't Hooft vertices, partial quenching, and rooted staggered QCD
Abstract
We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We also show that, due to the singular behavior of unphysical correlation functions as the massless limit is approached, order parameters for nonanomalous symmetries can be nonvanishing in finite volume if these symmetries act outside of the physical subspace. Using these results, we demonstrate that arguments recently given by Creutz  claiming to disprove the validity of rooted staggered QCD  are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.
 Authors:
 Department of Physics, Washington University, Saint Louis, MI 63130 (United States)
 Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 (United States)
 Raymond and Beverly Sackler School of Physics and Astronomy, TelAviv University, Ramat Aviv, 69978 (Israel)
 Physics Department, University of Washington, Seattle, WA 98195 (United States)
 Publication Date:
 OSTI Identifier:
 21205095
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 77; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.77.114504; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRELATION FUNCTIONS; ORDER PARAMETERS; QUANTUM CHROMODYNAMICS; QUARKS; QUENCHING; SYMMETRY; VALENCE
Citation Formats
Bernard, Claude, Golterman, Maarten, Shamir, Yigal, and Sharpe, Stephen R. 't Hooft vertices, partial quenching, and rooted staggered QCD. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.77.114504.
Bernard, Claude, Golterman, Maarten, Shamir, Yigal, & Sharpe, Stephen R. 't Hooft vertices, partial quenching, and rooted staggered QCD. United States. doi:10.1103/PHYSREVD.77.114504.
Bernard, Claude, Golterman, Maarten, Shamir, Yigal, and Sharpe, Stephen R. 2008.
"'t Hooft vertices, partial quenching, and rooted staggered QCD". United States.
doi:10.1103/PHYSREVD.77.114504.
@article{osti_21205095,
title = {'t Hooft vertices, partial quenching, and rooted staggered QCD},
author = {Bernard, Claude and Golterman, Maarten and Shamir, Yigal and Sharpe, Stephen R.},
abstractNote = {We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We also show that, due to the singular behavior of unphysical correlation functions as the massless limit is approached, order parameters for nonanomalous symmetries can be nonvanishing in finite volume if these symmetries act outside of the physical subspace. Using these results, we demonstrate that arguments recently given by Creutz  claiming to disprove the validity of rooted staggered QCD  are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.},
doi = {10.1103/PHYSREVD.77.114504},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 77,
place = {United States},
year = 2008,
month = 6
}

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We reply to Creutz's comments on our paper ''t Hooft vertices, partial quenching, and rooted staggered QCD'. We show that his criticisms are incorrect and result from a misunderstanding both of our work, and of the related work of Adams. 
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