IAS Amplitudes Group Meeting

Abstract: I will discuss the calculation of a complete set of Feynman integrals required to describe any scattering process at two loops involving four massless and a massive particle, such as the production of a Higgs boson in association with two jets at hadron colliders. Multi-loop multi-scale Feynman integrals are notoriously complicated functions to compute, with very rich branch-cut structures. I will describe an efficient approach to obtain the differential equations satisfied by a particularly convenient basis of this set of integrals. These differential equations expose the singularities of the integrals, giving important insights into their analytic structure and imposing strong constraints on the associated scattering amplitudes. Finally, I will present an algorithmic way to construct a basis of polylogarithmic functions that is suitable for the efficient numerical evaluation of these complicated integrals, as required for phenomenological applications.