Evidence for the Suppressed Decay B- -> DK-, D -> K+pi-

The suppressed decay chain B- -> DK-, D -> K+pi-, where D indicates a anti-D0 or D0 state, provides important information on the CP-violating angle phi_3. We measure the ratio R_{DK} of the decay rates to the favored mode B- -> DK-, D -> K-pi+ to be R_{DK} = [1.63^{+0.44}_{-0.41}(stat)^{+0.07}_{-0.13}(syst)] x 10^{-2}, which indicates the first evidence of the signal with a significance of 4.1sigma. We also measure the asymmetry A_{DK} between the charge-conjugate decays to be A_{DK} = -0.39^{+0.26}_{-0.28}(stat)^{+0.04}_{-0.03}(syst). The results are based on the full 772 x 10^6 B anti-B pair data sample collected at the Upsilon(4S) resonance with the Belle detector.Comment: 6 pages, 2 figures, 2 tables, accepted by Physical Review Letter

Long-time dynamics of resonant weakly nonlinear CGL equations

Consider a weakly nonlinear CGL equation on the torus~$\mathbb{T}^d$: u_t+i\Delta u=\epsilon [\mu(-1)^{m-1}\Delta^{m} u+b|u|^{2p}u+ ic|u|^{2q}u].\eqno{(*)} Here $u=u(t,x)$, $x\in\mathbb{T}^d$, $0<\epsilon<<1$, $\mu\geqslant0$, $b,c\in\mathbb{R}$ and $m,p,q\in\mathbb{N}$. Define \mbox{I(u)=(I_{\dk},\dk\in\mathbb{Z}^d)}, where I_{\dk}=v_{\dk}\bar{v}_{\dk}/2 and v_{\dk}, \dk\in\mathbb{Z}^d, are the Fourier coefficients of the function~$u$ we give. Assume that the equation $(*)$ is well posed on time intervals of order $\epsilon^{-1}$ and its solutions have there a-priori bounds, independent of the small parameter. Let $u(t,x)$ solve the equation $(*)$. If $\epsilon$ is small enough, then for $t\lesssim\epsilon^{-1}$, the quantity $I(u(t,x))$ can be well described by solutions of an {\it effective equation}: $$u_t=\epsilon[\mu(-1)^{m-1}\Delta^m u+ F(u)],$$ where the term $F(u)$ can be constructed through a kind of resonant averaging of the nonlinearity $b|u|^{2p}+ ic|u|^{2q}u$

Final-state Rescattering and SU(3) Symmetry Breaking in B->DK and B->DK^* Decays

The first observation of $\bar{B}^0_d\to D^0\bar{K}^0$ and $\bar{B}^0_d\to D^0\bar{K}^{*0}$ transitions by the Belle Collaboration allows us to do a complete isospin analysis of $B\to DK^{(*)}$ decay modes. We find that their respective isospin phase shifts are very likely to lie in the ranges $37^\circ \leq (\phi_1 -\phi_0)_{DK} \leq 63^\circ$ (or around $50^\circ$) and $25^\circ \leq (\phi_1 -\phi_0)_{DK^*} \leq 50^\circ$ (or around $35^\circ$), although the possibility $(\phi_1 -\phi_0)_{DK} = (\phi_1 -\phi_0)_{DK^*} = 0^\circ$ cannot be ruled out at present. Thus significant final-state rescattering effects are possible to exist in such exclusive $|\Delta B| = |\Delta C| = |\Delta S| =1$ processes. We determine the spectator and color-suppressed spectator quark-diagram amplitudes of $B\to DK$ and $B\to DK^*$ decays, and compare them with the corresponding quark-diagram amplitudes of $B\to D\pi$ and $B\to D\rho$ decays. The effects of SU(3) flavor symmetry breaking are in most cases understandable in the factorization approximation, which works for the individual isospin amplitudes. Very instructive predictions are also obtained for the branching fractions of rare $\bar{B}^0_d \to \bar{D}^0 \bar{K}^{(*)0}$, $B^-_u \to \bar{D}^0 K^{(*)-}$ and $B^-_u \to D^- \bar{K}^{(*)0}$ transitions.Comment: LaTex 14 pages (3 PS figures included). More delicate numerical results are presented. Version accepted for publication in Eur. Phys. J.

Implications of a DK Molecule at 2.32 GeV

We discuss the implications of a possible quasinuclear DK bound state at 2.32 GeV. Evidence for such a state was recently reported in D_s^+pi^o by the BaBar Collaboration. We first note that a conventional quark model c-sbar assignment is implausible, and then consider other options involving multiquark systems. An I=0 c sbar n nbar baryonium assignment is one possibility. We instead favor a DK meson molecule assignment, which can account for the mass and quantum numbers of this state. The higher-mass scalar c-sbar state expected at 2.48 GeV is predicted to have a very large DK coupling, which would encourage formation of an I=0 DK molecule. Isospin mixing is expected in hadron molecules, and a dominantly I=0 DK state with some I=1 admixture could explain both the narrow total width of the 2.32 GeV state as well as the observed decay to D_s^+ pi^o. Additional measurements that can be used to test this and related scenarios are discussed.Comment: 6 pages, 1 figur