On the fourth root prescription for dynamical staggered fermions

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 (det D_{staggered})^{1/4} = det D. Working in the flavour 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 localisation range vanishing ~ (a/m)^{1/2} for lattice spacing a -> 0. Prospects for the interacting case are also discussed, although we do not solve this case here.Comment: 29 pages, 2 figures; some revision and streamlining of the discussions; results unchanged; to appear in PR

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

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.Comment: Minor corrections. Revtex, 58 page

Chiral properties of two-flavor QCD in small volume and at large lattice spacing

We present results from simulations of two flavors of dynamical overlap fermions on 8^4 lattices at three values of the sea quark mass and a lattice spacing of about 0.16 fm. We measure the topological susceptibility and the chiral condensate. A comparison of the low-lying spectrum of the overlap operator with predictions from random matrix theory is made. To demonstrate the effect of the dynamical fermions, we compare meson two-point functions with quenched results. Algorithmic improvements over a previous publication and the performance of the algorithm are discussed.Comment: 16 pages, 12 figure

Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD Vacuum

Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.Comment: Talk presented at the DPF2000 Conferenc

On the pion cloud of the nucleon

We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.Comment: 7 pages, latex, 3 ps figures, minor change

Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and on the lattice

In this paper we use one-loop chiral perturbation theory in order to compare lattice computations of the K+ to pi+ pi0 decay amplitude with the experimental value. This makes it possible to investigate three systematic effects that plague lattice computations: quenching, finite-volume effects, and the fact that lattice computations have been done at unphysical values of the quark masses and pion external momenta (only this latter effect shows up at tree level). We apply our results to the most recent lattice computation, and find that all three effects are substantial. We conclude that one-loop corrections in chiral perturbation theory help in explaining the discrepancy between lattice results and the real-world value. We also revisit B_K, which is closely related to the K+ to pi+ pi0 decay amplitude by chiral symmetry.Comment: 50 pages, TeX, two eps figures included, minor changes, no changes in results or conclusions, version to appear in Phys.Rev.

Evidence for quenched chiral logs

Using the pole shifting procedure of the modified quenched approximation (MQA) to cure the exceptional configuration problem, accurate hadron hadron spectrum calculations can be obtained at very light quark mass. Here we use the MQA to extend and improve our previous investigation of chiral logs in the pion mass. At beta=5.7 for Wilson fermion, we see clear evidence for quenched chiral logarithms in the pion mass as a function of quark mass. The size of the observed chiral log exponent delta is in good agreement with the value obtained from a direct calculation of the eta' hairpin diagram.Comment: 3 pages, 4 figures, Lattice 98 tal

Capture rate and neutron helicity asymmetry for ordinary muon capture on hydrogen

Applying heavy-baryon chiral perturbation theory to ordinary muon capture (OMC) on a proton, we calculate the capture rate and neutron helicity asymmetry up to next-to-next-to-leading order. For the singlet hyperfine state, we obtain the capture rate Gamma_0 = 695 sec^{-1} while, for the triplet hyperfine state, we obtain the capture rate Gamma_1 = 11.9 sec^{-1} and the neutron asymmetry alpha_1 = 0.93. If the existing formalism is used to relate these atomic capture rates to Gamma_{liq}, the OMC rate in liquid hydrogen, then Gamma_{liq} corresponding to our improved values of Gamma_0 and Gamma_1 is found to be significantly larger than the experimental value, primarily due to the updated larger value of g_A. We argue that this apparent difficulity may be correlated to the specious anomaly recently reported for mu^- + p to n + nu_mu + gamma, and we suggest a possibility to remove these two "problems" simply and simultaneously by reexamining the molecular physics input that underlies the conventional analysis of Gamma_{liq}.Comment: 14 pages, 1 figur

The Strangeness Radius and Magnetic Moment of the Nucleon Revisited

We update Jaffe's estimate of the strange isoscalar radius and magnetic moment of the nucleon. We make use of a recent dispersion--theoretical fit to the nucleon electromagnetic form factors and an improved description of symmetry breaking in the vector nonet. We find $\mu_s = -0.24 \pm 0.03$~n.m. and $r_s^2 = 0.21 \pm 0.03$~fm$^2$. The strange formfactor $F_2^s (t)$ follows a dipole with a cut--off mass of 1.46~GeV, $F_2^s (t)= \mu_s (1-t/2.14 \, {\rm GeV}^2 )^{-2}$. These numbers should be considered as upper limits on the strange vector current matrix--elements in the nucleon.Comment: 8 pp, LaTeX, uses epsf, 1 figure in separate fil

A Three-Dimensional Treatment of the Three-Nucleon Bound State

Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces.Comment: 25 pages, 7 figures (34 eps files