4,965 research outputs found

### Staggered Chiral Perturbation Theory at Next-to-Leading Order

We study taste and Euclidean rotational symmetry violation for staggered
fermions at nonzero lattice spacing using staggered chiral perturbation theory.
We extend the staggered chiral Lagrangian to O(a^2 p^2), O(a^4) and O(a^2 m),
the orders necessary for a full next-to-leading order calculation of
pseudo-Goldstone boson masses and decay constants including analytic terms. We
then calculate a number of SO(4) taste-breaking quantities, which involve only
a small subset of these NLO operators. We predict relationships between SO(4)
taste-breaking splittings in masses, pseudoscalar decay constants, and
dispersion relations. We also find predictions for a few quantities that are
not SO(4) breaking. All these results hold also for theories in which the
fourth-root of the fermionic determinant is taken to reduce the number of quark
tastes; testing them will therefore provide evidence for or against the
validity of this trick.Comment: 39 pages, 6 figures (v3: corrected technical error in enumeration of
a subset of NLO operators; final conclusions unchanged

### 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 $T$ and altitude $y$''. 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 -

### Current Physics Results from Staggered Chiral Perturbation Theory

We review several results that have been obtained using lattice QCD with the
staggered quark formulation. Our focus is on the quantities that have been
calculated numerically with low statistical errors and have been extrapolated
to the physical quark mass limit and continuum limit using staggered chiral
perturbation theory. We limit our discussion to a brief introduction to
staggered quarks, and applications of staggered chiral perturbation theory to
the pion mass, decay constant, and heavy-light meson decay constants.Comment: 18 pages, 4 figures, commissioned review article, to appear in Mod.
Phys. Lett.

### 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

### The kaon B-parameter from unquenched mixed action lattice QCD

We present a preliminary calculation of B_K using domain-wall valence quarks
and 2+1 flavors of improved staggered sea quarks. Both the size of the residual
quark mass, which measures the amount of chiral symmetry breaking, and of the
mixed meson splitting Delta_mix, a measure of taste-symmetry breaking, show
that discretization effects are under control in our mixed action lattice
simulations. We show preliminary data for pseudoscalar meson masses, decay
constants and B_K. We discuss general issues associated with the chiral
extrapolation of lattice data, and, as an example, present a preliminary chiral
and continuum extrapolation of f_pi. The quality of our data shows that the
good chiral properties of domain-wall quarks, in combination with the light sea
quark masses and multiple lattice spacings available with the MILC staggered
configurations, will allow for a precise determination of B_K.Comment: 7 pages, 4 figures. Presented at the XXV International Symposium on
Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

### 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

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