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Nature of logarithmic divergence in one loop lattice Feynman integrals
Presenter: Jongjeong Kim — Seoul National University
David H. Adams, Jongjeong Kim, Weonjong Lee
We introduce a new approach to evaluating logarithmically divergent one-loop lattice Feynman integrals and use it to rigorously prove, under mild general conditions, that these always have the following expected and crucial structure: I(p,m,a)=f(p,m)log(aµ)+g(p,m,µ) up to terms which vanish for lattice spacing a→0. Here p and m denote collectively the external momenta and masses, and µ is an arbitrarily chosen mass scale. The factor f(p,m) is shown to coincide with the analogous factor in the corresponding continuum integral when the latter is regularized either by momentum cut-off or dimensional regularization. This is essential in order for the one-loop lattice QCD beta-function to coincide with the continuum one.
© 2006, University of Regensburg, Dept. of Physicscontact: lat07 at physik.uni-regensburg.de