Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator

TL;DR

This paper advances precision QCD for pseudoscalar Higgs decays by computing the one- and two-loop amplitudes for $A\to ggg$ and $A\to q\bar{q}g$ in an EFT with heavy quarks integrated out, expanded to higher orders in the dimensional regulator $\epsilon$. The authors derive UV renormalization and IR subtraction structures, including the operator mixing of $O_G$ and $O_J$ and the finite renormalization required for the axial current, and verify the IR poles against Catani’s predictions. They express the amplitudes in terms of Generalized Polylogarithms, map to prior Harmonic Polylogarithms for cross-checks, and implement the finite pieces in optimized FORTRAN-95 code suitable for Monte Carlo phase space integration. The work provides essential ingredients toward a full three-loop cross section for pseudo-scalar production in association with a jet, with implications for precise collider predictions and CP-odd scalar searches. The results are validated against existing NNLO/N3LO expectations and are made available to the community for immediate use in differential distributions at hadron colliders.

Abstract

We present for the first time the second-order corrections of pseudo-scalar($A$) Higgs decay to three parton to higher orders in the dimensional regulator. We compute the one and two-loop amplitudes for processes, $A\to ggg$ and $A\to q\bar{q}g$ in the effective theory framework. With suitable crossing of the external momenta, these calculations are well-suited for predicting the differential distribution of pseudo-scalar Higgs in association with a jet at hadron colliders, up to next-to-next-to-leading order (NNLO) in the strong coupling constant. These results expanded to higher orders in dimensional regulator will contribute to the full three loop cross section. We implement the finite pieces of the amplitudes in a numerical code which can be used with any Monte Carlo phase space generator.

Figures (7)

• Figure 1: Feynman diagram for $A$ decay to 3 partons at LO.
• Figure 2: Real part of $\mathcal{O}(\epsilon^0)_{\text{I}}$ for the process $S_{ggg}$
• Figure 3: Real part of $\mathcal{O}(\epsilon^1)_{\text{I}}$ for the process $S_{ggg}$
• Figure 4: Real part of $\mathcal{O}(\epsilon^2)_{\text{I}}$ for the process $S_{ggg}$
• Figure 5: Real part of $\mathcal{O}(\epsilon^0)_{\text{I}}$ for the process $S_{q\bar{q}g}$