4,003 research outputs found
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
Constructing and exploring wells of energy landscapes
Landscape paradigm is ubiquitous in physics and other natural sciences, but
it has to be supplemented with both quantitative and qualitatively meaningful
tools for analyzing the topography of a given landscape. We here consider
dynamic explorations of the relief and introduce as basic topographic features
``wells of duration and altitude ''. We determine an intrinsic
exploration mechanism governing the evolutions from an initial state in the
well up to its rim in a prescribed time, whose finite-difference approximations
on finite grids yield a constructive algorithm for determining the wells. Our
main results are thus (i) a quantitative characterization of landscape
topography rooted in a dynamic exploration of the landscape, (ii) an
alternative to stochastic gradient dynamics for performing such an exploration,
(iii) a constructive access to the wells and (iv) the determination of some
bare dynamic features inherent to the landscape. The mathematical tools used
here are not familiar in physics: They come from set-valued analysis
(differential calculus of set-valued maps and differential inclusions) and
viability theory (capture basins of targets under evolutionary systems) which
have been developed during the last two decades; we therefore propose a minimal
appendix exposing them at the end of this paper to bridge the possible gap.Comment: 28 pages, submitted to J. Math. Phys -
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 , where 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 and 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
Functional Integration Over Geometries
The geometric construction of the functional integral over coset spaces
is reviewed. The inner product on the cotangent space of
infinitesimal deformations of 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 , the
functional measure on the coset space 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 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
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
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
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