Master integrals for fermionic contributions to massless three-loop form factors

Abstract

In this Letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to View the MathML source, NFdot operatorN, and NF/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in epsilon (Porson), containing Γ-functions and hypergeometric functions of unit argument. In all other cases we derive multiple Mellin–Barnes representations from which the coefficients of the Laurent expansion in epsilon (Porson) are extracted in an analytical form. To obtain the finite part of the three-loop quark and gluon form factors, all coefficients through transcendentality six in the Riemann ζ-function have to be included.