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

Heinrich, G. ; Huber, T. ; Maitre, D.

Stanford Linear Accelerator Center

关键词: Phenomenology-Hep,Hepph, Hepth;    Form Factors;    Gluons;    Hypergeometric Functions;    72 Physics Of Elementary Particles And Fields;   

DOI  :  10.2172/920275
RP-ID  :  SLAC-PUB-13015
RP-ID  :  AC02-76SF00515
RP-ID  :  920275

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来源: UNT Digital Library

【 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.