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Title: '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:
 [1];  [2];  [3];  [4]
  1. Department of Physics, Washington University, Saint Louis, MI 63130 (United States)
  2. Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 (United States)
  3. Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Ramat Aviv, 69978 (Israel)
  4. 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
}
  • A recent criticism of the proof of the failure of the rooting procedure with staggered fermions is shown to be incorrect.
  • 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.
  • We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is constant up to O(a{sup 2}) effects.
  • Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the 'rooting trick' is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalizationmore » of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to 'rooted' staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.« less
  • We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian, including terms of O(a{sup 2}), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a{sup 2}) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a{sup 2}) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. Thesemore » predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc.) or to higher order in a{sup 2}. We show how it is possible that, for physical quark masses of O(a{sup 2}), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action. (c) 1999 The American Physical Society.« less