Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors

Understand

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 N_F^2, N_F*N, and N_F/N.

• Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in epsilon, containing Gamma-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 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 zeta-function have to be included.