General properties of logarithmically divergent one-loop lattice Feynman integrals

Details General properties of logarithmically divergent one-loop lattice Feynman integrals General properties of logarithmically divergent one-loop lattice Feynman integrals

2007-10-10

arxiv.org/abs/0710.1930v1

PoSLAT2007:266,2007

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg

Scientific paper

We prove that logarithmically divergent one-loop lattice Feynman integrals have the general form I(p,a) = f(p)log(aM)+g(p,M) up to terms which vanish for lattice spacing a -> 0. Here p denotes collectively the external momenta and M is an arbitrary mass scale. The f(p) is shown to be universal and to coincide with the analogous quantity in the corresponding continuum integral (regularized, e.g., by momentum cut-off). This is essential for universality of the lattice QCD beta-function and anomalous dimensions of renormalized lattice operators at one loop. The result and argument presented here are simplified versions of ones given in arXiv:0709.0781. A noteworthy feature of the argument here is that it does not involve Taylor expansion in external momenta, hence infra-red divergences associated with that expansion do not arise.

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