Open AccessMaster Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
Author(s) -
G Heinrich,
T Huber,
D Maitre
Publication year - 2007
Language(s) - English
Resource type - Reports
DOI - 10.2172/920275
Subject(s) - laurent series , dimensional regularization , massless particle , hypergeometric function , mathematical physics , riemann zeta function , loop (graph theory) , physics , regularization (linguistics) , mathematics , pure mathematics , hypergeometric distribution , combinatorics , renormalization , artificial intelligence , computer science
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