Master Integrals for Fermionic Contributions to Massless Three Loop Form Factors

摘要

In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those diagrams which are relevant for the fermionic contributions proportional to N2F, NF DTN, and NF /N. Working in dimensional regularisation, we express one of the diagrams in a closed form which is exact to all orders in, containing A-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 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 ae-function have to be included.