Calculation of Multi-scale, Multi-loop Integrals Using {\sf SecDec 3}

Abstract

In these proceedings the publicly available program SecDec is briefly described. Its main virtues and new features are summarized, including suggestions for an optimal usage of the program.

{\sf MBsums} --- a {\sf Mathematica} Package for the Representation of Mellin--Barnes Integrals by Multiple Sums

“…where f are conditions on the index that numerates terms (residues) in f (1) i . We obtain a list of K 1 elements after integrating over z2.…”

“…We obtain a list of K 1 elements after integrating over z2. Let us now assume that the user has chosen as second integration variable z5->R. Then we repeat the whole procedure on each f (1) i taking into account conditions c (1) i . So we produce analogous to (12) a list of cases…”

“…We also provide function SimplifyMBsums[sums] that takes each MBsum[] in the list sums in the form (9) where n1, n2 are summation indices in MBsum[f,c_i,l], then we make the substitutions n1 -> C [1] and n2 -> C[1] + C [2] in f and update c_i and l in MBsum[f,c_i,l]; C [1] and C [2] are new summation indices. We assume that C[] are integers.…”

“…One relies on sector decomposition. For an introduction given at this conference and for further references see [1]. We will report on the other approach, based on Mellin-Barnes representations [2,3,4,5,6,7,8,9,10,11,12].…”