[Show abstract][Hide abstract] ABSTRACT: We present a review of the properties of generalized domain wall Fermions,
based on a (real) M\"obius transformation on the Wilson overlap kernel,
discussing their algorithmic efficiency, the degree of explicit chiral
violations measured by the residual mass ($m_{res}$) and the Ward-Takahashi
identities. The M\"obius class interpolates between Shamir's domain wall
operator and Bori\c{c}i's domain wall implementation of Neuberger's overlap
operator without increasing the number of Dirac applications per conjugate
gradient iteration. A new scaling parameter ($\alpha$) reduces chiral
violations at finite fifth dimension ($L_s$) but yields exactly the same
overlap action in the limit $L_s \rightarrow \infty$. Through the use of 4d
Red/Black preconditioning and optimal tuning for the scaling $\alpha(L_s)$, we
show that chiral symmetry violations are typically reduced by an order of
magnitude at fixed $L_s$. At large $L_s$ we argue that the observed scaling for
$m_{res} = O(1/L_s)$ for Shamir is replaced by $m_{res} = O(1/L_s^2)$ for the
properly tuned M\"obius algorithm with $\alpha = O(L_s)$
[Show abstract][Hide abstract] ABSTRACT: The extraction of matrix elements from baryon three-point functions is complicated by the fact that the signal-to-noise drops rapidly as a function of time. Using a previously discussed method to improve the signal-to-noise for lattice two-point functions, we use this technique to do so for lattice three-point functions, using electromagnetic form factors for the nucleon and Delta as an example.
[Show abstract][Hide abstract] ABSTRACT: We discuss a new approach to reducing excited state contributions from two-
and three-point correlation functions in lattice simulations. For the purposes
of this talk, we focus on the Delta(1232) resonance and discuss how this new
method reduces excited state contamination from two-point functions and mention
how this will be applied to three-point functions to extract hadronic form
factors.
[Show abstract][Hide abstract] ABSTRACT: Most calculations in lattice Quantum Chromodynamics (QCD) involve the solution of a series of linear systems of equations with exceedingly large matrices and a large number of right hand sides. Iterative methods for these problems can be sped up significantly if we deflate approximations of appropriate invariant spaces from the initial guesses. Recently we have developed eigCG, a modification of the Conjugate Gradient (CG) method, which while solving a linear system can reuse a window of the CG vectors to compute eigenvectors almost as accurately as the Lanczos method. The number of approximate eigenvectors can increase as more systems are solved. In this paper we review some of the characteristics of eigCG and show how it helps remove the critical slowdown in QCD calculations. Moreover, we study scaling with lattice volume and an extension of the technique to nonsymmetric problems.
Journal of Physics Conference Series 08/2009; 180(1):012073. DOI:10.1088/1742-6596/180/1/012073
[Show abstract][Hide abstract] ABSTRACT: We calculate the magnetic dipole moment of the Δ(1232) and Ω- baryons with 2+1 flavors of clover fermions on anisotropic lattices using a background magnetic field. This is the first dynamical calculation of these magnetic moments using a background field technique. The calculation for Ω- is done at the physical strange quark mass, with the result in units of the physical nuclear magneton μΩ-=-1.93±0.08±0.12 (where the first error is statistical and the second is systematic) compared to the experimental number: -2.02±0.05. The Δ has been studied at three unphysical quark masses, corresponding to pion mass mπ=366, 438, and 548 MeV. The pion mass dependence is compared with the behavior obtained from chiral effective field theory.
[Show abstract][Hide abstract] ABSTRACT: We calculate the magnetic dipole moment of the Delta baryon using a background magnetic field on 2+1-flavors of clover fermions on anisotropic lattices. We focus on the finite volume effects that can be significant in background field studies, and thus we use two different spatial volumes in addition to several quark masses. Comment: 7 pages, 2 figures, contributed talk at Lattice 2008, to appear in the proceedings
[Show abstract][Hide abstract] ABSTRACT: A steady stream of developments in lattice QCD have made it possible today to begin to address the question of how nuclear
physics emerges from the underlying theory of strong interactions. A central role in this understanding play both the effective-field
theory description of nuclear forces and the ability to perform accurate non-perturbative calculations in low-energy QCD.
Here I present some recent results that attempt to extract important low-energy constants of the effective-field theory of
nuclear forces from lattice QCD.
European Physical Journal A 02/2007; 31(4):799-803. DOI:10.1140/epja/i2006-10267-5 · 2.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a study of the neutron electric dipole moment ($\vec d_N$) within the framework of lattice QCD with two flavors of dynamical lig ht quarks. The dipole moment is sensitive to the topological structure of the gaug e fields, and accuracy can only be achieved by using dynamical, or sea quark, calc ulations. However, the topological charge evolves slowly in these calculations, le ading to a relatively large uncertainty in $\vec d_N$. It is shown, using quenched configurations, that a better sampling of the charge d istribution reduces this problem, but because the CP even part of the fermion determinant is absent, both the topological charge dis tribution and $\vec d_N$ are pathological in the chiral limit. We discuss the statistical and systematic uncertainties arising from the topological charge distr ibution and unphysical size of the quark mass in our calculations and prospects fo r eliminating them. Our calculations employ the RBC collaboration two flavor domain wall fermion and DBW2 gauge action lattices with inverse lattice spacing $a^{-1}\approx$ 1.7 GeV, physical volume $V\approx (2$ fm)$^3$, and light quark mass roughly equal to the strange quark mass ($m_{sea}=0.03 $ and 0.04). We determine a value of the electric dipole moment that is zero withi n (statistical) errors, $|\vec d_N| = -0.04(20)$ e-$\theta$-fm at the smaller sea quark mass. Satisfactory results for the magnetic and electric form factors of the proton and neutron are also obtained and presented. Comment: 46 pages. Changed one author address
[Show abstract][Hide abstract] ABSTRACT: We introduce a new domain wall operator that represents a full (real) Möbius transformation of a given nonchiral Dirac kernel. Shamir's and Chiu/Boriçi's domain wall fermions are special cases of this new class. By tuning the parameters of the Möbius operator and by introducing a new Red/Black preconditioning, we are able to reduce the computational effort substantially.
[Show abstract][Hide abstract] ABSTRACT: We present numerical results for the kaon B-parameter, B_K, determined in the
quenched approximation of lattice QCD. Our simulations are performed using
domain-wall fermions and the renormalization group improved, DBW2 gauge action
which combine to give quarks with good chiral symmetry at finite lattice
spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme.
We study scaling by performing the simulation on two different lattices with
a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study
with an earlier calculation of B_K using two flavors of dynamical, domain-wall
quarks at a single lattice spacing to obtain
B_K(MS,NDR,mu=2GeV)=0.563(21)(39)(30), were the first error is statistical, the
second systematic (without quenching errors) and the third estimates the error
due to quenching.
[Show abstract][Hide abstract] ABSTRACT: We present preliminary results for nucleon dipole moments computed with domain wall fermions. Our main target is the electric dipole moment of the neutron arising from the theta term in the gauge part of the QCD lagrangian. The calculated magnetic dipole moments of the proton and neutron are in rough accord with experimental values. Comment: 3 pages. Contribution to the proceedings of Lattice 2004 (Fermilab)
[Show abstract][Hide abstract] ABSTRACT: A new class of domain wall fermions is defined that interpolates between
Shamir's and Bori\c{c}i's form without increasing the number of Dirac
applications per CG iteration. This class represents a full (real) M\"obius
transformation of the Wilson kernel. Simulations on quenched Wilson lattices
with $\beta = 6.0$ show that the number of lattice sites ($L_s$) in the fifth
dimension can be reduced by a factor of 2 or more at fixed value of chiral
symmetry violations measured by the residual mass ($m_{res}$).
[Show abstract][Hide abstract] ABSTRACT: This is an exploratory study of the lightest non-singlet scalar $q\bar q$ state on the lattice with two dynamical quarks. Domain Wall fermions are used for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$ and N_f=2. Since this statistical error-bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the Partially Quenched ChPT and find it describes lattice correlators well. The leading unphysical contribution in Partially Quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass 1.51(19) GeV from the partially quenched correlators is consistent with the dynamical result and has appreciably smaller error-bar.
[Show abstract][Hide abstract] ABSTRACT: We discuss how to extract renormalized from bare Polyakov loops in SU(N)
lattice gauge theories at nonzero temperature in four spacetime dimensions.
Single loops in an irreducible representation are multiplicatively renormalized
without mixing, through a renormalization constant which depends upon both
representation and temperature. The values of renormalized loops in the four
lowest representations of SU(3) were measured numerically on small, coarse
lattices. We find that in magnitude, condensates for the sextet and octet loops
are approximately the square of the triplet loop. This agrees with a large $N$
expansion, where factorization implies that the expectation values of loops in
adjoint and higher representations are just powers of fundamental and
anti-fundamental loops. For three colors, numerically the corrections to the
large $N$ relations are greatest for the sextet loop, $\leq 25%$; these
represent corrections of $\sim 1/N$ for N=3. The values of the renormalized
triplet loop can be described by an SU(3) matrix model, with an effective
action dominated by the triplet loop. In several ways, the deconfining phase
transition for N=3 appears to be like that in the $N=\infty$ matrix model of
Gross and Witten.
[Show abstract][Hide abstract] ABSTRACT: We discuss how to extract the values of renormalized Polyakov loops from the bare values measured on a lattice through numerical simulations. Results for three colors, and the four lowest representations, are presented. The data suggests that a simple matrix-valued mean field theory may serve, to a good approximation, near the deconfining transition.
[Show abstract][Hide abstract] ABSTRACT: We compute chiral logarithms in the presence of “taste” symmetry breaking of staggered fermions. The lagrangian of Lee and Sharpe is generalized and then used to calculate the logs in π and K masses. We correct an error in Ref. [1]. MILC data with three light dynamical flavors can be well fit by our formulas. However, two new chiral parameters, which describeO(a2) hairpin diagrams for taste-nonsinglet mesons, enter in the fits. To obtain precise results for the physicalO(p4) coefficients, these new parameters will need to be bounded.
[Show abstract][Hide abstract] ABSTRACT: We study theqq¯ singlet and non-singlet scalar-meson masses using domain wall fermions and the quenched approximation. The singlet mass is found to be smaller than the non-singlet mass and indicates that the lowest singlet meson state could be lighter than 1 GeV. The two-point functions for very small quark masses are compared with expectations from the small-volume chiral perturbation theory and the presence of fermionic zero modes.
[Show abstract][Hide abstract] ABSTRACT: We study the chiral properties of quenched domain wall fermions with several gauge actions. We demonstrate that the residual chiral symmetry breaking, which is present for a finite number of lattice sites in the fifth dimension ($L_s$), can be substantially suppressed using improved gauge actions. In particular the Symanzik action, the Iwasaki action, and a renormalization group improved gauge action, called doubly blocked Wilson (DBW2), are studied and compared to the Wilson action. All improved gauge actions studied show a reduction in the additive residual quark mass, $\mres$. Remarkably, in the DBW2 case $\mres$ is roughly two orders of magnitude smaller than the Wilson gauge action at $a^{-1}=2$ GeV and $L_s=16$. Significant reduction in $\mres$ is also realized at stronger gauge coupling corresponding to $a^{-1}=1.3$ GeV. As our numerical investigation indicates, this reduction is achieved by reducing the number of topological lattice dislocations present in the gauge field configurations. We also present detailed results for the quenched light hadron spectrum and the pion decay constant using the DBW2 gauge action. Comment: 50 pages, 25 figures, RevTeX formated, minor corrections
Physical Review D 11/2002; 69(7). DOI:10.1103/PhysRevD.69.074504 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We present preliminary results for the heavy-light leptonic decay constants in the presence of three light dynamical flavors. We generate dynamical configurations with improved staggered and gauge actions and analyze them for heavy-light physics with tadpole improved clover valence quarks. When the scale is set by $m_\rho$, we find an increase of approximately 23% in $f_B$ with three dynamical flavors over the quenched case. Discretization errors appear to be small (of order 3% or less) in the quenched case but have not yet been measured in the dynamical case.