Lattice regularization for chiral perturbation theory
Abstract
The SU(3) chiral lagrangian for the lightest octets of mesons and baryons is constructed on a spacetime lattice. The lattice spacing acts as an ultraviolet momentum cutoff which appears directly in the Lagrangian so chiral symmetry remains explicit. As the lattice spacing vanishes, Feynman loop diagrams typically become divergent due to inverse powers of the lattice spacing, and these divergences get absorbed into counterterms such that the standard results of dimensional regularization are obtained. At nonzero lattice spacing, the Lagrangian represents an effective theory that is valid for momenta below both the chiral scale and the lattice spacing scale. A third order calculation of the octet baryon masses and the pion-nucleon sigma term is presented, where the lattice spacing is chosen to correspond to the scale of baryon substructure. Nonleading chiral corrections are found to be substantially smaller in this effective theory than in the dimensional regularization (zero lattice spacing) limit.Keywords
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