Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

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.Comment: 26 pages, 2 figures (using psfig). Version to appear in PRD (clarifications added to introduction and section 6; typos corrected; references updated

One-loop matching coefficients for improved staggered bilinears

We calculate one-loop matching factors for bilinear operators composed of improved staggered fermions. We compare the results for different improvement schemes used in the recent literature, all of which involve the use of smeared links. These schemes aim to reduce, though not completely eliminate, O(a^2) discretization errors. We find that all these improvement schemes substantially reduce the size of matching factors compared to unimproved staggered fermions. The resulting corrections are comparable to, or smaller than, those found with Wilson and domain-wall fermions. In the best case (``Fat-7'' and mean-field improved HYP links) the corrections are 10 % or smaller at 1/a = 2 GeV.Comment: 13 pages, 1 figure (misleading sentence in sec. II removed; version to appear in Physical Review D

Enhanced structure-function relationship in glaucoma with an anatomically and geometrically accurate neuroretinal rim measurement

yesPurpose: To evaluate the structure–function relationship between disc margin–based rim area (DM-RA) obtained with confocal scanning laser tomography (CSLT), Bruch's membrane opening–based horizontal rim width (BMO-HRW), minimum rim width (BMO-MRW), peripapillary retinal nerve fiber layer thickness (RNFLT) obtained with spectral-domain optical coherence tomography (SD-OCT), and visual field sensitivity. Methods: We examined 151 glaucoma patients with CSLT, SD-OCT, and standard automated perimetry on the same day. Optic nerve head (ONH) and RNFL with SD-OCT were acquired relative to a fixed coordinate system (acquired image frame [AIF]) and to the eye-specific fovea-BMO center (FoBMO) axis. Visual field locations were mapped to ONH and RNFL sectors with fixed Garway-Heath (VFGH) and patient-specific (VFPS) maps customized for various biometric parameters. Results: Globally and sectorally, the structure–function relationships between DM-RA and VFGH, BMO-HRWAIF and VFGH, and BMO-HRWFoBMO and VFPS were equally weak. The R2 for the relationship between DM-RA and VFGH ranged from 0.1% (inferonasal) to 11% (superotemporal) whereas that between BMO-HRWAIF and VFGH ranged from 0.1% (nasal) to 10% (superotemporal). Relatively stronger global and sectoral structure–function relationships with BMO-MRWAIF and with BMO-MRWFoBMO were obtained. The R2 between BMO-MRWAIF and VFGH ranged from 5% (nasal) to 30% (superotemporal), whereas that between BMO-MRWFoBMO and VFPS ranged from 5% (nasal) to 25% (inferotemporal). The structure–function relationship with RNFLT was not significantly different from that with BMO-MRW, regardless of image acquisition method. Conclusions: The structure–function relationship was enhanced with BMO-MRW compared with the other neuroretinal rim measurements, due mainly to its geometrically accurate properties

Chiral Lagrangian Parameters for Scalar and Pseudoscalar Mesons

The results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched lattice QCD are presented. For two values of lattice spacing, $\beta=5.7$ ($a \approx .18$ fm) and 5.9 ($a \approx .12$ fm), we probe the light quark mass region using clover improved Wilson fermions with the MQA pole-shifting ansatz to treat the exceptional configuration problem. The quenched chiral loop parameters $m_0$ and $\alpha_{\Phi}$ are determined from a study of the pseudoscalar hairpin correlator. From a global fit to the meson correlators, estimates are obtained for the relevant chiral Lagrangian parameters, including the Leutwyler parameters $L_5$ and $L_8$. Using the parameters obtained from the singlet and nonsinglet pseudoscalar correlators, the quenched chiral loop effect in the nonsinglet scalar meson correlator is studied. By removing this QCL effect from the lattice correlator, we obtain the mass and decay constant of the ground state scalar, isovector meson $a_0$.Comment: 36 pages, 12 figures, LaTe

The Leptonic Decay Constants of Qˉq\bar{Q}q Mesons and the Lattice Resolution

We present a high statistics study of the leptonic decay constant $f_P$ of heavy pseudoscalar mesons using propagating heavy Wilson quarks within the quenched approximation, on lattices covering sizes from about 0.7~fm to 2~fm. Varying $\beta$ between 5.74 and 6.26 we observe a sizeable $a$ dependence of $f_P$ when one uses the quark field normalization that was suggested by Kronfeld and Mackenzie, compared with the weaker dependence observed for the standard relativistic norm. The two schemes come into agreement when one extrapolates to $a \rightarrow 0$. The extrapolations needed to reach the continuum quantity $f_B$ introduce large errors and lead to the value $f_B=0.18(5)$~GeV in the quenched approximation. This suggests that much more effort will be needed to obtain an accurate lattice prediction for $f_B$.Comment: 11 pages Latex + 5 tables + 8 postscript figures, unix shell archive, DESY preprint DESY 93-17

New results on cut-off effects in spectroscopy with the fixed point action

Our study on the cut-off effects in quenched light hadron spectroscopy and pion scattering length with the fixed point action is extended by results obtained at a lattice spacing a=0.102 fm in a box of size L=1.8 fm. The cut-off effects are small, but clearly seen as the resolution is increased from a=0.153 fm to a=0.102 fm. In the quark mass region where the errors are small and under control, our results on the APE plot lie close to the extrapolated numbers of the CP-PACS Collaboration.Comment: 15 pages, 11 figures, reference correcte

The nucleon's strange electromagnetic and scalar matrix elements

Quenched lattice QCD simulations and quenched chiral perturbation theory are used together for this study of strangeness in the nucleon. Dependences of the matrix elements on strange quark mass, valence quark mass and momentum transfer are discussed in both the lattice and chiral frameworks. The combined results of this study are in good agreement with existing experimental data and predictions are made for upcoming experiments. Possible future refinements of the theoretical method are suggested.Comment: 24 pages, 9 figure

Searching for chiral logs in the static-light decay constant

Using the clover fermion action in unquenched QCD with pion masses as low as 420 MeV, we look for evidence for chiral logs in the static-light decay constant. There is some evidence for a chiral log term, if the original static theory of Eichten and Hill is used. However, the more precise data from the static action of the ALPHA collaboration do not show any evidence for non-linear dependence of the static-light decay constant on the light quark mass. We make some comments on the connection between chiral perturbation theory for decay constants of the pion and static-light meson

Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks

We present results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios in the presence of two flavors of light sea quarks ($N_f=2$). We use Wilson light valence quarks and Wilson and static heavy valence quarks; the sea quarks are simulated with staggered fermions. Additional quenched simulations with nonperturbatively improved clover fermions allow us to improve our control of the continuum extrapolation. For our central values the masses of the sea quarks are not extrapolated to the physical $u$, $d$ masses; that is, the central values are "partially quenched." A calculation using "fat-link clover" valence fermions is also discussed but is not included in our final results. We find, for example, $f_B = 190 (7) (^{+24}_{-17}) (^{+11}_{-2}) (^{+8}_{-0})$ MeV, $f_{B_s}/f_B = 1.16 (1) (2) (2) (^{+4}_{-0})$, $f_{D_s} = 241 (5) (^{+27}_{-26}) (^{+9}_{-4}) (^{+5}_{-0})$ MeV, and $f_{B}/f_{D_s} = 0.79 (2) (^{+5}_{-4}) (3) (^{+5}_{-0})$, where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched $N_f=2$ approximation, the error due to the missing strange sea quark and to partial quenching, and an estimate of the effects of chiral logarithms at small quark mass. The last error, though quite significant in decay constant ratios, appears to be smaller than has been recently suggested by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other lattice computations to date, the lattice $u,d$ quark masses are not very light and chiral log effects may not be fully under control.Comment: Revised version includes an attempt to estimate the effects of chiral logarithms at small quark mass; central values are unchanged but one more systematic error has been added. Sections III E and V D are completely new; some changes for clarity have also been made elsewhere. 82 pages; 32 figure

Kaon B Parameter in Quenched QCD

I calculate the kaon B-parameter with a lattice simulation in quenched approximation. The lattice simulation uses an action possessing exact lattice chiral symmetry, an overlap action. Computations are performed at two lattice spacings, about 0.13 and 0.09 fm (parameterized by Wilson gauge action couplings beta=5.9 and 6.1) with nearly the same physical volumes and quark masses. I describe particular potential difficulties which arise due to the use of such a lattice action in finite volume. My results are consistent with other recent lattice determinations using domain-wall fermions.Comment: 23 pages, Revtex, 16 postscript figure