Structure of logarithmically divergent one-loop lattice Feynman integrals

Details Structure of logarithmically divergent one-loop lattice Feynman integrals Structure of logarithmically divergent one-loop lattice Feynman integrals

2007-09-06

arxiv.org/abs/0709.0781v3

Phys.Rev.D77:045010,2008

Physics

High Energy Physics

High Energy Physics - Lattice

26 pages (after reformatting using revtex); typos corrected; to appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.77.045010

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 cut-off or dimensional regularization. The non-universal 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.

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