Two loop QCD amplitudes for di-pseudo scalar production in gluon fusion

Arunima Bhattacharya,Prakash Mathews,Maguni Mahakhud,V Ravindran

doi:10.1007/jhep02(2020)121

Abstract

We compute the radiative corrections to the four-point amplitude g+g → A+A in massless Quantum Chromodynamics (QCD) up to order {alpha}_s^4 in perturbation theory. We used the effective field theory that describes the coupling of pseudo-scalars to gluons and quarks directly, in the large top quark mass limit. Due to the CP odd nature of the pseudo-scalar Higgs boson, the computation involves careful treatment of chiral quantities in dimensional regularisation. The ultraviolet finite results are shown to be consistent with the universal infrared structure of QCD amplitudes. The infrared finite part of these amplitudes constitutes the important component of any next to next to leading order corrections to observables involving pair of pseudo-scalars at the Large Hadron Collider.

Highlights

JHEP02(2020)121 loops compared to those in the full theory
The computation of virtual corrections is technically challenging [18] as pseudo scalar Higgs boson couples to SM fields through two composite operators that mix under renormalisation
We have presented the two loop virtual amplitudes that are relevant for studying production of pair of pseudo-scalar Higgs bosons in gluon fusion subprocess at the LHC

Summary

Effective Lagrangian

We use the effective lagrangian (2.1) to obtain amplitudes for the production of pair of pseudo-scalar Higgs bosons A of mass mA up to two loop level in perturbative QCD. The Lorentz indices in this determinant, could be considered as d-dimensional and the consequence would be, addition of only the inessential O( ) terms to the renormalisated quantity [46] This prescription though is not without consequence — a finite renormalisation of the axial vector current [47] is required in order to fulfill the chiral Ward identities and the Adler-Bardeen theorem. The matrix element that would contribute to the g + g → A + A amplitude can be obtained via the insertion of two renormalised operators [OG] (eq (2.25)) and [OJ ] (eq (2.24)) for each A, which would involve the following operator insertion between gluon states: g|[OGOG]|g ; g|[OGOJ ]|g and g|[OJ OJ ]|g. For earlier works on this, see [51, 52]

Calculation of the amplitude

Infrared factorization

Discussion and conclusions