QCD chiral Lagrangian on the lattice, strong coupling expansion, and Ward identities with Wilson fermions
- 15 July 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 56 (2) , 1101-1120
- https://doi.org/10.1103/physrevd.56.1101
Abstract
We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the general structure of the lattice effective Lagrangian, we perform an analytical calculation at the leading order of the strong-coupling and large- expansion. We find that the explicit chiral symmetry breaking, introduced on the lattice by the Wilson term, is reproduced in the effective theory by a set of additional terms, which do not have direct correspondence in the continuum chiral Lagrangian. We argue that these terms can be conveniently reabsorbed by a suitable renormalization procedure. This is shown explicitly at the leading order of the strong-coupling and large- expansion. In fact, we find that at this order, as is known to be the case in the opposite weak-coupling limit, the vector and axial Ward identities of the continuum theory are reproduced on the lattice provided that the bare quark mass and the lattice operators are properly renormalized.
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This publication has 19 references indexed in Scilit:
- Chiral perturbation theory to one loopPublished by Elsevier ,2004
- Chiral perturbation theoryProgress in Particle and Nuclear Physics, 1995
- Chiral perturbation theoryReports on Progress in Physics, 1995
- Chiral perturbation theory on the lattice: Strong coupling expansionNuclear Physics B, 1994
- Recent developments in chiral perturbation theoryReports on Progress in Physics, 1993
- The role of resonances in chiral perturbation theoryNuclear Physics B, 1989
- Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCDNuclear Physics B, 1981
- Spontaneous chiral symmetry breaking for a U(N) gauge theory on a latticeNuclear Physics B, 1981
- Phenomenological LagrangiansPhysica A: Statistical Mechanics and its Applications, 1979
- Dynamical Approach to Current AlgebraPhysical Review Letters, 1967