A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization
Abstract
Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the UV-divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.
Cite
@article{arxiv.hep-ph/0609282,
title = {A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization},
author = {Georg Sulyok},
journal= {arXiv preprint arXiv:hep-ph/0609282},
year = {2017}
}
Comments
19 pages (single column), the result of previous versions is further evaluated leading to a closed analytic expression for the UV-divergent part of an arbitrary one-loop tensor coefficient, title is modified accordingly, a sign error in the appendix (C_{00000000}) has been corrected, a mathematica notebook containing an implementation of the newly derived formula is attached