Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion

TL;DR

The paper addresses the need for precise two-loop amplitudes in gluon-fusion production of electroweak vector-boson pairs, allowing off-shell and unequal-mass vector bosons to improve NNLO QCD predictions for four-lepton final states. It develops a projection-operator framework to extract 20 tensor form factors and reduces loop integrals to master integrals via IBP using FIRE, with master integrals built on prior work and evaluated numerically. The authors validate the results against IR predictions and independent calculations, and demonstrate numerical stability across kinematic regimes. The analytic results are implemented in Fortran and set the stage for NLO QCD corrections to gg -> VV, with potential applications to Higgs background modeling and off-shell width analyses; future work includes including massive-quark contributions.

Abstract

We compute the part of the two-loop virtual amplitude for the process $gg \to V_1 V_2 \to (l_1 \bar l'_{1}) (l_2 \bar l'_2)$, where $V_{1,2}$ are arbitrary electroweak gauge bosons, that receives contributions from loops of massless quarks. Invariant masses of electroweak bosons are allowed to be different from each other. Our result provides an important ingredient for improving the description of gluon fusion contribution to the production of four-lepton final states at the LHC.

Figures (2)

• Figure 1: Representative two-loop diagrams that describe production of vector boson pairs in gluon fusion.
• Figure 2: The ratio of finite parts of two- and one-loop helicity amplitudes $R_2 = | A_2(LL) + A_2(LR)|/(|A_1(LL)| + |A_1(LR)|)$ as a function of the vector-boson scattering angle.