Lower limit in semiclassical form for the number of bound states in a central potential

We identify a class of potentials for which the semiclassical estimate $N^{\text{(semi)}}=\frac{1}{\pi}\int_0^\infty dr\sqrt{-V(r)\theta[-V(r)]}$ of the number $N$ of (S-wave) bound states provides a (rigorous) lower limit: $N\ge {{N^{\text{(semi)}}}}$, where the double braces denote the integer part. Higher partial waves can be included via the standard replacement of the potential $V(r)$ with the effective $\ell$-wave potential $V_\ell^{\text{(eff)}}(r)=V(r)+\frac{\ell(\ell+1)}{r^2}$. An analogous upper limit is also provided for a different class of potentials, which is however quite severely restricted.Comment: 9 page

Upper limit on the critical strength of central potentials in relativistic quantum mechanics

In the context of relativistic quantum mechanics, where the Schr\"odinger equation is replaced by the spinless Salpeter equation, we show how to construct a large class of upper limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant, $g$, of the central potential, $V(r)=-g v(r)$. This critical value is the value of $g$ for which a first $\ell$-wave bound state appears.Comment: 8 page

Lower bounds for the spinless Salpeter equation

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in $L^p(\R^n)$ for some $p>n$ ($n=1$ or 3). An extension to confining potentials, which are not in $L^p(\R^n)$, is also presented.Comment: 11 pages, 2 figures. Contribution to a special issue of Journal of Nonlinear Mathematical Physics in honour of Francesco Calogero on the occasion of his seventieth birthda

Upper limit on the number of bound states of the spinless Salpeter equation

We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case ($m=0$), for the existence of at least one $\ell$-wave bound states: $C(\ell,p/(p-1))$ $\int_0^{\infty}dr r^{p-1} |V^-(r)|^p\ge 1$, where $C(\ell,p/(p-1))$ is a known function of $\ell$ and $p>1$.Comment: 18 page

B decays to final states including D_s^{(*)} and D^*

The e^+e^- annihilation data recorded with the BABAR detector has been used to study B decays to D_s^(*) and D^* mesons. The production fraction of inclusive D_s^(*) and the corresponding momentum spectra have been determined. Exclusive decays B^0 --> D^{*-}D_s^{(*)+} have been identified with a partial reconstruction technique and their branching fractions have been measured. We also report branching fraction measurements for the exclusive hadronic modes B^0 --> D^{*-} pi^+ and B^0 --> D^{*-} rho^+.Comment: 5 pages, 4 postscript figures, contributed paper to DPF200

Scattering solutions of the spinless Salpeter equation

A method to compute the scattering solutions of a spinless Salpeter equation (or a Schrodinger equation) with a central interaction is presented. This method relies on the 3-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same grid points. It can be easily extended to the case of coupled channel equations and to the case of non-local interactions.Comment: 7 page

A Measurement of the Ratio of the W + 1 Jet to Z + 1 Jet Cross Sections with ATLAS

The measurement of hadronic activity recoiling against W and Z vector bosons provides an important test of perturbative QCD, as well as a method of searching for new physics in a model independent fashion. We present a study of the cross-section ratio for the production of W and Z gauge bosons in association with exactly one jet Rjet = {\sigma}(W + 1jet)/{\sigma}(Z + 1jet), in pp collisions at \surds = 7 TeV. The study is performed in the electron and muon channels with data collected with the ATLAS detector at the LHC. The ratio Rjet is studied as a function of the cumulative transverse momentum distribution of the jet. This result can be compared to NLO pQCD calculations and the prediction from LO matrix element + parton shower generators.Comment: 8 pages, 4 figures, conference proceedings for DPF 201