QCD chiral Lagrangian on the lattice, strong coupling expansion, and Ward identities with Wilson fermions

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.56.1101· OSTI ID:527088

Levi, A R; Lubicz, V; Rebbi, C ^[1]

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1. Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States)

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-N 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-N 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. {copyright} {ital 1997} {ital The American Physical Society}

• Research Organization: Boston University
• DOE Contract Number: FG02-91ER40676
• OSTI ID: 527088
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHIRAL SYMMETRY
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
LATTICE FIELD THEORY
QUANTUM CHROMODYNAMICS
RENORMALIZATION
STRONG-COUPLING MODEL
SYMMETRY BREAKING
WARD IDENTITY