Status of two-loop automation in OpenLoops
he development of a fully automated tool for the numerical calculation
of NNLO corrections to scattering amplitudes is a highly desirable goal for the LHC era.
In our approach, D-dimensional two-loop amplitudes are decomposed into Feynman integrals with four-dimensional numerators as well as (D-4)-dimensional remainders, which can contribute to the finite result through the interaction with the poles of Feynman integrals.
The integrals with four-dimensional numerators are then expressed as tensor integrals in the loop momenta contracted with tensor coefficients.
Hence, the calculation can be structured into the computation of the tensor coefficients, the treatment of (D-4)-dimensional numerator parts
the reduction of the tensor integrals and the evaluation of the resulting master integrals.
In this talk, we present the status of OpenLoops with respect to all these building blocks. We present an algorithm to numerically construct the tensor coefficients for two-loop amplitudes in a highly efficient way, exploiting factorisation properties of the Feynman integrands. This algorithm is completely generic and has been fully implemented and tested for QED and QCD corrections to the Standard Model.
We also present our method to reconstruct the contributions stemming from the interplay of (D-4)-dimensional numerator parts through universal rational counterterms, as well as the computation of the full set of rational terms of UV origin for QCD and QED corrections to the SM.
These rational counterterms have been implemented in OpenLoops and are currently being tested with an in-house library for the reduction of simple tensor integrals.
Finally, we give an outlook of the next steps towards the automation of two-loop calculations in OpenLoops.
Room Caldirola (Università degli Studi di Milano)