34,959 research outputs found
A Lattice Study of the Gluon Propagator in Momentum Space
We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the
gluon propagator both in time at zero 3-momentum and in momentum space. From
the former quantity we obtain evidence for a dynamically generated effective
mass, which at beta=6.0 and beta=6.3 increases with the time separation of the
sources, in agreement with earlier results. The momentum space propagator G(k)
provides further evidence for mass generation. In particular, at beta=6.0, for
k less than 1 GeV, the propagator G(k) can be fit to a continuum formula
proposed by Gribov and others, which contains a mass scale b, presumably
related to the hadronization mass scale. For higher momenta Gribov's model no
longer provides a good fit, as G(k) tends rather to follow an inverse power
law. The results at beta=6.3 are consistent with those at beta=6.0, but only
the high momentum region is accessible on this lattice. We find b in the range
of three to four hundred MeV and the exponent of the inverse power law about
2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1
GeV) G(k) is best fit to a simple massive boson propagator with mass m. We
argue that such a discrepancy may be related to a lack of scaling for low
momenta at beta=5.7. {}From our results, the study of correlation functions in
momentum space looks promising, especially because the data points in Fourier
space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture
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.
Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe
I develop a renormalization-group blocking framework for lattice QCD with
staggered fermions. Under plausible, and testable, assumptions, I then argue
that the fourth-root recipe used in numerical simulations is valid in the
continuum limit. The taste-symmetry violating terms, which give rise to
non-local effects in the fourth-root theory when the lattice spacing is
non-zero, vanish in the continuum limit. A key role is played by reweighted
theories that are local and renormalizable on the one hand, and that
approximate the fourth-root theory better and better as the continuum limit is
approached on the other hand.Comment: Minor corrections. Revtex, 58 page
Modular Invariant of Quantum Tori II: The Golden Mean
In our first article in this series ("Modular Invariant of Quantum Tori I:
Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of
quantum tori was defined. In this paper, we consider the case of the quantum
torus associated to the golden mean. We show that the modular invariant is
approximately 9538.249655644 by producing an explicit formula for it involving
weighted versions of the Rogers-Ramanujan functions
Penguin diagrams for improved staggered fermions
We calculate, at the one loop level, penguin diagrams for improved staggered
fermion operators constructed using various fat links. The main result is that
diagonal mixing coefficients with penguin operators are identical between the
unimproved operators and the improved operators using such fat links as Fat7,
Fat7+Lepage, , HYP (I) and HYP (II). In addition, it turns out
that the off-diagonal mixing vanishes for those constructed using fat links of
Fat7, and HYP (II). This is a consequence of the the fact that
the improvement by various fat links changes only the mixing with higher
dimension operators and off-diagonal operators. The results of this paper,
combined with those for current-current diagrams, provide the complete matching
at the one loop level with all corrections of included.Comment: 11 pages, 4 figure
Lattice results for the decay constant of heavy-light vector mesons
We compute the leptonic decay constants of heavy-light vector mesons in the
quenched approximation. The reliability of lattice computations for heavy
quarks is checked by comparing the ratio of vector to pseudoscalar decay
constant with the prediction of Heavy Quark Effective Theory in the limit of
infinitely heavy quark mass. Good agreement is found. We then calculate the
decay constant ratio for B mesons: .
We also quote quenched MeV.Comment: 11 pages, 3 postscript figs., revtex; two references adde
Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks
We present results for , , , and their ratios in
the presence of two flavors of light sea quarks (). We use Wilson light
valence quarks and Wilson and static heavy valence quarks; the sea quarks are
simulated with staggered fermions. Additional quenched simulations with
nonperturbatively improved clover fermions allow us to improve our control of
the continuum extrapolation. For our central values the masses of the sea
quarks are not extrapolated to the physical , masses; that is, the
central values are "partially quenched." A calculation using "fat-link clover"
valence fermions is also discussed but is not included in our final results. We
find, for example,
MeV, , MeV, and , where in each case the first error is
statistical and the remaining three are systematic: the error within the
partially quenched approximation, the error due to the missing strange
sea quark and to partial quenching, and an estimate of the effects of chiral
logarithms at small quark mass. The last error, though quite significant in
decay constant ratios, appears to be smaller than has been recently suggested
by Kronfeld and Ryan, and Yamada. We emphasize, however, that as in other
lattice computations to date, the lattice quark masses are not very light
and chiral log effects may not be fully under control.Comment: Revised version includes an attempt to estimate the effects of chiral
logarithms at small quark mass; central values are unchanged but one more
systematic error has been added. Sections III E and V D are completely new;
some changes for clarity have also been made elsewhere. 82 pages; 32 figure
Er doped oxide nanoparticles in silica based optical fibres
Erbium doped materials are of great interest in optical telecommunications
due to the Er3+ intra-4f emission at 1.54 ?m. Erbium doped fibre amplifiers
(EDFA) were developed in silica glass because of the low losses at this
wavelength and the reliability of this glass. Developments of new rare earth
doped fibre amplifiers aim to control their spectroscopic properties including
shape and width of the gain curve and optical quantum efficiency. Standard
silica glass modifiers, such as aluminium, result in very good properties in
current EDFA. However, for more drastic spectroscopic changes, more important
modifications of the rare earth ions local environment are required. To address
this aim, we present a fibre fabrication route creating rare earth doped
calcia?silica or calcia?phosphosilica nanoparticles embedded in silica glass.
By adding alkaline earth elements such as calcium, in low concentration, one
can obtain a glass with an immisci- bility gap so that phase separation occurs
with an appropriate heat treatment. We investigated the role of two elements:
calcium and phosphorus (a standard silica modifier). Scanning electron
microscopy shows that nanoparticles are only observed when calcium is
incorporated. The size of the particles is determined to be around 50 nm in
preform samples. The nature of these particles depends on phosphorus content:
without P, electron diffraction shows that the particles are amorphous whilst
they are partially crystalline when phosphorus is added. In addition through
use of energy dispersive x-ray techniques, we have shown that erbium ions are
located in the nanoparticles
Chiral logs with staggered fermions
We compute chiral logarithms in the presence of "taste" symmetry breaking of
staggered fermions. The lagrangian of Lee and Sharpe is generalized and then
used to calculate the logs in and masses. We correct an error in Ref.
[1] [C. Bernard, hep-lat/0111051]; the issue turns out to have implications for
the comparison with simulations, even at tree level. MILC data with three light
dynamical flavors can be well fit by our formulas. However, two new chiral
parameters, which describe order hairpin diagrams for taste-nonsinglet
mesons, enter in the fits. To obtain precise results for the physical
coefficients at order , these new parameters will need to be bounded, at
least roughly.Comment: talk presented by C. Bernard at Lattice2002(spectrum); 3 pages, 2
figure
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