A quasi-finite basis for multi-loop Feynman integrals

Abstract

We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical limitations of the original procedure by employing integration by parts reduction.

Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence

“…Therefore we have calculated all the integrals numerically using the program SecDec-3.0 [20]. We partially used a finite basis [29] for the planar master integrals, as far as it turned out to be beneficial for the numerical integration.…”

Renormalization group functions of $\phi^4$ theory in the MS-scheme to six loops

“…These problems can in principle be avoided with the help of IBP relations, because it is always possible to write a Feynman integral in terms of master integrals without subdivergences [68]. Unfortunately, such IBP reductions are too complicated in our case.…”

On the calculation of soft phase space integral

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