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 N{sub F}{sup 2}, N{sub F} {center_dot} N, and N{sub F}/N. Working in dimensional regularization, we express one of the diagrams in a closed form which is exact to all orders in {epsilon}, containing {Lambda}-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.

[发布日期] 2007-11-28

[学科分类] 物理（综合）

[关键词] FORM FACTORS;GLUONS;HYPERGEOMETRIC FUNCTIONS;QUARKS Phenomenology-HEP;HEPPH;HEPTH