Charm and Bottom Semileptonic Decays

We review the present status of theoretical attempts to calculate the semileptonic charm and bottom decays and then present a calculation of these decays in the light--front frame at the kinematic point $q^2=0$. This allows us to evaluate the form factors at the same value of $q^2$, even though the allowed kinematic ranges for charm and bottom decays are very different. Also, at this kinematic point the decay is given in terms of only one form factor $A_{0}(0)$. For the ratio of the decay rates given by the E653 collaboration we show that the determination of the ratio of the Cabibbo--Kobayashi--Maskawa (CKM) matrix elements is consistent with that obtained from the unitarity constraint. At present, though, the unitarity method still has greater accuracy. Since comparisons of the semileptonic decays into $\rho$ and either electrons or muons will be available soon from the E791 Fermilab experiment, we also look at the massive muon case. We show that for a range of $q^2$ the $SU(3)_F$ symmetry breaking is small even though the contributions of the various helicity amplitudes becomes more complicated. For $B$ decays, the decay $B \rightarrow K^{*} \ell \bar{\ell}$ at $q^2=0$ involves an extra form factor coming from the photon contribution and so is not amenable to the same kind of analysis, leaving only the decay $B \rightarrow K^{*}\nu \bar{\nu}$ as a possibility. As the mass of the decaying particle increases we note that the $SU(3)$ symmetry becomes badly broken at $q^2=0$.Comment: Latex, 19 pages, two figures are attached, a minor change in the manuscript related to thi

Transition Form Factors between Pseudoscalar and Vector Mesons in Light-Front Dynamics

We study the transition form factors between pseudoscalar and vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing the light-front calculation in the $q^+ =0$ frame in parallel with the manifestly covariant calculation, we note that the suspected nonvanishing zero-mode contribution to the light-front current $J^+$ does not exist in our analysis of transition form factors. We also perform the light-front calculation in a purely longitudinal $q^+ > 0$ frame and confirm that the form factors obtained directly from the timelike region are identical to the ones obtained by the analytic continuation from the spacelike region. Our results for the $B \to D^* l \nu_l$ decay process satisfy the constraints on the heavy-to-heavy semileptonic decays imposed by the flavor independence in the heavy quark limit.Comment: 20 pages, 14 figure

(D* to D + gamma) and (B* to B + gamma) as derived from QCD Sum Rules

The method of QCD sum rules in the presence of the external electromagnetic $F_{\mu\nu}$ field is used to analyze radiative decays of charmed or bottomed mesons such as $D^{\ast}\to D\gamma$ and $B^{\ast}\to B\gamma$, with the susceptibilities obtained previously from the study of baryon magnetic moments. Our predictions on $D^{\ast}$ decays agree very well with the experimental data. There are differences among the various theoretical predictions on $B^{\ast}$ decays but the data are not yet available.Comment: 11 pages, Late

Vertex functions for d-wave mesons in the light-front approach

While the light-front quark model (LFQM) is employed to calculate hadronic transition matrix elements, the vertex functions must be pre-determined. In this work we derive the vertex functions for all d-wave states in this model. Especially, since both of $^3D_1$ and $^3S_1$ are $1^{--}$ mesons, the Lorentz structures of their vertex functions are the same. Thus when one needs to study the processes where $^3D_1$ is involved, all the corresponding formulas for $^3S_1$ states can be directly applied, only the coefficient of the vertex function should be replaced by that for $^3D_1$. The results would be useful for studying the newly observed resonances which are supposed to be d-wave mesons and furthermore the possible 2S-1D mixing in $\psi'$ with the LFQM.Comment: 12 pages, 2 figures, some typos corrected and more discussions added. Accepted by EPJ

Possible explanation of the discrepancy of the light-cone QCD sum rule calculation of g(D*Dpi) coupling with experiment

The introduction of an explicit negative radial excitation contribution in the hadronic side of the light cone QCD sum rule (LCSR) of Belyaev, Braun, Khodjamirian and Ruckl, can explain the large experimental value of g(D*Dpi), recently measured by CLEO. At the same time, it considerably improves the stability of the sum rule when varying the Borel parameter.Comment: 9 pages, 1 PostScript 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

Isospin-mixing corrections for fp-shell Fermi transitions

Isospin-mixing corrections for superallowed Fermi transitions in {\it fp}-shell nuclei are computed within the framework of the shell model. The study includes three nuclei that are part of the set of nine accurately measured transitions as well as five cases that are expected to be measured in the future at radioactive-beam facilities. We also include some new calculations for $^{10}$C. With the isospin-mixing corrections applied to the nine accurately measured $ft$ values, the conserved-vector-current hypothesis and the unitarity condition of the Cabbibo-Kobayashi-Maskawa (CKM) matrix are tested.Comment: 13 pages plus five tables. revtex macro

Light-Front Approach for Heavy Pentaquark Transitions

Assuming the two diquark structure for the pentaquark state as advocated in the Jaffe-Wilczek model, there exist exotic parity-even anti-sextet and parity-odd triplet heavy pentaquark baryons. The theoretical estimate of charmed and bottom pentaquark masses is quite controversial and it is not clear whether the ground-state heavy pentaquark lies above or below the strong-decay threshold. We study the weak transitions of heavy pentaquark states using the light-front quark model. In the heavy quark limit, heavy-to-heavy pentaquark transition form factors can be expressed in terms of three Isgur-Wise functions: two of them are found to be normalized to unity at zero recoil, while the third one is equal to 1/2 at the maximum momentum transfer, in accordance with the prediction of the large-Nc approach or the quark model. Therefore, the light-front model calculations are consistent with the requirement of heavy quark symmetry. Numerical results for form factors and Isgur-Wise functions are presented. Decay rates of the weak decays Theta_b+ to Theta_c0 pi+ (rho+), Theta_c0 to Theta+ pi- (rho-), Sigma'_{5b}+ to Sigma'_{5c}0 pi+ (rho+) and Sigma'_{5c}0 to N_8+ pi- (rho-) with Theta_Q, Sigma'_{5Q} and N_8 being the heavy anti-sextet, heavy triplet and light octet pentaquarks, respectively, are obtained. For weakly decaying Theta_b+ and Theta_c0, the branching ratios of Theta_b+ to Theta_c0 pi+, Theta_c0 to Theta+ pi- are estimated to be at the level of 10^{-3} and a few percents, respectively.Comment: 33 pages, 3 figures, version to be published in Phys. Rev.

Consistent treatment of spin-1 mesons in the light-front formalism

We analyze the matrix element of the electroweak current between q \qb vector meson states in the framework of a covariant extension of the light-front formalism. The light-front matrix element of a one-body current is naturally associated with zero modes, which affect some of the form factors that are necessary to represent the Lorentz structure of the light-front integral. The angular condition contains some information on zero modes, i.e., only if the effect of zero modes is accounted for correctly, is it satisfied. With plausible assumptions we derive from the angular condition several consistency conditions which can be used quite generally to determine the zero mode contribution of form factors. The correctness of this method is tested by the phenomenological success of the derived form factors. We compare the predictions of our formalism with those of the standard light-front approach and with available data. As examples we discuss the magnetic moment of the $\rho$, the coupling constant $g_{D^\ast D \pi}$, and the coupling constants of the pseudoscalar density, $g_\pi$ and $g_K$, which provide a phenomenological link between constituent and current quark masses.Comment: 36 pages, figure 1 is include

Study of Radiative Leptonic D Meson Decays

We study the radiative leptonic $D$ meson decays of D^+_{(s)}\to \l^+\nu_{\l}\gamma (\l=e,\mu,\tau), $D^0\to \nu\bar{\nu}\gamma$ and D^0\to \l^+\l^-\gamma ($l=e,\mu$) within the light front quark model. In the standard model, we find that the decay branching ratios of $D^+_{(s)}\to e^+\nu_e\gamma$, $D^+_{(s)}\to\mu^+\nu_{\mu}\gamma$ and $D^+_{(s)}\to\tau^+\nu_{\tau}\gamma$ are $6.9\times 10^{-6}$ ($7.7\times 10^{-5}$), $2.5\times 10^{-5}$ ($2.6\times 10^{-4}$), and $6.0\times 10^{-6}$ ($3.2\times 10^{-4}$), and that of D^0\to\l^+\l^-\gamma (\l=e,\mu) and $D^0\to\nu\bar{\nu}\gamma$ are $6.3\times 10^{-11}$ and $2.7\times 10^{-16}$, respectively.Comment: 23 pages, 6 Figures, LaTex file, a reference added, to be published in Mod. Phys. Lett.