Abstract
We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, $q \bar{q} \to V V$, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion.
Highlights
Class of two-loop Feynman integrals: two-loop four-point functions with internal massless propagators and two massive external legs
Working in dimensional regularization with d = 4 − 2 space-time dimensions, we identify the relevant master integrals (MI) and derive differential equations for them employing integrationby-parts (IBP) [22, 23] and Lorentz-invariance (LI) [24] reductions through the Laporta algorithm [25] implemented in the Reduze code [26, 27]
The master integrals are determined by solving these differential equations [24, 28,29,30] and matching generic solutions to appropriate boundary values obtained in special kinematical limits
Summary
We choose the propagators of the three topologies as listed in table 1 As it is well known, using IBPs, LIs and symmetry relations all Feynman integrals described by these three integral families can be reduced to a small subset, the master integrals. We performed this reduction for all integrals relevant for our process using the automated codes Reduze 1 and Reduze 2 [26, 27, 43, 44]. In the present work we conclude the computation of all non-planar MIs in Topo C
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
