10,440 research outputs found

### Partially Quenched QCD with Non-Degenerate Dynamical Quarks

We discuss the importance of using partially quenched theories with three
degenerate quarks for extrapolating to QCD, and present some relevant results
from chiral perturbation theory.Comment: LATTICE99 talk. 3 pages, 2 figures. Uses epsf and espcrc2.st

### 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 Unphysical Simulations

We calculate various properties of pseudoscalar mesons in partially quenched
QCD using chiral perturbation theory through next-to-leading order. Our results
can be used to extrapolate to QCD from partially quenched simulations, as long
as the latter use three light dynamical quarks. In other words, one can use
unphysical simulations to extract physical quantities - in this case the quark
masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our
proposal for determining L_7 makes explicit use of an unphysical (yet
measurable) effect of partially quenched theories, namely the double-pole that
appears in certain two-point correlation functions. Most of our calculations
are done for sea quarks having up to three different masses, except for our
result for L_7, which is derived for degenerate sea quarks.Comment: 26 pages, 12 figures (discussion on discretization errors at end of
sec. IV clarified; minor improvements in presentation; results unchanged

### 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

### Notes on Certain (0,2) Correlation Functions

In this paper we shall describe some correlation function computations in
perturbative heterotic strings that, for example, in certain circumstances can
lend themselves to a heterotic generalization of quantum cohomology
calculations. Ordinary quantum chiral rings reflect worldsheet instanton
corrections to correlation functions involving products of Dolbeault cohomology
groups on the target space. The heterotic generalization described here
involves computing worldsheet instanton corrections to correlation functions
defined by products of elements of sheaf cohomology groups. One must not only
compactify moduli spaces of rational curves, but also extend a sheaf
(determined by the gauge bundle) over the compactification, and linear sigma
models provide natural mechanisms for doing both. Euler classes of obstruction
bundles generalize to this language in an interesting way.Comment: 51 pages, LaTeX; v2: typos fixed; v3: more typos fixe

### Lattice QCD data versus Chiral Perturbation Theory: the case of $M_\pi$

I present a selection of recent lattice data by major collaborations for the
pseudo-Goldstone boson masses in full ($N_f=2$) QCD, where the valence quarks
are chosen exactly degenerate with the sea quarks. At least the more chiral
points should be consistent with Chiral Perturbation Theory for the latter to
be useful in extrapolating to physical masses. Perspectives to reliably
determine NLO Gasser-Leutwyler coefficients are discussed.Comment: 3 pages, 4 figures, ICHEP 2002, v2: one statement clarified, one ref.
adde

### Partially quenched chiral perturbation theory without $\Phi_0$

This paper completes the argument that lattice simulations of partially
quenched QCD can provide quantitative information about QCD itself, with the
aid of partially quenched chiral perturbation theory. A barrier to doing this
has been the inclusion of $\Phi_0$, the partially quenched generalization of
the $\eta'$, in previous calculations in the partially quenched effective
theory. This invalidates the low energy perturbative expansion, gives rise to
many new unknown parameters, and makes it impossible to reliably calculate the
relation between the partially quenched theory and low energy QCD. We show that
it is straightforward and natural to formulate partially quenched chiral
perturbation theory without $\Phi_0$, and that the resulting theory contains
the effective theory for QCD without the $\eta'$. We also show that previous
results, obtained including $\Phi_0$, can be reinterpreted as applying to the
theory without $\Phi_0$. We contrast the situation with that in the quenched
effective theory, where we explain why it is necessary to include $\Phi_0$.
We also compare the derivation of chiral perturbation theory in partially
quenched QCD with the standard derivation in unquenched QCD. We find that the
former cannot be justified as rigorously as the latter, because of the absence
of a physical Hilbert space. Finally, we present an encouraging result:
unphysical double poles in certain correlation functions in partially quenched
chiral perturbation theory can be shown to be a property of the underlying
theory, given only the symmetries and some plausible assumptions.Comment: 45 pages, no figure

### 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

### D-branes, B fields, and Ext groups

In this paper we extend previous work on calculating massless boundary Ramond
sector spectra of open strings to include cases with nonzero flat B fields. In
such cases, D-branes are no longer well-modelled precisely by sheaves, but
rather they are replaced by `twisted' sheaves, reflecting the fact that gauge
transformations of the B field act as affine translations of the Chan-Paton
factors. As in previous work, we find that the massless boundary Ramond sector
states are counted by Ext groups -- this time, Ext groups of twisted sheaves.
As before, the computation of BRST cohomology relies on physically realizing
some spectral sequences. Subtleties that cropped up in previous work also
appear here.Comment: 23 pages, LaTeX; v2: typos fixed; v3: reference adde

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