Vector vibrations and the Ioffe-Regel crossover in disordered lattices

The spectral density for vector vibrations in the f.c.c. lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and compared with that for electrons. The weak-scattering regime for external long-wavelength vibrational plane waves is shown to be due to sum-rule correlations in the dynamical matrix. A secondary peak below the Brillouin peak for sufficiently large wavevectors is found for the lattice models. The results obtained are supported by precise numerical solutions.Comment: 21 pages, 13 figure

Renormalizing Heavy Quark Effective Theory at O(1/m_Q^3)

We present a calculation of the renormalized HQET Lagrangian at order O(1/m_Q^3) in the one particle sector. The anomalous dimensions of local operators and time ordered products of dimension 7 contributing at this order are calculated in the one loop approximation. We show that a careful treatment of the time ordered products is necessary to arrive at a gauge independent renormalized lagrangian. Our result sets the stage for an investigation of reparametrization invariance at O(1/m_Q^3).Comment: Latex, epsfig. Improved teXnology and modified conclusions. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Reparameterization Invariance Revisited

Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on operators that do not vanish under the equation of motion to order $1/m^2$, and to be related by a redefinition of the heavy quark field. We give a new, very straightforward proof that that the reparameterization invariance constraints apply to all orders in $\alpha_s$ under matching to full QCD and renormalization-group running, at least up to and including $O(1/m^2)$.Comment: 20 pages, no figures, Latex. Revised version: Discussion of reparameterization invariance constraints on class-II operators adde

Nature of vibrational eigenmodes in topologically disordered solids

We use a local projectional analysis method to investigate the effect of topological disorder on the vibrational dynamics in a model glass simulated by molecular dynamics. Evidence is presented that the vibrational eigenmodes in the glass are generically related to the corresponding eigenmodes of its crystalline counterpart via disorder-induced level-repelling and hybridization effects. It is argued that the effect of topological disorder in the glass on the dynamical matrix can be simulated by introducing positional disorder in a crystalline counterpart.Comment: 7 pages, 6 figures, PRB, to be publishe

Contributions of order O(mquark2){\cal O}(m_{\rm quark}^2) to Kℓ3K_{\ell 3} form factors and unitarity of the CKM matrix

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays

The Determination of alpha_s from Tau Decays Revisited

We revisit the determination of alpha_s(m_tau) using a fit to inclusive tau hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K_4 in the expansion of the Adler function, (2) new precision measurements from BABAR of e+e- annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on tau branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction and show that the effect of the incomplete knowledge of the series is reduced by using the so-called contour-improved calculation, as opposed to fixed-order perturbation theory which manifests convergence problems. The corresponding theoretical uncertainties are studied at the tau and Z mass scales. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit gives alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007, where the first error is experimental and the second theoretical. After evolution to M_Z we obtain alpha_s(M_Z) = 0.1212 +- 0.0005 +- 0.0008 +- 0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding NNNLO value derived from essentially the Z width in the global electroweak fit. The alpha_s(M_Z) determination from tau decays is the most precise one to date.Comment: 22 pages, 7 figure

Spectator Effects in Heavy Quark Effective Theory at O(1/m_Q^3)

We complete the one loop renormalization of the HQET lagrangian at O(1/m_Q^3) including four fermion operators with two heavy and two light quark fields in the operator basis. It is shown that as a consequence the short distance coefficients of the operators bilinear in the heavy quark field receive nontrivial corrections.Comment: Latex, Latex-extension epsfig. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints

Study of 3-prong Hadronic τ\tau Decays with Charged Kaons

Using a sample of 4.7/fb integrated luminosity accumulated with the CLEO-II detector at the Cornell Electron Storage Ring (CESR), we have measured the branching fractions of the tau lepton into $K^- h^+ \pi^- \nu_\tau$ and $K^- K^+ \pi^- \nu_\tau$ relative to $h^- h^+ h^- \nu_\tau; K^- h^+ \pi^- \pi^0\nu_\tau$ and $K^- K^+ \pi^- \pi^0\nu_\tau$ relative to $h^- h^+ h^- \pi^0 \nu_\tau$. The relative branching fractions are: (5.16+-0.20+-0.50)*$10^{-2}$, (1.52+-0.14+-0.29)*$10^{-2}$, (2.54+-0.44+-0.39)*$10^{-2}$ and $<0.0154$ at 95% C.L., respectively. Coupled with additional experimental information, we use our results to extract information on the structure of three-prong tau decays to charged kaons.Comment: 16 pages postscript file also available through http://w4.lns.cornell.edu/public/CLN

tau-->eta(eta')2pi nu, 3pi nu and WZW anomaly

The effects of the anomalous contact terms are taken into account in tau to eta(eta')2pi nu decay. tau to 3pi nu is computed. Theoretical result agrees with data. It is the first time the anomalous vertex eta aa is tested. An a_{1} resonance is predicted in the final state. The decay rate of tau to eta'3pi nu is predicted.Comment: 15 pages, one latex file for the paper and one p-script file for the figur