TY - JOUR

T1 - Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph

AU - Primo, Amedeo

AU - Tancredi, Lorenzo

N1 - Publisher Copyright:
© 2017 The Author(s)

PY - 2017/8

Y1 - 2017/8

N2 - We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear differential equations. The solution of the system requires finding a 3×3 matrix of homogeneous solutions. We show how the maximal cut can be used to determine all entries of this matrix in terms of products of elliptic integrals of first and second kind of suitable arguments. All independent solutions are found by performing the integration which defines the maximal cut on different contours. Once the homogeneous solution is known, the inhomogeneous solution can be obtained by use of Euler's variation of constants.

AB - We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear differential equations. The solution of the system requires finding a 3×3 matrix of homogeneous solutions. We show how the maximal cut can be used to determine all entries of this matrix in terms of products of elliptic integrals of first and second kind of suitable arguments. All independent solutions are found by performing the integration which defines the maximal cut on different contours. Once the homogeneous solution is known, the inhomogeneous solution can be obtained by use of Euler's variation of constants.

UR - http://www.scopus.com/inward/record.url?scp=85020185944&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2017.05.018

DO - 10.1016/j.nuclphysb.2017.05.018

M3 - Article

AN - SCOPUS:85020185944

SN - 0550-3213

VL - 921

SP - 316

EP - 356

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

ER -