Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar b \rightarrow ZH$ at NNLO in QCD

Understand

Production of the Higgs boson, $H$ in association with a massive vector boson, $V$, i.e., the $VH$ process, plays an important role in the explorations of Higgs physics at the Large Hadron Collider, both for a precise study of Higgs' Standard Model couplings and for probing New Physics.

• In this publication we present the two-loop corrections in massless quantum chromodynamics (QCD) to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling, which is a necessary ingredient of the full next-to-next-to-leading-order QCD corrections to the $VH$ process in the five-flavour scheme.
• The computation is performed by projecting the D-dimensional scattering amplitude directly onto an appropriate set of Lorentz structures related to the linear polarisation states of the $Z$ boson.
• We provide analytic expressions of the complete set of renormalised polarised amplitudes in terms of polylogarithms of maximum weight four.