We show that the exclusive decay B→ K^∗γ can be related to the semileptonic decay B→ρ eν̅ using heavy-quark symmetry and SU(3) flavor symmetry. A direct measurement of the q^2-spectrum for the semileptonic decay can provide relevant information for the exclusive rare decay.

We consider nonleptonic Cabibbo-allowed ${\ensuremath{\Lambda}}_{b}$ decays in the factorization approximation. We calculate nonleptonic decays of the type ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}P$ and ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}V$ relative to $\overline{{B}_{d}^{0}}\ensuremath{\rightarrow}{D}^{+}P$ and $\overline{{B}_{d}^{0}}\ensuremath{\rightarrow}{D}^{+}V$ where we include among the pseudoscalar states and the vector states the newly discovered ${D}_{s}$ resonances, ${D}_{s}(2317)$ and ${D}_{s}(2460).$ In the ratio of ${\ensuremath{\Lambda}}_{b}$ decays to ${D}_{s}(2317)$ and ${D}_{s}(2460)$ relative to the $\overline{{B}_{d}^{0}}$ decays to these states, the poorly known decay constants of ${D}_{s}(2317)$ and ${D}_{s}(2460)$ cancel, leading to predictions that can shed light on the nature of these new states. In general, we predict the ${\ensuremath{\Lambda}}_{b}$ decays to be larger than the corresponding $\overline{{B}_{d}^{0}}$ decays and in particular we find the branching ratio for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}{D}_{s}(2460)$ can be between four to five times the branching ratio for $\overline{{B}_{d}^{0}}\ensuremath{\rightarrow}{D}^{+}{D}_{s}(2460).$ This enhancement of ${\ensuremath{\Lambda}}_{b}$ branching ratios follows primarily from the fact that more partial waves contribute in ${\ensuremath{\Lambda}}_{b}$ decays than in $\overline{{B}_{d}^{0}}$ decays. Our predictions are largely independent of model calculations of hadronic inputs like form factors and decay constants.

A sufficient condition is derived for the Lanczos tensor potential such that the Weyl tenser remains conformal. This condition is then applied to the metric of a conformally flat space-time, and the corresponding Lanczos tensor potential is obtained.

We consider the weak decays of a B meson to final states that are mixtures of S-wave radially excited components. We consider non leptonic decays of the type $B \to \rho' \pi/B \to \rho \pi$, $B \to \omega' \pi/B \to \omega \pi$ and $B \to \phi' \pi/B \to \phi \pi$ where $\rho'$, $\omega'$ and $\phi'$ are higher $\rho$, $\omega$ and $\phi$ resonances. We find such decays to have larger or similar branching ratios compared to decays where the final state $\rho$, $\omega$ and $\phi$ are in the ground state. We also study the effect of radial mixing in the vector and the pseudoscalar systems generated from hyperfine interaction and the annihilation term. We find the effects of radial mixing to be small and generally negligible for all practical purposes in the vector system. However, in the $\eta-\eta^{\prime}$ system the effects of radial mixing are appreciable and seriously affect decay branching ratios for $B \to \eta(\eta')K(K^*)$. In particular we find that nonstandard $\eta(\eta')$ mixing can resolve the puzzles in $B \to \eta(\eta')K$ decays.

We consider the possibility of measuring both sin(2{beta}) and cos(2{beta}) in the KM unitarity triangle using the process B{sup 0}{yields}D{sup *+}D{sup *-}K{sub s}. This decay mode has a higher branching fraction [O(1%)] than the mode B{sup 0}{yields}D{sup *+}D{sup *-}. We use the factorization assumption and heavy hadron chiral perturbation theory to estimate the branching fraction and polarization. The time dependent rate for B{sup 0}(t){yields}D{sup *+}D{sup *-}K{sub s} can be used to measure sin(2{beta}) and cos(2{beta}). Furthermore, examination of the D{sup *+}K{sub s} mass spectrum may be the best way to experimentally find the broad 1{sup +} p-wave D{sub s} meson. (c) 2000 The American Physical Society.

We consider the possibility of measuring both sin(2 beta) and cos(2 beta) in the KM unitarity triangle using the process B-0 --> D*D+*K--(s). This decay mode has a higher branching fraction [O(1%)] than the mode B-0 --> D*+D"-. We use the factorization assumption and heavy hadron chiral perturbation theory to estimate the branching fraction and polarization. The time dependent rate for B-0(t) --> D*D+*K--(s) can be used to measure sin(2 beta) and cos(2 beta). Furthermore, examination of the D*K-+(s) mass spectrum may be the best way to experimentally find the broad 1(+) p-wave D-s meson.

We consider the possibility of measuring both $\mathrm{sin}(2\ensuremath{\beta})$ and $\mathrm{cos}(2\ensuremath{\beta})$ in the KM unitarity triangle using the process ${B}^{0}\ensuremath{\rightarrow}{D}^{*+}{D}^{*\ensuremath{-}}{K}_{s}.$ This decay mode has a higher branching fraction $[O(1%)]$ than the mode ${B}^{0}\ensuremath{\rightarrow}{D}^{*+}{D}^{*\ensuremath{-}}.$ We use the factorization assumption and heavy hadron chiral perturbation theory to estimate the branching fraction and polarization. The time dependent rate for ${B}^{0}(t)\ensuremath{\rightarrow}{D}^{*+}{D}^{*\ensuremath{-}}{K}_{s}$ can be used to measure $\mathrm{sin}(2\ensuremath{\beta})$ and $\mathrm{cos}(2\ensuremath{\beta}).$ Furthermore, examination of the ${D}^{*+}{K}_{s}$ mass spectrum may be the best way to experimentally find the broad ${1}^{+}$ p-wave ${D}_{s}$ meson.

We consider the possibility of measuring sin(2β) in the KM unitarity triangle using the process B0→D*+D*−Ks. This decay mode has a higher branching fraction (O(1%)) than the mode B0→D*+D*−. We use the factorization assumption and heavy hadron chiral perturbation theory to estimate the branching fraction and polarization. The time dependent rate B0(t)→D*+D*−Ks can be used to measure sin(2β) and cos(2β). Furthermore, examination of the D*+Ks mass spectrum may be the best way to experimentally find the broad 1+p-wave Ds meson.

Isospin predictions for the semi-leptonic and non-leptonic decays of the Λb baryon are given where isospin conservation of the strong interactions constrains the possible final states in Λb decays. Since the baryon hyperfine splittings depend upon light quark dynamics and do not decrease with increasing heavy quark mass, this leads in general to to phase space enhancements in Λb decays relative to B meson decays for the same underlying quark transitions making the Λb lifetime smaller than the B lifetime. Phase space enhancements in Λb decays relative to B decays can be understood in terms of hyperfine interactions in the heavy quark system. The quark-hadron duality for baryons appears to be broken.

We calculate the S and P wave phase shifts in $\Lambda - \pi$ scattering at the $\Xi$ mass using the full relativistic $SU(3)_L \times SU(3)_R$ chiral perturbation theory. We get small phase shifts similar to previous calculations using $ SU(2)_L \times SU(2)_R$ chiral perturbation theory in the heavy baryon limit. We also consider possible off--shell effects in the coupling of the Rarita-Schwinger particle $\Sigma^*(1385)$. Using SU(3) we estimate the off--shell coupling of the $\Sigma^*$ to $\Lambda \pi$ from the off--shell coupling of the $\Delta$ to $N \pi$ which is obtained from a fit to the pion--nucleon data. We find that the contributions from the off--shell coupling can be of the same size as the other terms in the $\Lambda \pi$ scattering amplitude.

We calculate the S and P wave phase shifts in � −� scattering at themass using the full relativistic SU(3)L × SU(3)R chiral perturbation theory. We get small phase shifts similar to previous calculations using SU(2)L×SU(2)R chiral perturbation theory in the heavy baryon limit. We also consider possible off-shell effects in the coupling of the Rarita-Schwinger particle �(1385). Using SU(3) we estimate the off-shell coupling of the �� to �� from the off-shell coupling of theto Nwhich is obtained from a fit to the pion-nucleon data. We find that the contributions from the off-shell coupling can be of the same size as the other terms in the �� scattering amplitude.

An extension of the left-right symmetric model has been constructed which gives in a natural way the three lepton decay modes of the proton which have been suggested as an explanation for the atmospheric neutrino anomaly. We write down the potential which after minimization gives the proper choice of the Higgs spectrum. With this Higgs spectrum we then study the evolution of the gauge coupling constants and point out that for consistency one has to include effects of gravity.

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 = 0. This allows us to evaluate the form factors at the same value of q, even though the allowed kinematic ranges for charm and bottom decays are very di erent. Also, at this kinematic point the decay is given in terms of only one form factor A0(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. For B decays, the decay B ! K `̀ at q = 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 ! K  as a possibility. As the mass of the decaying particle increases we note that the SU(3) symmetry becomes badly broken at q = 0.