TY - JOUR

T1 - On the maximal cut of Feynman integrals and the solution of their differential equations

AU - Primo, Amedeo

AU - Tancredi, Lorenzo

N1 - Publisher Copyright:
© 2017 The Authors

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ=(4−d)/2, where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.

AB - The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ=(4−d)/2, where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.

UR - http://www.scopus.com/inward/record.url?scp=85009227362&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2016.12.021

DO - 10.1016/j.nuclphysb.2016.12.021

M3 - Article

AN - SCOPUS:85009227362

SN - 0550-3213

VL - 916

SP - 94

EP - 116

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

ER -