Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve a Bethe-Salpeter (BS) equation exactly without any approximation if the kernel of the BS equation exactly is instantaneous, and take positronium as an example to illustrate the general features of the solutions. As a middle stage, a set of coupled and self-consistent integration equations for a few scalar functions can be equivalently derived from the BS equation always, which are solvable accurately. For positronium, precise corrections to those of the Schr\"odinger equation in order $v$ (relative velocity) in eigenfunctions, in order $v^2$ in eigenvalues, and the possible mixing, such as that between $S$ ($P$) and $D$ ($F$) components in $J^{PC}=1^{--}$ ($J^{PC}=2^{++}$) states as well, are determined quantitatively. Moreover, we also point out that there is a problematic step in the classical derivation which was proposed first by E.E. Salpeter. Finally, we emphasize that for the effective theories (such as NRQED and NRQCD etc) we should pay great attention on the corrections indicated by the exact solutions.Comment: 4 pages, replace for shortening the manuscrip

QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson

The QCD radiative corrections to the leptonic decay rate of the $B_c$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The $B_c$ decay constant is factored into a sum of NRQCD matrix elements each multiplied by a short-distance coefficient. The short-distance coefficient for the leading matrix element is calculated to order $\alpha_s$ by matching a perturbative calculation in full QCD with the corresponding perturbative calculation in NRQCD. This short-distance correction decreases the leptonic decay rate by approximately $15\%$.Comment: Changed Eq. 2 to read 1/(8 \pi), put in a missing i M_{B_c} in Eq. 18, and put in a normalisation factor of 2 M_{B_c} in Eq. 19

CP Violation from Dimensional Reduction: Examples in 4+1 Dimensions

We provide simple examples of the generation of complex mass terms and hence CP violation through dimensional reduction.Comment: 6 pages, typos corrected, 1 reference adde

Poor screening and nonadiabatic superconductivity in correlated systems

In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half-filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the $T_c$-$\delta$ phase diagram of cuprates. Experimental evidences are also discussed.Comment: 12 Pages, 6 Figures, Accepted on Physical Review

Hadron yields and spectra in Au+Au collisions at the AGS

Inclusive double differential multiplicities and rapidity density distributions of hadrons are presented for 10.8 A GeV/c Au+Au collisions as measured at the AGS by the E877 collaboration. The results indicate that large amounts of stopping and collective transverse flow effects are present. The data are also compared to the results from the lighter Si+Al system.Comment: 12 pages, latex, 10 figures, submitted to Nuclear Physics A (Quark Matter 1996 Proceedings

Nonequilibrium Evolution of Correlation Functions: A Canonical Approach

We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analog of the $\phi^{4}$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to ${\cal O}(\lambda^2)$. These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established and the physical implications of the set of equations are discussed with particular emphasis on thermalization.Comment: Revtex, 32 pages; substantial new material dealing with non-equilibrium evolution beyond Hartree approx. based on the LvN formalism, has been adde

Measurement of the D+ and Ds+ decays into K+K-K+

We present the first clear observation of the doubly Cabibbo suppressed decay D+ --> K-K+K+ and the first observation of the singly Cabibbo suppressed decay Ds+ --> K-K+K+. These signals have been obtained by analyzing the high statistics sample of photoproduced charm particles of the FOCUS(E831) experiment at Fermilab. We measure the following relative branching ratios: Gamma(D+ --> K-K+K+)/Gamma(D+ --> K-pi+pi+) = (9.49 +/- 2.17(statistical) +/- 0.22(systematic))x10^-4 and Gamma(Ds+ --> K-K+K+)/Gamma(Ds+ --> K-K+pi+) = (8.95 +/- 2.12(statistical) +2.24(syst.) -2.31(syst.))x10^-3.Comment: 10 pages, 8 figure

New Measurements of the D+ to K* mu nu Form Factor Ratios

Using a large sample of D+ to K- pi+ mu+ nu decays collected by the FOCUS photoproduction experiment at Fermilab, we present new measurements of two semileptonic form factor ratios: rv and r2. We find rv = 1.504 \pm 0.057 \pm 0.039 and r2 = 0.875 \pm 0.049 \pm 0.064. Our form factor results include the effects of the s-wave interference discussed in a previous paper.Comment: 12 pages, 5 figure

Study of Hadronic Five-Body Decays of Charmed Mesons

We study the decay of D+ and Ds+ mesons into charged five body final states, and report the discovery of the decay mode D+ -> K+K-Pi+Pi+Pi-, as well as measurements of the decay modes D+ -> K-Pi+Pi+Pi+Pi-, Ds+ -> K+K-Pi+Pi+Pi-, Ds+ -> PhiPi+Pi+Pi- and D+/Ds+ -> Pi+Pi+Pi+Pi-Pi-. An analysis of the resonant substructure is also included, with evidence suggesting that both decays proceed primarily through an a1 vector resonance.Comment: 11 pages, 3 figure

Observation of a 1750 MeV/c^2 Enhancement in the Diffractive Photoproduction of K^+K^-

Using the FOCUS spectrometer with photon beam energies between 20 and 160 \gev, we confirm the existence of a diffractively photoproduced enhancement in $K^+K^-$ at 1750 \mevcc with nearly 100 times the statistics of previous experiments. Assuming this enhancement to be a single resonance with a Breit-Wigner mass shape, we determine its mass to be $1753.5\pm 1.5\pm 2.3$ \mevcc and its width to be $122.2\pm 6.2\pm 8.0$ \mevcc. We find no corresponding enhancement at 1750 \mevcc in $K^*K$, and again neglecting any possible interference effects we place limits on the ratio $\Gamma (X(1750) \to K^*K)/\Gamma (X(1750) \to K^+K^-)$. Our results are consistent with previous photoproduction experiments, but, because of the much greater statistics, challenge the common interpretation of this enhancement as the $\phi (1680)$ seen in $e^+e^-$ annihilation experiments.Comment: 10 pages, 5 figure