Schr\"odinger Equation for Heavy Mesons Expanded in 1/mQ1/m_Q

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schr\"odinger equation for $Q\bar q$ bound states described by a hamiltonian, we systematically develop a perturbation theory in $1/m_Q$ which enables one to solve the Schr\"odinger equation to obtain masses and wave functions of the bound states in any order of $1/m_Q$. It is shown that positive energy projection with respect to the heavy quark sector of a wave function is, at each order of perturbation, proportional to the 0-th order solution. There appear also negative components of the wave function except for the 0-th order, which contribute also to higher order corrections to masses.Comment: 14 pages, uses REVTeX style file

Spectroscopy and Decays of Heavy Mesons

Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with experimental data for $D/B$ mesons at each level of perturbation. Meson wave functions obtained thereby can be used to calculate ordinary form factors as well as Isgur-Wise functions for semileptonic weak decays and other physical quantities. All the above calculations are expanded in $1/m_Q$ order by order to determine parameters as well as to compare with results of Heavy Quark Effective Theory.Comment: 4 page

Chiral Particle Decay of Heavy-Light Mesons in a Relativistic Potential Model

Partial decay widths of the heavy-light mesons, $D, D_s, B,$ and $B_s$, emitting one chiral particle ($\pi$ or $K$) are evaluated in the framework of a relativistic potential model. Decay amplitudes are calculated by keeping the Lorentz invariance as far as possible and use has been made of the Lorentz-boosted relativistic wave functions of the heavy-light mesons. One of predictions of our calculation is very narrow widths of a few keV for yet undsicovered $B_s(0^+, 1^+)$ mesons corresponding to ${^{2S+1}L_J}={^3P_0}$ and $"{^3P_1}"$ assuming their masses to be 5617 and 5682 MeV, respectively, as calculated in our former paper. In the course of our calculation, new sum rules are discovered on the decay widths in the limit of $m_Q\to \infty$. Among these rules, $\Gamma(D_{s0}^*(2317)\to D_s+\pi)=\Gamma (D_{s1}(2460)\to D_s^*+\pi)$ and $\Gamma(B_{s0}^*(5615)\to B_s+\pi)=\Gamma (B_{s1}(5679)\to B_s^*+\pi)$ are predicted to hold with a good accuracy.Comment: 14pages, 6table

Consistent Definitions of Flux and Electric and Magnetic Current in Abelian Projected SU(2) Lattice Gauge Theory

Through the use of a lattice U(1) Ward-Takahashi identity, one can find a precise definition of flux and electric four-current that does not rely on the continuum limit. The magnetic four-current defined for example by the DeGrand-Toussaint construction introduces order a^2 errors in the field distributions. We advocate using a single definition of flux in order to be consistent with both the electric and magnetic Maxwell's equations at any lattice spacing. In a U(1) theory the monopoles are slightly smeared by this choice, i.e. are no longer associated with a single lattice cube. In Abelian projected SU(2) the consistent definition suggests further modifications. For simulations in the scaling window, we do not foresee large changes in the standard analysis of the dual Abrikosov vortex in the maximal Abelian gauge because the order a^2 corrections have small fluctuations and tend to cancel out. However in other gauges, the consequences of our definitions could lead to large effects which may help in understanding the choice of gauge. We also examine the effect of truncating all monopoles except for the dominant cluster on the profile of the dual Abrikosov vortex.Comment: 12 pages, 4 eps figures, Confinement 2003 contributed tal

Is the Z^+(4430) a radially excited state of D_s?

We present the interpretation that the recently discovered Z^+(4430) by the Belle Collaboration can be a radial excitation of the cs-bar state. We give an explicit cs-bar candidate for this state by calculating the mass value in our semirelativistic quark potential model and also give a natural interpretation on the reason why the decay mode Z-> J/\psi \pi^+ has not yet been seen while Z-> \psi' \pi can be seen.Comment: 6 pages, 4 figure

Mixing angle between 3P1^3P_1 and 1P1^1P_1 in HQET

Some claim that there are two independent mixing angles ($\theta = 35.3^\circ$, $-54.7^\circ$) between $^3P_1$ and $^1P_1$ states of heavy-light mesons in heavy quark symmetric limit, and others claim there is only one ($\theta = 35.3^\circ$). We clarify the difference between these two and suggest which should be adopted. General arguments on the mixing angle between $^3L_L$ and $^1L_L$ of heavy-light mesons are given in HQET and a general relation is derived in heavy quark mass limit as well as that including the first order correction in $1/m_Q$.Comment: 6 pages, 1 tabl

Decay properties of the heavy-light mesons

We study the decay properties of a heavy-light meson. We reformulate the decay amplitudes for the heavy-light systems and find a new way to calculate decay rates. Applying this formulation, we find a new sum rule for the radiative decays of one heavy-light meson into another, $H_1\to H_2+\gamma$ with various combinations of $H_i$.Comment: an invited talk at "New Frontiers in QCD 2010" held at Kyot