Strong and Weak Phases from Time-Dependent Measurements of B→ππB \to \pi \pi

Time-dependence in $B^0(t) \to \pi^+ \pi^-$ and \ob(t) \to \pi^+ \pi^- is utilized to obtain a maximal set of information on strong and weak phases. One can thereby check theoretical predictions of a small strong phase $\delta$ between penguin and tree amplitudes. A discrete ambiguity between $\delta \simeq 0$ and $\delta \simeq \pi$ may be resolved by comparing the observed charge-averaged branching ratio predicted for the tree amplitude alone, using measurements of $B \to \pi l \nu$ and factorization, or by direct comparison of parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix with those determined by other means. It is found that with 150 fb$^{-1}$ from BaBar and Belle, this ambiguity will be resolvable if no direct CP violation is found. In the presence of direct CP violation, the discrete ambiguity between $\delta$ and $\pi - \delta$ becomes less important, vanishing altogether as $|\delta| \to \pi/2$. The role of measurements involving the lifetime difference between neutral $B$ eigenstates is mentioned briefly.Comment: 14 pages, LaTeX, 5 figures, to be published in Phys. Rev. D. Updated version with one reference change

Non-paraxial Split-step Finite-difference Method for Beam Propagation

A method based on symmetrized splitting of the propagation operator in the finite difference scheme for non-paraxial beam propagation is presented. The formulation allows the solution of the second order scalar wave equation without having to make the slowly varying envelope and one-way propagation approximations. The method is highly accurate and numerically efficient. Unlike most Padé approximant based methods, it is non-iterative in nature and requires less computation. The method can be used for bi-directional propagation as well

Test of Factorization Hypothesis from Exclusive Non-leptonic B decays

We investigate the possibility of testing factorization hypothesis in non-leptonic exclusive decays of B-meson. In particular, we considered the non factorizable \bar{B^0} -> D^{(*)+} D_s^{(*)-} modes and \bar{B^0} -> D^{(*)+} (\pi^-, \rho^-) known as well-factorizable modes. By taking the ratios BR(\bar{B^0}-> D^{(*)+}D_s^{(*)-})/BR(\bar{B^0}-> D^{(*)+}(\pi^-,\rho^-)), we found that under the present theoretical and experimental uncertainties there's no evidence for the breakdown of factorization description to heavy-heavy decays of the B meson.Comment: 11 pages; submitted to PR

Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Nonfactorizable contributions in B decays to charmonium: the case of B−→K−hcB^- \to K^- h_c

Nonleptonic $B$ to charmonium decays generally show deviations from the factorization predictions. For example, the mode $B^- \to K^- \chi_{c0}$ has been experimentally observed with sizeable branching fraction while its factorized amplitude vanishes. We investigate the role of rescattering effects mediated by intermediate charmed meson production in this class of decay modes, and consider $B^- \to K^- h_c$ with $h_c$ the $J^{PC}=1^{+-}$ $\bar c c$ meson. Using an effective lagrangian describing interactions of pairs of heavy-light $Q{\bar q}$ mesons with a quarkonium state, we relate this mode to the analogous mode with $\chi_{c0}$ in the final state. We find ${\cal B}(B^- \to K^- h_c)$ large enough to be measured at the $B$ factories, so that this decay mode could be used to study the poorly known $h_c$.Comment: RevTex, 16 pages, 2 eps figure

Charmless B→PPB \to PP decays using flavor SU(3) symmetry

The decays of $B$ mesons to a pair of charmless pseudoscalar ($P$) mesons are analyzed within a framework of flavor SU(3). Symmetry breaking is taken into account in tree ($T$) amplitudes through ratios of decay constants; exact SU(3) is assumed elsewhere. Acceptable fits to $B \to \pi \pi$ and $B \to K \pi$ branching ratios and CP asymmetries are obtained with tree, color-suppressed ($C$), penguin ($P$), and electroweak penguin ($P_{EW}$) amplitudes. Crucial additional terms for describing processes involving $\eta$ and $\eta'$ include a large flavor-singlet penguin amplitude ($S$) as proposed earlier and a penguin amplitude $P_{tu}$ associated with intermediate $t$ and $u$ quarks. For the $B^+ \to \pi^+ \eta'$ mode a term $S_{tu}$ associated with intermediate $t$ and $u$ quarks also may be needed. Values of the weak phase $\gamma$ are obtained consistent with an earlier analysis of $B \to VP$ decays, where $V$ denotes a vector meson, and with other analyses of CKM parameters.Comment: 26 pages, 1 figure. To be submitted to Phys. Rev. D. Reference update

Partial Wave Analysis of J/ψ→γ(K+K−π+π−)J/\psi \to \gamma (K^+K^-\pi^+\pi^-)

BES data on $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$ are presented. The $K^*\bar K^*$ contribution peaks strongly near threshold. It is fitted with a broad $0^{-+}$ resonance with mass $M = 1800 \pm 100$ MeV, width $\Gamma = 500 \pm 200$ MeV. A broad $2^{++}$ resonance peaking at 2020 MeV is also required with width $\sim 500$ MeV. There is further evidence for a $2^{-+}$ component peaking at 2.55 GeV. The non-$K^*\bar K^*$ contribution is close to phase space; it peaks at 2.6 GeV and is very different from $K^{*}\bar{K^{*}}$.Comment: 15 pages, 6 figures, 1 table, Submitted to PL

Weak Phase γ\gamma from Bs(t)→K+K−B_s(t) \to K^+ K^-

We re-examine the time-dependent rates of \bs(t) \to K^+ K^- and \obs(t) \to K^+ K^-, including a lifetime difference between neutral \bs mass eigenstates. The two rates, normalized by the rate of \bs \to \ko \ok, are used to obtain ambiguity-free information on a strong phase and on the weak phase $\gamma$. We discuss the sensitivity of extracting $\gamma$ to the measured quantities, and find that an error of $\pm 10^\circ$ in $\gamma$ is possible for a sample of several thousand \bs(t) \to K^+ K^- decays. This study is complementary to a recent similar analysis of the U-spin related decays \bo(t) \to \pi^+\pi^- and \ob(t) \to \pi^+\pi^-.Comment: 12 pages, LaTeX, 3 figures, revised version submitted to Phys. Rev.

Measurements of J/psi Decays into 2(pi+pi-)eta and 3(pi+pi-)eta

Based on a sample of 5.8X 10^7 J/psi events taken with the BESII detector, the branching fractions of J/psi--> 2(pi+pi-)eta and J/psi-->3(pi+pi-)eta are measured for the first time to be (2.26+-0.08+-0.27)X10^{-3} and (7.24+-0.96+-1.11)X10^{-4}, respectively.Comment: 11 pages, 6 figure