Two-Loop QCD Helicity Amplitudes for Higgs Production Associated with a Vector Boson through Bottom Quark Annihilation

Abstract

We present the two-loop QCD corrections to the amplitude of the Higgs production associated with a Z boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottomquark Yukawa coupling. The computation is performed by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarisation states of the Z boson. We cross-check the finite remainders through a computation based on conventional form factor decomposition. We show that for physical observables, an ultimate D-dimensional form factor decomposition of amplitudes is not necessary which has a huge potential to simplify a multiloop computation. We compute numerically the resulting cross sections under the softvirtual approximation to NNLO and find it three orders of magnitude smaller than that of the s-channel.

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

“…As demonstrated in refs. [76,79,80], however, this scheme dependence does not affect the finite remainder of the amplitude in the limit ε → 0.…”