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 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.
Cite
@article{arxiv.0711.3590,
title = {Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors},
author = {G. Heinrich and T. Huber and D. Maitre},
journal= {arXiv preprint arXiv:0711.3590},
year = {2008}
}
Comments
12 pages, 1 figure. References added and updated. Appendix on evaluation of Mellin-Barnes integrals added. Version to appear in PLB