrow Hq$.
• Figure 2: Examples of two-loop Feynman diagrams that contribute to the process $gg\rightarrow Hg$.
• Figure 3: Examples of two-loop Feynman diagrams that contribute to the process $q\bar{q}\rightarrow Hg$.
• Figure 4: The two-loop scalar Feynman corresponding to $\mathcal{I}_{\rm NPL}(0,1,1,1,2,0,1,1,0)$.