Automatic Evaluation of Scattering Amplitudes and Application to Heavy-Quark Pair Production in Hadron Collisions

We present the development of a framework for the automatic evaluation of the two-loop virtual corrections of scattering amplitudes in Quantum Chromodynamics (QCD). In this framework, we combine the usage of state-of-the-art software for diagram generation, integral decomposition, and master integral (numerical) evaluation. In particular, we employed FeynArts and FeynCalc for the generation of the integrand corresponding to each diagram, which is decomposed in terms of MasterIntegrals (MIs) by KIRA. The MIs are evaluated by AMFlow, which is based on the numerical solution of systems of differential equations through the auxiliary mass flow method. The whole algorithm has been implemented for parallel calculation, as prototype code to be launched on a supercomputer. As a case study, we consider the scattering amplitude for the production of a pair of heavy quark-antiquark flavors in proton collision, for both the light quark-antiquark annihilation and the gluon fusion channels, which have been a cornerstone of the precision LHC program and are now even relevant for Astroparticle Physics. The purpose of the Very Large Volume Neutrino telescopes (like IceCube and KM3NeT) is to measure neutrinos of astrophysical origin. For this measurement, an accurate evaluation of the flux of prompt neutrinos produced in the atmosphere is fundamental. However, this evaluation is currently limited by theoretical predictions of the charm-anticharm pair production cross-section. In this work, we tried to address the amplitude valuation related to this process.