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

Bounds on Heavy-to-Heavy Mesonic Form Factors

We provide upper and lower bounds on the form factors for B -> D, D^* by utilizing inclusive heavy quark effective theory sum rules. These bounds are calculated to leading order in Lambda_QCD/m_Q and alpha_s. The O(alpha_s^2 beta_0) corrections to the bounds at zero recoil are also presented. We compare our bounds with some of the form factor models used in the literature. All the models we investigated failed to fall within the bounds for the combination of form factors (omega^2 - 1)/(4 omega)|omega h_{A2}+h_{A3}|^2.Comment: 27 pages, 10 figure

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

Large-basis shell-model calculation of 10C->10B Fermi matrix element

We use a $4\hbar\Omega$ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the 10C->10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of T=1 partial waves. Our results suggest the isospin- mixing correction $\delta_{C}\approx 0.1$, which is compatible with previous calculations. The correction obtained in those calculations, performed in a $0\hbar\Omega$ space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained $\delta_{C}$ correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.Comment: 14 pages. REVTEX. 3 PostScript figure

Calculated corrections to superallowed Fermi beta decay: New evaluation of the nuclear-structure-dependent terms

The measured $ft$-values for superallowed $0^{+} \to 0^{+}$ nuclear $\beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by more than two standard deviations -- but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.Comment: Revtex4, one figur

A consistent treatment for pion form factors in space-like and time-like regions

We write down some relevant matrix elements for the scattering and decay processes of the pion by considering a quark-meson vertex function. The pion charge and transition form factors $F_\pi$, $F_{\pi\gamma}$, and $F_{\pi\gamma^*}$ are extracted from these matrix elements using a relativistic quark model on the light-front. We found that, the form factors $F_\pi$ and $F_{\pi\gamma}$ in the space-like region agree well with experiment. Furthermore, the branching ratios of all observed decay modes of the neutral pion, that are related to the form factors $F_{\pi\gamma}$ and $F_{\pi\gamma^*}$ in the time-like region, are all consistent with the data as well. Additionally, $F_\pi$ in the time-like region, which deals with the nonvalence contribution, is also discussed.Comment: 24 pages, 6 figures, to appear in Phys. Rev.

Weak Decays in the light--front Quark Model

We study the form factors of heavy--to--heavy and heavy--to--light weak decays using the light--front relativistic quark model. For the heavy--to--heavy B \ra D^{(\ast)} semileptonic decays we calculate the corresponding Isgur--Wise function for the whole kinematic region. For the heavy--to--light B\ra P and B\ra V semileptonic decays we calculate the form factors at $q^2 = 0$; in particular, we have derived the dependence of the form factors on the $b$--quark mass in the m_b \ra \infty limit. This dependence can not be produced by extrapolating the scaling behavior of the form factors at $q^2_{max}$ using the single--pole assumption. This shows that the $q^2$ dependence of the form factors in regions far away from the zero--recoil could be much more complicated than that predicted by the single--pole assumption.Comment: 24 pages, Latex, Postscript figure included at the en

The exclusive \bar{B} --> \pi e^+ e^- and \bar{B} --> \rho e^+ e^- decays in the two Higgs doublet model with flavor changing neutral currents

We calculate the leading logarithmic QCD corrections to the matrix element of the decay b --> d e^+ e^- in the two Higgs doublet model with tree level flavor changing currents (model III). We continue studying the differential branching ratio and the CP violating asymmetry for the exclusive decays B --> \pi e^+ e^- and B --> \rho e^+ e^- and analysing the dependencies of these quantities on the selected model III parameters, \xi^{U,D}, including the leading logarithmic QCD corrections. Further, we present the forward-backward asymmetry of dileptons for the decay B --> \rho e^+ e^- and discuss the dependencies to the model III parameters. We observe that there is a possibility to enhance the branching ratios and suppress the CP violating effects for both decays in the framework of the model III. Therefore, the measurements of these quantities will be an efficient tool to search the new physics beyond the SM.Comment: 27 pages, 14 Figure

Charge form factor of π\pi and KK mesons

The charge form factor of $\pi$ and $K$ mesons is evaluated adopting a relativistic constituent quark model based on the light-front formalism. The relevance of the high-momentum components of the meson wave function, for values of the momentum transfer accessible to $CEBAF$ energies, is illustrated. The predictions for the elastic form factor of $\pi$ and $K$ mesons are compared with the results of different relativistic approaches, showing that the measurements of the pion and kaon form factors planned at $CEBAF$ could provide information for discriminating among various models of the meson structure.Comment: 8 pages, latex, 4 figures available as separate .uu fil

The transition form factors for semi-leptonic weak decays of J/ψJ/\psi in QCD sum rules

Within the Standard Model, we investigate the semi-leptonic weak decays of $J/\psi$. The various form factors of $J/\psi$ transiting to a single charmed meson ($D^{(*)}_{(d,s)}$) are studied in the framework of the QCD sum rules. These form factors fully determine the rates of the weak semi-leptonic decays of $J/\psi$ and provide valuable information about the non-perturbative QCD effects. Our results indicate that the decay rate of the semi-leptonic weak decay mode $J/\psi \to D^{(*)-}_{s}+e^{+}+\nu_{e}$ is at order of $10^{-10}$.Comment: 28 pages, 6 figures, revised version to be published in Eur.Phys.J.