Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-11-22
Phys.Lett.B662:344-352,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
12 pages, 1 figure. References added and updated. Appendix on evaluation of Mellin-Barnes integrals added. Version to appear i
Scientific paper
10.1016/j.physletb.2008.03.028
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.
Heinrich Georg
Huber Tobias
Maitre D.
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