Chiral perturbation theory for the quenched approximation of QCD
Abstract
We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a Lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in {ital f}{sub {ital K}}/{ital f}{sub {pi}}, {ital m}{sub {pi}}, {ital m}{sub {ital K}}, and the ratio of {l angle}{ital {bar s}s}{r angle} to {l angle}{ital {bar u}u}{r angle}. The leading finitevolume corrections to these quantities are also computed. Problems for future study are described.
 Authors:
 (Department of Physics, Washington University, St. Louis, Missouri 63130 (United States))
 Publication Date:
 OSTI Identifier:
 7183948
 DOE Contract Number:
 AC0278ER04915
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review, D (Particles Fields); (United States); Journal Volume: 46:2
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; PERTURBATION THEORY; ALGORITHMS; CHIRALITY; FERMIONS; FEYNMAN DIAGRAM; GOLDSTONE BOSONS; LAGRANGIAN FUNCTION; MATRIX ELEMENTS; MESONMESON INTERACTIONS; PROPAGATOR; PSEUDOSCALAR MESONS; SCATTERING; BOSONS; DIAGRAMS; ELEMENTARY PARTICLES; FIELD THEORIES; FUNCTIONS; HADRONHADRON INTERACTIONS; HADRONS; INTERACTIONS; MATHEMATICAL LOGIC; MESONS; PARTICLE INTERACTIONS; PARTICLE PROPERTIES; POSTULATED PARTICLES; QUANTUM FIELD THEORY; 662230*  Quantum Chromodynamics (1992); 662340  Hadron Interactions (1992)
Citation Formats
Bernard, C.W., and Golterman, M.F.L. Chiral perturbation theory for the quenched approximation of QCD. United States: N. p., 1992.
Web. doi:10.1103/PhysRevD.46.853.
Bernard, C.W., & Golterman, M.F.L. Chiral perturbation theory for the quenched approximation of QCD. United States. doi:10.1103/PhysRevD.46.853.
Bernard, C.W., and Golterman, M.F.L. Wed .
"Chiral perturbation theory for the quenched approximation of QCD". United States.
doi:10.1103/PhysRevD.46.853.
@article{osti_7183948,
title = {Chiral perturbation theory for the quenched approximation of QCD},
author = {Bernard, C.W. and Golterman, M.F.L.},
abstractNote = {We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a Lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in {ital f}{sub {ital K}}/{ital f}{sub {pi}}, {ital m}{sub {pi}}, {ital m}{sub {ital K}}, and the ratio of {l angle}{ital {bar s}s}{r angle} to {l angle}{ital {bar u}u}{r angle}. The leading finitevolume corrections to these quantities are also computed. Problems for future study are described.},
doi = {10.1103/PhysRevD.46.853},
journal = {Physical Review, D (Particles Fields); (United States)},
number = ,
volume = 46:2,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 1992},
month = {Wed Jul 15 00:00:00 EDT 1992}
}

Low energy constants of $SU\left(2\right)$ partially quenched chiral perturbation theory from ${N}_{f}=2+1$ domain wall QCD
Here, we have performed fits of the pseudoscalar masses and decay constants, from a variety of the RBCUKQCD Collaboration’s domain wall fermion ensembles, to SU(2) partially quenched chiral perturbation theory at nexttoleading order (NLO) and nexttonexttoleading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched lowenergy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of lowenergy constants to make predictions for mass splittings due to QCD isospinbreaking effects and the Swave ππ scattering lengths.more »Cited by 3 
Doubly heavy baryons and quarkdiquark symmetry in quenched and partially quenched chiral perturbation theory
We extend the chiral Lagrangian with heavy quarkdiquark symmetry to quenched and partially quenched theories. These theories are used to derive formulae for the chiral extrapolation of masses and hyperfine splittings of doubly heavy baryons in lattice QCD simulations. A quarkdiquark symmetry prediction for the hyperfine splittings of heavy mesons and doubly heavy baryons is rather insensitive to chiral corrections in both quenched and partially quenched QCD. Extrapolation formulae for the doubly heavy baryon electromagnetic transition moments are also determined for the partially quenched theory. 
Doubly heavy baryons and quarkdiquark symmetry in quenched and partially quenched chiral perturbation theory
We extend the chiral Lagrangian with heavy quarkdiquark symmetry to quenched and partially quenched theories. These theories are used to derive formulas for the chiral extrapolation of masses and hyperfine splittings of double heavy baryons in lattice QCD simulations. A quarkdiquark symmetry prediction for the hyperfine splittings of heavy mesons and doubly heavy baryons is rather insensitive to chiral corrections in both quenched and partially quenched QCD. Extrapolation formulas for the doubly heavy baryon electromagnetic transition moments are also determined for the partially quenched theory. 
Continuum Limit of Lattice QCD with Staggered Quarks in the Quenched Approximation: A Critical Role for the Chiral Extrapolation
We calculate the light quark spectrum of lattice QCD in the quenched approximation using staggered quarks. We take the light quark mass, infinite volume, continuum limit. With nonlinear chiral extrapolations, we find that the nucleon to {rho} mass ratio is m{sub N}thinsp/m{sub {rho}}=1.254{plus_minus}0.018{plus_minus} 0.028 , where the errors are statistical and systematic (within the quenched approximation), respectively. Since the experimental value is 1.22, our results indicate that the error due to quenching is {approx_lt}5{percent} . {copyright} {ital 1998} {ital The American Physical Society}