We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The master integrals are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one-or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.

No abstract

We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the wellknown sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator ǫ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.