7,525 research outputs found

### Staggered fermion matrix elements using smeared operators

We investigate the use of two kinds of staggered fermion operators, smeared
and unsmeared. The smeared operators extend over a $4^4$ hypercube, and tend to
have smaller perturbative corrections than the corresponding unsmeared
operators. We use these operators to calculate kaon weak matrix elements on
quenched ensembles at $\beta=6.0$, 6.2 and 6.4. Extrapolating to the continuum
limit, we find $B_K(NDR, 2 GeV)= 0.62\pm 0.02(stat)\pm 0.02(syst)$. The
systematic error is dominated by the uncertainty in the matching between
lattice and continuum operators due to the truncation of perturbation theory at
one-loop. We do not include any estimate of the errors due to quenching or to
the use of degenerate $s$ and $d$ quarks. For the $\Delta I = {3/2}$
electromagnetic penguin operators we find $B_7^{(3/2)} = 0.62\pm 0.03\pm 0.06$
and $B_8^{(3/2)} = 0.77\pm 0.04\pm 0.04$. We also use the ratio of unsmeared to
smeared operators to make a partially non-perturbative estimate of the
renormalization of the quark mass for staggered fermions. We find that tadpole
improved perturbation theory works well if the coupling is chosen to be
\alpha_\MSbar(q^*=1/a).Comment: 22 pages, 1 figure, uses eps

### Physical Results from Partially Quenched Simulation

We describe how one can use chiral perturbation theory to obtain results for
physical quantities, such as quark masses, using partially quenched
simulations.Comment: Written version of two talks at DPF 2000. 6 pages, 2 figure

### Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e.
those in which the valence and sea quark masses, $m_V$ and $m_S$, are
different. I point out that for lattice fermions which retain some chiral
symmetry on the lattice, e.g. staggered fermions, the leading order prediction
of the chiral expansion is that the mass of the pion depends only on $m_V$, and
is independent of $m_S$. This surprising result is shown to receive corrections
from loop effects which are of relative size $m_S \ln m_V$, and which thus
diverge when the valence quark mass vanishes. Using partially quenched chiral
perturbation theory, I calculate the full one-loop correction to the mass and
decay constant of pions composed of two non-degenerate quarks, and suggest
various combinations for which the prediction is independent of the unknown
coefficients of the analytic terms in the chiral Lagrangian. These results can
also be tested with Wilson fermions if one uses a non-perturbative definition
of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected
(alpha_4 is replaced by alpha_4/2

### Spectra of D-branes with Higgs vevs

In this paper we continue previous work on counting open string states
between D-branes by considering open strings between D-branes with nonzero
Higgs vevs, and in particular, nilpotent Higgs vevs, as arise, for example,
when studying D-branes in orbifolds. Ordinarily Higgs vevs can be interpreted
as moving the D-brane, but nilpotent Higgs vevs have zero eigenvalues, and so
their interpretation is more interesting -- for example, they often correspond
to nonreduced schemes, which furnishes an important link in understanding old
results relating classical D-brane moduli spaces in orbifolds to Hilbert
schemes, resolutions of quotient spaces, and the McKay correspondence. We give
a sheaf-theoretic description of D-branes with Higgs vevs, including nilpotent
Higgs vevs, and check that description by noting that Ext groups between the
sheaves modelling the D-branes, do in fact correctly count open string states.
In particular, our analysis expands the types of sheaves which admit on-shell
physical interpretations, which is an important step for making derived
categories useful for physics.Comment: 46 pages, LaTeX; v2: typos fixed; v3: more typos fixe

### Comforting sentences from the warming room at Inchcolm abbey

A fragmentary inscription from the ïŹfteenth century is reconstructed and its source identified, offering an insight into the use of one proverbial source of morally and spiritually encouraging sentences, and opening another little window on to the books available to the canons of Inchcolm

### Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark
masses are different. In this paper we calculate the nonanalytic one-loop
corrections of some physical quantities: the chiral condensate, weak decay
constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude,
using partially quenched chiral perturbation theory. Our results for weak decay
constants and masses agree with, and generalize, results of previous work by
Sharpe. We compare B_K and the K+ decay amplitude with their real-world values
in some examples. For the latter quantity, two other systematic effects that
plague lattice computations, namely, finite-volume effects and unphysical
values of the quark masses and pion external momenta are also considered. We
find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in
Phys. Rev.

### Observations on discretization errors in twisted-mass lattice QCD

I make a number of observations concerning discretization errors in
twisted-mass lattice QCD that can be deduced by applying chiral perturbation
theory including lattice artifacts. (1) The line along which the PCAC quark
mass vanishes in the twisted mass-twisted mass plane makes an angle to the
untwisted mass axis which is a direct measure of O(a) terms in the chiral
Lagrangian, and is found numerically to be large; (2) Numerical results for
pionic quantities in the mass plane show the qualitative properties predicted
by chiral perturbation theory, in particular an asymmetry in slopes between
positive and negative untwisted quark masses; (3) By extending the description
of the ``Aoki regime'' (where m_q is of size a^2 Lambda_QCD^3) to
next-to-leading order in chiral perturbation theory I show how the phase
transition lines and lines of maximal twist (using different definitions)
extend into this region, and give predictions for the functional form of pionic
quantities; (4) I argue that the recent claim that lattice artifacts at maximal
twist have apparent infrared singularities in the chiral limit results from
expanding about the incorrect vacuum state. Shifting to the correct vacuum (as
can be done using chiral perturbation theory) the apparent singularities are
summed into non-singular, and furthermore predicted, forms. I further argue
that there is no breakdown in the Symanzik expansion in powers of lattice
spacing, and no barrier to simulating at maximal twist in the Aoki regime.Comment: 20 pages, 6 figures. Published version. More typos corrected, and
summary paragraph added to sections II and I

### 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.

### Chiral corrections to the axial charges of the octet baryons from quenched QCD

We calculate one-loop correction to the axial charges of the octet baryons
using quenched chiral perturbation theory, in order to understand chiral
behavior of the axial charges in quenched approximation to quantum
chromodynamics (QCD). In contrast to regular behavior of the full QCD chiral
perturbation theory result, $c_0+c_{l2}m_\pi^2\,\ln{m_\pi^2}+\cdots$, we find
that the quenched chiral perturbation theory result,
$c_0^Q+(c_{l0}^Q+c_{l2}^Qm_\pi^2)\ln{m_\pi^2}+c_2^Q m_\pi^2+\cdots$, is
singular in the chiral limit.Comment: standard LaTeX, 16 pages, 4 epsf figure

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