Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator

Abstract

In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N${}^3$LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H$+$jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, $H\to ggg$, $H\to q\bar{q}g$, in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.

32 pages; 3 figures, 3 tables; ancillary files with results in Mathematica format; v2 Fixed typos in Section 5 and unified the integration measure in Appendix B and the ancillary files, version accepted for publication in JHEP; v3 Fixed typos in formulas 5.5, 5.9, and A.2-A.4; in anc/, the colour layer "F2" was called "D2" by mistake; results also available at https://xjetamps.hepforge.org/

References in corpus (11)

• Higgs boson gluon-fusion production in N3LO QCD
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Expansion by regions: revealing potential and Glauber regions automatically
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• NNLO QCD corrections to Higgs boson production at large transverse momentum
• On the highest transcendentality in N=4 SUSY
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Exact top-quark mass dependence in hadronic Higgs production

Cited by in corpus (8)

• Next-to-leading order electroweak corrections to $gg\to HH$ and $gg\to gH$ in the large-$m_t$ limit
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Learning Feynman integrals from differential equations with neural networks
• The two-loop Higgs impact factor
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes