Summing Over World-Sheet Boundaries

The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the embedding coordinates. A light-cone parameterization of such boundaries is also discussed.Comment: 10 page

Large NN Solution of the 2D Supersymmetric Yang-Mills Theory

The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented with some simple equations as consequence of supersymmetry, form a closed set of equations for Wilson loops and related quantities in the two dimensional super-gauge theory. We solve these equations. It appears that the planar Wilson loops are described by the Nambu string without folds. We also discuss how to put the model on a spatial lattice, where a peculiar gauge is chosen in order to keep one supersymmetry on the lattice. Supersymmetry is unbroken in this theory. We comment on possible generalization of these considerations to other models.Comment: 22 pages, 5 figures included, harvma

Abelian Decomposition of Sp(2N) Yang-Mills Theory

In the previous paper, we generalized the method of Abelian decomposition to the case of SO(N) Yang-Mills theory. This method that was proposed by Faddeev and Niemi introduces a set of variables for describing the infrared limit of a Yang-Mills theory. Here, we extend the decomposition method further to the general case of four-dimensional Sp(2N) Yang-Mills theory. We find that the Sp(2N) connection decomposes according to irreducible representations of SO(N).Comment: latex, 8 page

Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method

Two-photon and two-gluon annihilation rates of P-wave scalar charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. We solved the full Salpeter equation with a well defined relativistic wave function and calculated the transition amplitude using the Mandelstam formalism. Our model dependent estimates for the decay widths: $\Gamma(\chi_{c0} \to 2\gamma)=3.78$ keV, $\Gamma(\chi'_{c0} \to 2\gamma)=3.51$ keV, $\Gamma(\chi_{b0} \to 2\gamma)=48.8$ eV and $\Gamma(\chi'_{b0} \to 2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: $\Gamma_{tot}(\chi_{c0})=10.3$ MeV, $\Gamma_{tot}(\chi'_{c0})=9.61$ MeV, $\Gamma_{tot}(\chi_{b0})=0.887$ MeV and $\Gamma_{tot}(\chi'_{b0})=0.914$ MeV.Comment: 8 pages, 1 figure, 4 table

Radiative E1 decays of X(3872)

Radiative E1 decay widths of $\rm X(3872)$ are calculated through the relativistic Salpeter method, with the assumption that $\rm X(3872)$ is the $\chi_{c1}$(2P) state, which is the radial excited state of $\chi_{c1}$(1P). We firstly calculated the E1 decay width of $\chi_{c1}$(1P), the result is in agreement with experimental data excellently, then we calculated the case of $\rm X(3872)$ with the assignment that it is $\chi_{c1}$(2P). Results are: {\Gamma}({\rm X(3872)}\rightarrow \gamma \sl J/\psi)=33.0 keV, ${\Gamma}({\rm X(3872)}\rightarrow \gamma \psi(2S))=146$ keV and ${\Gamma}({\rm X(3872)}\rightarrow \gamma \psi(3770))=7.09$ keV. The ratio {{\rm Br(X(3872)}\rightarrow\gamma\psi(2{\rm S}))}/{{\rm Br(X(3872)}\rightarrow \gamma {\sl J}/\psi)}=4.4 agrees with experimental data by BaBar, but larger than the new up-bound reported by Belle recently. With the same method, we also predict the decay widths: ${\Gamma}(\chi_{b1}(1\rm P))\rightarrow \gamma \Upsilon(1\rm S))=30.0$ keV, ${\Gamma}(\chi_{b1}(2\rm P))\rightarrow \gamma \Upsilon(1\rm S))=5.65$ keV and ${\Gamma}(\chi_{b1}(2\rm P))\rightarrow \gamma \Upsilon(2S))=15.8$ keV, and the full widths: ${\Gamma}(\chi_{b1}(1\rm P))\sim 85.7$ keV, ${\Gamma}(\chi_{b1}(2\rm P))\sim 66.5$ keV.Comment: 9 pages, 4 figures, 2 tables, version to be published in Phys. Lett.

Is DsJ+(2632)D^{+}_{sJ}(2632) the first radial excitation of Ds∗(2112)D_{s}^{*}(2112)?

We present a quantitative analysis of the $D^{+}_{sJ}(2632)$ observed by SELEX mainly focusing on the assumption that $D^{+}_{sJ}(2632)$ is the first radial excitation of the $1^{-}$ ground state $D^{*}_{s}(2112)$. By solving the instantaneous Bethe-Salpeter equation, we obtain the mass $2658\pm 15$ MeV for the first excited state, which is about 26 MeV heavier than the experimental value $2632\pm 1.7$ MeV. By means of PCAC and low-energy theorem we calculate the transition matrix elements and obtain the decay widths: $\Gamma(D^{+}_{sJ}\to D^{+}_s\eta)=4.07\pm 0.34$ MeV, $\Gamma(D^{+}_{sJ}\to D^{0}K^{+}) \simeq \Gamma(\Gamma(D^{+}_{sJ}\to D^{+}K^{0})=8.9\pm 1.2$ MeV, and the ratio $\Gamma(D^{+}_{sJ}\to D^{0}K^{+})/\Gamma(D^{+}_{sJ}\to D^{+}_{s}\eta)=2.2\pm 0.2$ as well. This ratio is quite different from the SELEX data $0.14\pm 0.06$. The summed decay width of those three channels is approximately 21.7 MeV, already larger than the observed bound for the full width ($\leq 17$ MeV). Furthermore, assuming $D_{sJ}^+(2632)$ is $1^{-}$ state, we also explore the possibility of $S-D$ wave mixing to explain the SELEX observation. Based on our analysis, we suspect that it is too early to conclude that $D^{+}_{sJ}(2632)$ is the first radial excitation of the $1^{-}$ ground state $D^{*}_{s}(2112)$. More precise measurements of the relative ratios and the total decay width are urgently required especially for $S-D$ wave mixing.Comment: 12 pages, 8 figure

Strong Decays of the Radial Excited States B(2S)B(2S) and D(2S)D(2S)

The strong OZI allowed decays of the first radial excited states $B(2S)$ and $D(2S)$ are studied in the instantaneous Bethe-Salpeter method, and by using these OZI allowed channels we estimate the full decay widths: $\Gamma_{B^0(2S)}=24.4$ MeV, $\Gamma_{B^+(2S)}=23.7$ MeV, $\Gamma_{D^0(2S)}=11.3$ MeV and $\Gamma_{D^+(2S)}=11.9$ MeV. We also predict the masses of them: $M_{B^0(2S)}=5.777$ GeV, $M_{B^+(2S)}=5.774$ GeV, $M_{D^0(2S)}=2.390$ GeV and $M_{D^+(2S)}=2.393$ GeV.Comment: 6 pages, 1 figur

Compton scattering in a unitary approach with causality constraints

Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In the approach the effects of the non-pole contribution arising from pion dressing are expressed in terms of (half-off-shell) form factors and the nucleon self-energy. These quantities are constructed through the application of dispersion integrals to the pole contribution of loop diagrams, the same as those included in the calculation of the amplitudes through a K-matrix formalism. The prescription of minimal substitution is used to restore gauge invariance. The resulting relativistic-covariant model combines constraints from unitarity, causality, and crossing symmetry.Comment: 25 pages, 9 ps-figure

Nonperturbative Determination of Heavy Meson Bound States

In this paper we obtain a heavy meson bound state equation from the heavy quark equation of motion in heavy quark effective theory (HQET) and the heavy meson effective field theory we developed very recently. The bound state equation is a covariant extention of the light-front bound state equation for heavy mesons derived from light-front QCD and HQET. We determine the covariant heavy meson wave function variationally by minimizing the binding energy $\bar{\Lambda}$. Subsequently the other basic HQET parameters $\lambda_1$ and $\lambda_2$, and the heavy quark masses $m_b$ and $m_c$ can also be consistently determined.Comment: 15 pages, 1 figur

Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription

We find the exact non-perturbative expression for a simple Wilson loop of arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription. The result differs from the standard pure exponential area-law of YM_2, but still exhibits confinement as well as invariance under area-preserving diffeomorphisms and generalized axial gauge transformations. We show that the large N limit is NOT a good approximation to the model at finite N and conclude that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound state solutions. The main significance of our results derives from the importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE