Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks

We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution to the muon anomalous magnetic moment, a_\mu = (g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q^2 region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble (a=0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm)^3, we find a_\mu^{HLO} = (713 \pm 15) \times 10^{-10} and (748 \pm 21) \times 10^{-10} where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering systematic uncertainties not eliminated in this study, we view this as agreement with the current best calculations using the experimental cross section for e^+e^- annihilation to hadrons, 692.4 (5.9) (2.4)\times 10^{-10}, and including the experimental decay rate of the tau lepton to hadrons, 711.0 (5.0) (0.8)(2.8)\times 10^{-10}. We discuss several ways to improve the current lattice calculation.Comment: 44 pages, 4 tables, 17 figures, more discussion on matching the chpt calculation to lattice calculation, typos corrected, refs added, version to appear in PR

K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory

We calculate results for K to pi and K to 0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low energy constants of the chiral effective theory can be determined. The low energy constants of these matrix elements are necessary for an understanding of the Delta I=1/2 rule, and for calculations of epsilon'/epsilon using current lattice QCD simulations.Comment: 43 pages, 2 figures, uses RevTeX, added and updated reference

Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory

Durr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion determinant to remove unwanted degrees of freedom ("tastes"). Further, I argue that the singularities in SChPT are absent in most commonly-computed quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.Comment: 14 pages, 1 figure. v3: Spurious symbol, introduced by conflicting tex macros, removed. Clarification of discussion in several place

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.

Discretization effects and the scalar meson correlator in mixed-action lattice simulations

We study discretization effects in a mixed-action lattice theory with domain-wall valence quarks and Asqtad-improved staggered sea quarks. At the level of the chiral effective Lagrangian, discretization effects in the mixed-action theory give rise to two new parameters as compared to the lowest order Lagrangian for staggered fermions -- the residual quark mass, m_res, and the mixed valence-sea meson mass-splitting, Delta_mix. We find that the size of m_res is approximately four times smaller than our lightest valence quark mass on our coarser lattice spacing, and comparable to that of simulations by RBC and UKQCD. We also find that the size of Delta_mix is comparable to the smallest of the staggered meson taste-splittings measured by MILC. Because lattice artifacts are different in the valence and sea sectors of the mixed-action theory, they give rise to unitarity-violating effects that disappear in the continuum limit. Such effects are expected to be mild for many quantities of interest, but are significant in the case of the isovector scalar (a_0) correlator. Specifically, once m_res, Delta_mix, and two other parameters that can be determined from the light pseudoscalar spectrum are known, the two-particle intermediate state "bubble" contribution to the scalar correlator is completely predicted within mixed-action chiral perturbation theory (MAChPT). We find that the behavior of the scalar meson correlator is quantitatively consistent with the MAChPT prediction; this supports the claim that MAChPT describes the dominant unitarity-violating effects in the mixed-action theory and can be used to remove lattice artifacts and recover physical quantities.Comment: 33 pages, 12 figure

Existence and uniqueness for Mean Field Games with state constraints

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption

Light hadrons with improved staggered quarks: approaching the continuum limit

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0- meson propagators, and we make a preliminary mass computation for a radially excited 0- meson.Comment: 43 pages, 16 figure

Functional Integration Over Geometries

The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber $\cal G$, the functional measure on the coset space ${\cal M}/{\cal G}$ is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where $\cal G$ is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\it i.e.} metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov-Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed.Comment: 68 pages, Latex document using Revtex Macro package, Contribution to the special issue of the Journal of Mathematical Physics on Functional Integration, to be published July, 1995

Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions

In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, the Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a P\'{e}ano like theorem for ordinary differential equations of fractional order.Comment: accepted IJBC, 5 pages, 1 figur

Dual-species quantum degeneracy of potassium-40 and rubidium-87 on an atom chip

In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time.Comment: 8 pages, 4 figures. To be published in the Proceedings of the 20th International Conference on Atomic Physics, 2006 (Innsbruck, Austria