Improvement of the staggered fermion operators

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 non-local effects in the fourth-root theory when the lattice spacing is non-zero, 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. * Electronic address: shamir@post.tau.ac.il

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“…While Ref. [32] discusses the taste-basis Dirac operator in the case α 0 → ∞, the result (H7) generalizes to α 0 < ∞.…”

Section: Aspects Of Scaling In the Interacting Theorymentioning

confidence: 96%

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

Shamir

2007

Phys. Rev. D

110

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“…The second step uses only transformations that map the 2 4 hypercube onto itself, which are related to spin and taste transformations in the continuum [23]. As is well known, there are no dimension 5 operators [24,25]. At dimension 6 one finds purely gluonic operators, fermion bilinears and four-fermion operators.…”

Section: Continuum Effective Lagrangian For Staggered Quarksmentioning

confidence: 99%

Staggered chiral perturbation theory at next-to-leading order

2005

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We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to O(a 2 p 2 ), O(a 4 ) and O(a 2 m), the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of SO(4) taste-breaking quantities, which involve only a small subset of these NLO operators. We predict relationships between SO(4) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not SO(4) breaking. All these results hold also for theories in which the fourth-root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.

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“…This is well known for the gauge theory, and has been shown in Refs. [12,13] for staggered fermions.…”

Section: The Continuum Effective Actionmentioning

confidence: 99%

“…A for notation), but this sign cancels in the four-fermion operators since all bilinears appear in flavor diagonal pairs. The generators in (13) anticommute and square to +1, and so generate the Clifford group Γ 4 . They lie within the flavor group SU(4), but not within the SO(4) subgroup (which is composed of matrices containing an even number of ξ µ ).…”

Section: Symmetries Of the Effective Actionmentioning

confidence: 99%

Partial flavor symmetry restoration for chiral staggered fermions

1999

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We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a 2 ), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a 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 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. These 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), nor to higher order in a 2 . We show how it is possible that, for physical quark masses of O(a 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.

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Improvement of the staggered fermion operators

Cited by 25 publications

References 12 publications

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

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

Staggered chiral perturbation theory at next-to-leading order

Partial flavor symmetry restoration for chiral staggered fermions

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