A variational method from the variance of energy

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second order extension of the gaussian effective potential.Comment: 5 ps figure

Renormalization-Group flow for the field strength in scalar self-interacting theories

We consider the Renormalization-Group coupled equations for the effective potential V(\phi) and the field strength Z(\phi) in the spontaneously broken phase as a function of the infrared cutoff momentum k. In the k \to 0 limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(\phi), indicates a sharp peaking of Z(\phi) close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.Comment: 10 pages, 3 Figures, version accepted for publication in Phys. Lett.

Perturbation Theory with a Variational Basis: the Generalized Gaussian Effective Potential

The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial dimensions. The problem of the renormalization of the mass is discussed in details. Thermal corrections are incorporated. The comparison between the finite temperature generalized Gaussian effective potential and the finite temperature effective potential is critically analyzed. The phenomenon of the restoration at high temperature of the symmetry broken at zero temperature is discussed.Comment: RevTex, 49 pages, 16 eps figure

Wave functions and decay constants of BB and DD mesons in the relativistic potential model

With the decay constants of $D$ and $D_s$ mesons measured in experiment recently, we revisit the study of the bound states of quark and antiquark in $B$ and $D$ mesons in the relativistic potential model. The relativistic bound state wave equation is solved numerically. The masses, decay constants and wave functions of $B$ and $D$ mesons are obtained. Both the masses and decay constants obtained here can be consistent with the experimental data. The wave functions can be used in the study of $B$ and $D$ meson decays.Comment: more discussion added, to appear in EPJ

The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files

Using Heavy Quark Spin Symmetry in Semileptonic BcB_c Decays

The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.Comment: RevTex, 22 pages, 2 figure

Semileptonic and nonleptonic B decays to three charm quarks: B->J/psi (eta_c) D l nu and J/psi (eta_c) D pi

We evaluate the form factors describing the semileptonic decays $\bar{B^0}\to J/\psi (\eta_c) D^+ \ell^- \bar \nu_\ell$, within the framework of a QCD relativistic potential model. This decay is complementary to $\bar{B^0}\to J/\psi (\eta_c) D^+ \pi^-$ in a phase space region where a pion factors out.We estimate the branching ratio for these semileptonic and nonleptonic channels, finding $\mathcal{BR}(\bar{B^0} \to J/\psi (\eta_c) D^+ \ell \nu_\ell) \simeq 10^{-13}$, $\mathcal{BR}(\bar{B^0} \to J/\psi D^+ \pi^-) = 3.1 \times 10^{-8}$ and $\mathcal{BR}(\bar{B^0} \to \eta_c D^+ \pi^-) = 3.5 \times 10^{-8}$.Comment: 14 pages, 4 figure

Covariant Light-Front Approach for s-wave and p-wave Mesons: Its Application to Decay Constants and Form Factors

We study the decay constants and form factors of the ground-state s-wave and low-lying p-wave mesons within a covariant light-front approach. Numerical results of the form factors for transitions between a heavy pseudoscalar meson and an s-wave or p-wave meson and their momentum dependence are presented in detail. In particular, form factors for heavy-to-light and B to D** transitions, where D** denotes generically a p-wave charmed meson, are compared with other model calculations. The experimental measurements of the decays B^- to D** pi^- and B to D D**_s are employed to test the decay constants of D**_s and the B to D** transition form factors. The heavy quark limit behavior of the decay constants and form factors is examined and it is found that the requirement of heavy quark symmetry is satisfied. The universal Isgur-Wise (IW) functions, one for s-wave to s-wave and two for s-wave to p-wave transitions, are obtained. The values of IW functions at zero recoil and their slope parameters can be used to test the Bjorken and Uraltsev sum rules.Comment: 59 pages, 6 figures. Version to appear in Phys. Rev. D. Changes are: (i) D_s to phi transition form factors are discussed and compared with the recent FOCUS measurements and (ii) zero mode effects are clarifie

A Grand Canonical Ensemble Approach to the Thermodynamic Properties of the Nucleon in the Quark-Gluon Coupling Model

In this paper, we put forward a way to study the nucleon's thermodynamic properties such as its temperature, entropy and so on, without inputting any free parameters by human hand, even the nucleon's mass and radius. First we use the Lagrangian density of the quark gluon coupling fields to deduce the Dirac Equation of the quarks confined in the gluon fields. By boundary conditions we solve the wave functions and energy eigenvalues of the quarks, and thus get energy-momentum tensor, nucleon mass, and density of states. Then we utilize a hybrid grand canonical ensemble, to generate the temperature and chemical potentials of quarks, antiquarks of three flovars by the four conservation laws of the energy and the valence quark numbers, after which, all other thermodynamic properties are known. The only seemed free paremeter, the nucleon radius is finally determined by the grand potential minimal principle.Comment: 5 pages, LaTe

The Star-Forming Galaxy Contribution to the Cosmic MeV and GeV Gamma-Ray Background

While star-forming galaxies could be major contributors to the cosmic GeV $\gamma$-ray background, they are expected to be MeV-dim because of the "pion bump" falling off below ~100 MeV. However, there are very few observations of galaxies in the MeV range, and other emission processes could be present. We investigate the MeV background from star-forming galaxies by running one-zone models of cosmic ray populations, including Inverse Compton and bremsstrahlung, as well as nuclear lines (including $^{26}$Al), emission from core-collapse supernovae, and positron annihilation emission, in addition to the pionic emission. We use the Milky Way and M82 as templates of normal and starburst galaxies, and compare our models to radio and GeV--TeV $\gamma$-ray data. We find that (1) higher gas densities in high-z normal galaxies lead to a strong pion bump, (2) starbursts may have significant MeV emission if their magnetic field strengths are low, and (3) cascades can contribute to the MeV emission of starbursts if they emit mainly hadronic $\gamma$-rays. Our fiducial model predicts that most of the unresolved GeV background is from star-forming galaxies, but this prediction is uncertain by an order of magnitude. About ~2% of the claimed 1 MeV background is diffuse emission from star-forming galaxies; we place a firm upper limit of <~10% based on the spectral shape of the background. The star-formation contribution is constrained to be small, because its spectrum is peaked, while the observed background is steeply falling with energy through the MeV-GeV range.Comment: Published in ApJ, 27 pages, emulateapj format. Readers may be interested in the concurrent paper by Chakraborty and Fields (arXiv:1206.0770), a calculation of the Inverse Compton background from star-forming galaxie