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 $1/m_Q$, where $m_Q$ 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 $B\to\pi$ and $D\to K$ 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, $\bar{\rm Fat7}$, HYP (I) and HYP (II). In addition, it turns out that the off-diagonal mixing vanishes for those constructed using fat links of Fat7, $\bar{\rm Fat7}$ 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 ${\cal O}(g^2)$ 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: $f_{B^*}/f_B= 1.01(0.01)(^{+0.04}_{-0.01})$. We also quote quenched $f_{B^*}=177(6)(17)$ 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 $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios in the presence of two flavors of light sea quarks ($N_f=2$). 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 $u$, $d$ 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, $f_B = 190 (7) (^{+24}_{-17}) (^{+11}_{-2}) (^{+8}_{-0})$ MeV, $f_{B_s}/f_B = 1.16 (1) (2) (2) (^{+4}_{-0})$, $f_{D_s} = 241 (5) (^{+27}_{-26}) (^{+9}_{-4}) (^{+5}_{-0})$ MeV, and $f_{B}/f_{D_s} = 0.79 (2) (^{+5}_{-4}) (3) (^{+5}_{-0})$, where in each case the first error is statistical and the remaining three are systematic: the error within the partially quenched $N_f=2$ 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 $u,d$ 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 $\pi$ and $K$ 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 $a^2$ hairpin diagrams for taste-nonsinglet mesons, enter in the fits. To obtain precise results for the physical coefficients at order $p^4$, these new parameters will need to be bounded, at least roughly.Comment: talk presented by C. Bernard at Lattice2002(spectrum); 3 pages, 2 figure