Ginsparg-Wilson Valence Quarks Research Articles

Erratum: KaonB-parameter in mixed action chiral perturbation theory [Phys. Rev. D75, 034502 (2007)

We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B_K by an amount of O(a^2). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B_K for pure G-W lattice fermions. We also present a numerical study of the mixed B_K expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

Erratum: Baryons with Ginsparg-Wilson quarks in a staggered sea [Phys. Rev. D72, 094501 (2005)

We determine the masses and magnetic moments of the octet baryons in chiral perturbation theory formulated for a mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea quarks. Taste-symmetry breaking does not occur at next-to-leading order in the combined lattice-spacing and chiral expansion. Expressions derived for masses and magnetic moments are required for addressing lattice artifacts in mixed-action simulations of these observables.

Two meson systems with Ginsparg-Wilson valence quarks

Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulas. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulas, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretizations, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulas do not depend on the unknown constant CMix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I=1 KK scattering length does not depend on CMix in contrast to the I=3/2 Kpi scattering length. In addition, we show that these observables combined with fK/fpi and the I=2 pipi scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I=1 KK scattering length.

KaonB-parameter in mixed action chiral perturbation theory

We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an {Omicron}(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of {Omicron}(a{sup 2}). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B{sub K} for pure G-W lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

Erratum: Extrapolations of lattice meson form factors [Phys. Rev. D74, 034514 (2006)

We use chiral perturbation theory to study the extrapolations necessary to make physical predictions from lattice QCD data for the electromagnetic form factors of pseudoscalar mesons. We focus on the quark mass, momentum, lattice spacing, and volume dependence and apply our results to simulations employing mixed actions of Ginsparg-Wilson valence quarks and staggered sea quarks. To determine charge radii at quark masses on the lattices currently used, we find that all extrapolations except the one to infinite volume make significant contributions to the systematic error.

Extrapolations of lattice meson form factors

We use chiral perturbation theory to study the extrapolations necessary to make physical predictions from lattice QCD data for the electromagnetic form factors of pseudoscalar mesons. We focus on the quark mass, momentum, lattice spacing, and volume dependence and apply our results to simulations employing mixed actions of Ginsparg-Wilson valence quarks and staggered sea quarks. To determine charge radii at quark masses on the lattices currently used, we find that all extrapolations except the one to infinite volume make significant contributions to the systematic error.

Ginsparg-Wilson pions scattering in a sea of staggered quarks

We calculate isospin 2 pion-pion scattering in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We point out that for some scattering channels, the power-law volume dependence of two-pion states in nonunitary theories such as partially quenched or mixed action QCD is identical to that of QCD. Thus one can extract infinite-volume scattering parameters from mixed action simulations. We then determine the scattering length for both 2 and $2+1$ sea quarks in the isospin limit. The scattering length, when expressed in terms of the pion mass and the decay constant measured on the lattice, has no contributions from mixed valence-sea mesons, thus it does not depend upon the parameter, ${C}_{\mathrm{Mix}}$, that appears in the chiral Lagrangian of the mixed theory. In addition, the contributions which nominally arise from operators appearing in the mixed action $\mathcal{O}({a}^{2}{m}_{q})$ Lagrangian exactly cancel when the scattering length is written in this form. This is in contrast to the scattering length expressed in terms of the bare parameters of the chiral Lagrangian, which explicitly exhibits all the sicknesses and lattice spacing dependence allowed by a partially quenched mixed action theory. These results hold for both 2 and $2+1$ flavors of sea quarks.

Baryons with Ginsparg-Wilson quarks in a staggered sea

We determine the masses and magnetic moments of the octet baryons in chiral perturbation theory formulated for a mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea quarks. Taste-symmetry breaking does not occur at next-to-leading order in the combined lattice spacing and chiral expansion. Expressions derived for masses and magnetic moments are required for addressing lattice artifacts in mixed-action simulations of these observables.

PQChPT with staggered sea and valence Ginsparg–Wilson quarks: vector meson masses

We consider partially quenched, mixed chiral perturbation theory with staggered sea and Ginsparg–Wilson valence quarks in order to extract a chiral-continuum extrapolation expression for the vector meson mass up to order , at one-loop level. Based on general principles, we accomplish the task without explicitly constructing a sophisticated, heavy vector meson chiral Lagrangian.

Chiral perturbation theory for staggered sea quarks and Ginsparg-Wilson valence quarks

We study lattice QCD with staggered sea and Ginsparg-Wilson valence quarks. The Symanzik effective action for this mixed lattice theory, including the lattice spacing contributions of O(a^2), is derived. Using this effective theory we construct the leading order chiral Lagrangian. The masses and decay constants of pseudoscalars containing two Ginsparg-Wilson valence quarks are computed at one loop order.

Hadronic electromagnetic properties at finite lattice spacing

Electromagnetic properties of the octet mesons as well as the octet and decuplet baryons are augmented in quenched and partially quenched chiral perturbation theory to include $O(a)$ corrections due to lattice discretization. We present the results for the $\mathrm{SU}(3)$ flavor group in the isospin limit as well as the results for $\mathrm{SU}(2)$ flavor with nondegenerate quarks. These corrections will be useful for extrapolation of lattice calculations using Wilson valence and sea quarks, as well as calculations using Wilson sea quarks and Ginsparg-Wilson valence quarks.

Chiral perturbation theory for lattice QCD at (a2)

The O(a2) contributions to the chiral effective Lagrangian for lattice QCD with Wilson fermions are constructed. The results are generalized to partially quenched QCD with Wilson fermions as well as to the “mixed” lattice theory with Wilson sea quarks and Ginsparg-Wilson valence quarks.

Nucleon properties at finite lattice spacing in chiral perturbation theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.

Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.