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The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear combination of so-called master integrals. To do this, public (AIR, FIRE, REDUZE, LiteRed, KIRA) and private codes based on solving integration by parts relations are used. However, the choice of the master integrals provided by these codes is not always optimal. We present an algorithm to improve a given basis of the master integrals, as well as its computer implementation; see also a competitive variant [1].
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbi
We present the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric integrations for a basis of finite integrals, we give analytic resul
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integral
We present $text{Fuchsia}$ $-$ an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $partial_x,mathbf{f}(x,epsilon) = mathbb{A}(x,epsilon),mathbf{f}(x,epsilon)$ finds a basis t
We present analytical results for master integrals emerging in the computation of differential rates for inclusive weak decays of heavy flavors at next-to-leading order (NLO) in QCD. As an immediate physical application, these master integrals allow