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The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit

Thomas Becher·Kirill Melnikov
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Abstract

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (``master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.

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Thomas Becher, Kirill Melnikov. 2002-07-17. The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit. https://doi.org/10.1103/physrevd.66.074508

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