Structure of logarithmically divergent one-loop lattice Feynman integrals
Adams, David H.
Date of Issue2008
School of Physical and Mathematical Sciences
For logarithmically divergent one-loop lattice Feynman integrals I(p,a) , subject to mild general conditions, we prove the following expected and crucial structural result: I(p,a)=f(p)log(aM)+g(p)+h(p,M) up to terms which vanish for lattice spacing a→0 . Here p denotes collectively the external momenta and M is a mass scale which may be chosen arbitrarily. The f(p) and h(p,M) are shown to be universal and coincide with analogous quantities in the corresponding continuum integral when the latter is regularized either by momentum cutoff or dimensional regularization. The nonuniversal term g(p) is shown to be a homogeneous polynomial in p of the same degree as f(p) . This structure is essential for consistency between renormalized lattice and continuum formulations of QCD at one loop.
Physical and Mathematical Sciences
Physical review D
© 2008 The American Physical Society. This paper was published in Physical Review D and is made available as an electronic reprint (preprint) with permission of The American Physical Society. The paper can be found at the following official DOI: http://dx.doi.org/10.1103/PhysRevD.77.045010 . One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.