skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

Abstract

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to nonlocal effects in the fourth-root theory when the lattice spacing is nonzero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.

Authors:
 [1]
  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv (Israel)
Publication Date:
OSTI Identifier:
21020083
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevD.75.054503; (c) 2007 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; CHANNELING; COMPUTERIZED SIMULATION; FERMIONS; LATTICE FIELD THEORY; QUANTUM CHROMODYNAMICS; RENORMALIZATION; SYMMETRY

Citation Formats

Shamir, Yigal. Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.054503.
Shamir, Yigal. Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe. United States. doi:10.1103/PHYSREVD.75.054503.
Shamir, Yigal. Thu . "Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe". United States. doi:10.1103/PHYSREVD.75.054503.
@article{osti_21020083,
title = {Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe},
author = {Shamir, Yigal},
abstractNote = {I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to nonlocal effects in the fourth-root theory when the lattice spacing is nonzero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.},
doi = {10.1103/PHYSREVD.75.054503},
journal = {Physical Review. D, Particles Fields},
number = 5,
volume = 75,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2007},
month = {Thu Mar 01 00:00:00 EST 2007}
}
  • Consistency of present day lattice QCD simulations with dynamical ('sea') staggered fermions requires that the determinant of the staggered-fermion Dirac operator, det(D), be equal to det{sup 4}(D{sub rg})det(T) where D{sub rg} is a local one-flavor lattice Dirac operator, and T is a local operator containing only excitations with masses of the order of the cutoff. Using renormalization-group (RG) block transformations I show that, in the limit of infinitely many RG steps, the required decomposition exists for the free staggered operator in the 'flavor representation'. The resulting one-flavor Dirac operator D{sub rg} satisfies the Ginsparg-Wilson relation in the massless case. Imore » discuss the generalization of this result to the interacting theory.« less
  • With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator D such that (detD{sub staggered}){sup 1/4}=detD. Working in the flavor field representation we show that in the free field case there is a simple and natural candidate D satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with a localization range vanishing {approx}{radical}(a/m) for lattice spacing a{yields}0. Prospects for the interacting case are also discussed, although we do not solve this case here.
  • Staggered chiral perturbation theory (S{chi}PT) takes into account the 'fourth-root trick' for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, n{sub F}=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces n{sub F}=4 to n{sub F}=1. One can then treat nondegeneratemore » quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of n{sub F}=3, 2, or 1. An apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular, the restoration of taste symmetry, S{chi}PT then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a mixed theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of S{chi}PT, so that a variety of possible new routes for testing this validity are opened.« less
  • We perform a renormalization-group analysis of the dynamical symmetry breaking in QCD based on the Nambu--Jona-Lasinio approach. We show how the mass scale that the fermions acquire in dynamical symmetry breaking can be calculated in terms of the invariant cutoff. We also determine the high-energy behavior of the quark two-point function.
  • A one-loop renormalization group analysis of the order v{sup 2} relativistic corrections to the static QCD potential is presented. The velocity renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv{sup 2}) terms. The results are compared to previous calculations in the literature. (c) 2000 The American Physical Society.