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Title: Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume

Abstract

We study the quark mass function on hypercubic lattices in a large range of physical volumes and cutoffs. To avoid the very large Wilson term artefact, we exploit the relation between the quark mass function and the pseudoscalar vertex in the continuum. We extrapolate to the chiral limit. In function of the physical volume, we observe a striking discontinuity in the properties of chiral extrapolation around a physical volume L{sub c{approx_equal}}6 GeV{sup -1}=1.2 fm. It is present in the quark mass function, which collapses to zero, as well as in the pion mass and the quark condensate as directly calculated from the pseudoscalar correlator. It is strongly reminiscent of the phenomenon of chiral symmetry restoration observed by Neuberger and Narayanan at N{sub C}={infinity} around the same physical length. In the case of spontaneous symmetry breaking, we confirm that the operator product expansion of the quark mass function, involving the quark condensate, is not operative at the available momenta, even taking into account the unusually large high order corrections to the Wilson coefficient calculated by Chetyrkin and Maier; the gap remains large, around a factor 2, even at the largest momenta available to us (p{approx_equal}6 GeV).

Authors:
; ; ; ;  [1];  [2]
  1. Laboratoire de Physique Theorique, Universite de Paris XI, Batiment 210, 91405 Orsay Cedex (France)
  2. Departamento Fisica Aplicada, Fac. Ciencias Experimentales, Universidad de Huelva, 21071 Huelva (Spain)
Publication Date:
OSTI Identifier:
21409963
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.81.094504; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; CORRECTIONS; EXTRAPOLATION; GEV RANGE 01-10; MASS; OPERATOR PRODUCT EXPANSION; PIONS; QUARK CONDENSATION; QUARKS; SYMMETRY BREAKING; BOSONS; ELEMENTARY PARTICLES; ENERGY RANGE; FERMIONS; GEV RANGE; HADRONS; MATHEMATICAL SOLUTIONS; MESONS; NUMERICAL SOLUTION; PARTICLE PROPERTIES; PSEUDOSCALAR MESONS; SERIES EXPANSION; SYMMETRY

Citation Formats

Boucaud, Ph, Leroy, J -P, Le Yaouanc, A, Micheli, J, Pene, O, and Rodriguez-Quintero, J. Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.094504.
Boucaud, Ph, Leroy, J -P, Le Yaouanc, A, Micheli, J, Pene, O, & Rodriguez-Quintero, J. Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume. United States. doi:10.1103/PHYSREVD.81.094504.
Boucaud, Ph, Leroy, J -P, Le Yaouanc, A, Micheli, J, Pene, O, and Rodriguez-Quintero, J. Sat . "Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume". United States. doi:10.1103/PHYSREVD.81.094504.
@article{osti_21409963,
title = {Quark pseudoscalar vertex and quark mass function with clover fermions: Spontaneous symmetry breaking, operator product expansion, symmetry restoration at small volume},
author = {Boucaud, Ph and Leroy, J -P and Le Yaouanc, A and Micheli, J and Pene, O and Rodriguez-Quintero, J},
abstractNote = {We study the quark mass function on hypercubic lattices in a large range of physical volumes and cutoffs. To avoid the very large Wilson term artefact, we exploit the relation between the quark mass function and the pseudoscalar vertex in the continuum. We extrapolate to the chiral limit. In function of the physical volume, we observe a striking discontinuity in the properties of chiral extrapolation around a physical volume L{sub c{approx_equal}}6 GeV{sup -1}=1.2 fm. It is present in the quark mass function, which collapses to zero, as well as in the pion mass and the quark condensate as directly calculated from the pseudoscalar correlator. It is strongly reminiscent of the phenomenon of chiral symmetry restoration observed by Neuberger and Narayanan at N{sub C}={infinity} around the same physical length. In the case of spontaneous symmetry breaking, we confirm that the operator product expansion of the quark mass function, involving the quark condensate, is not operative at the available momenta, even taking into account the unusually large high order corrections to the Wilson coefficient calculated by Chetyrkin and Maier; the gap remains large, around a factor 2, even at the largest momenta available to us (p{approx_equal}6 GeV).},
doi = {10.1103/PHYSREVD.81.094504},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 9,
volume = 81,
place = {United States},
year = {2010},
month = {5}
}