Statistics Of The Burst Model At Super-critical Phase

We investigate the statistics of a model of type-I X-ray burst [Phys. Rev. E, {\bf 51}, 3045 (1995)] in its super-critical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time evolution of the percentage of space covered by burnable clusters. A relation between the time-average and the peak percentage of space covered by burnable clusters is also derived.Comment: 11 Pages in Revtex 3.0. Two figures available by sending request to [email protected]

Direct CP violation in two-body hadronic charmed meson decays

Motivated by the recent observation of CP violation in the charm sector by LHCb, we study direct CP asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes which arise mainly from final-state rescattering can be extracted from the data. Consequently, direct CP asymmetry $a_{dir}^{\rm (tree)}$ at tree level can be reliably estimated. In general, it lies in the range $10^{-4}<a_{dir}^{\rm (tree)}<10^{-3}$. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for $D\to VP$ modes. Since weak penguin annihilation receives long-distance contributions from the color-allowed tree amplitude followed by final-state rescattering, it is expected to give the dominant contribution to the direct CP violation in the decays $D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$ in which $a_{dir}^{\rm (tree)}$ is absent. The maximal $\Delta a_{CP}^{\rm dir}$, the direct CP asymmetry difference between the above-mentioned two modes, allowed in the SM is around -0.25%, more than $2\sigma$ away from the current world average of $-(0.645\pm 0.180)$.Comment: 19 pages, 2 figures; typos correcte

Analysis of Two-Body Decays of Charmed Baryons Using the Quark-Diagram Scheme

We give a general formulation of the quark-diagram scheme for the nonleptonic weak decays of baryons. We apply it to all the decays of the antitriplet and sextet charmed baryons and express their decay amplitudes in terms of the quark-diagram amplitudes. We have also given parametrizations for the effects of final-state interactions. For SU(3) violation effects, we only parametrize those in the horizontal $W$-loop quark diagrams whose contributions are solely due to SU(3)-violation effects. In the absence of all these effects, there are many relations among various decay modes. Some of the relations are valid even in the presence of final-state interactions when each decay amplitude in the relation contains only a single phase shift. All these relations provide useful frameworks to compare with future experiments and to find out the effects of final-state interactions and SU(3) symmetry violations.Comment: 28 pages, 20 Tables in landscape form, 4 figures. Main changes are: (i) some errors in the Tables and in the relations between the quark-diagram amplitudes of this paper and those of Ref.[10] are corrected, (ii) improvements are made in the presentation so that comparisons with previous works and what have been done to include SU(3) breaking and final-state interactions are more clearly stated; to appear in the Physical Review

Comments on the Quark Content of the Scalar Meson f0(1370)f_0(1370)

Based on the measurements of $(D_s^+,D^+)\to f_0(1370)\pi^+$ we determine, in a model independent way, the allowed $s\bar s$ content in the scalar meson $f_0(1370)$. We find that, on the one hand, if this isoscalar resonance is a pure $n\bar n$ state [ $n\bar n\equiv(u\bar u+d\bar d)/\sqrt{2} ]$, a very large $W$-annihilation term will be needed to accommodate $D_s^+\to f_0(1370)\pi^+$. On the other hand, the $s\bar s$ component of $f_0(1370)$ should be small enough to avoid excessive $D_s^+\to f_0(1370)\pi^+$ induced from the external $W$-emission. Measurement of $f_0(1370)$ production in the decay $D_s^+\to K^+K^-\pi^+$ will be useful to test the above picture. For the decay $D^0\to f_0(1370)\bar K^0$ which is kinematically barely or even not allowed, depending on the mass of $f_0(1370)$, we find that the finite width effect of $f_0(1370)$ plays a crucial role on the resonant three-body decay $D^0\to f_0(1370)\bar K^0\to\pi^+\pi^-\bar K^0$.Comment: 12 pages, 2 figure

Hadronic Charmed Meson Decays Involving Tensor Mesons

Charmed meson decays into a pseudoscalar meson P and a tensor meson T are studied. The charm to tensor meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise (ISGW) quark model. It is shown that the Cabibbo-allowed decay $D_s^+\to f_2(1270)\pi^+$ is dominated by the W-annihilation contribution and has the largest branching ratio in $D\to TP$ decays. We argue that the Cabibbo-suppressed mode $D^+\to f_2(1270)\pi^+$ should be suppressed by one order of magnitude relative to $D_s^+\to f_2(1270)\pi^+$. When the finite width effect of the tensor resonances is taken into account, the decay rate of $D\to TP$ is generally enhanced by a factor of $2\sim 3$. Except for $D_s^+\to f_2(1270)\pi^+$, the predicted branching ratios of $D\to TP$ decays are in general too small by one to two orders of magnitude compared to experiment. However, it is very unlikely that the $D\to T$ transition form factors can be enhanced by a factor of $3\sim 5$ within the ISGW quark model to account for the discrepancy between theory and experiment. As many of the current data are still preliminary and lack sufficient statistic significance, more accurate measurements are needed to pin down the issue.Comment: 11 page

Hadronic Charmed Meson Decays Involving Axial Vector Mesons

Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an axial-vector meson are studied. The charm to axial-vector meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole momentum dependence of the $D\to K$ transition form factor and the presence of a sizable long-distance $W$-exchange are the two key ingredients for understanding the data of $D\to \bar Ka_1$. The $K_{1A}-K_{1B}$ mixing angle of the strange axial-vector mesons is found to be $\approx \pm37^\circ$ or $\pm58^\circ$ from $\tau\to K_1\nu_\tau$ decays. The study of $D\to K_1(1270)\pi, K_1(1400)\pi$ decays excludes the positive mixing-angle solutions. It is pointed out that an observation of the decay $D^0\to K_1^-(1400)\pi^+$ at the level of $5\times 10^{-4}$ will rule out $\theta\approx -37^\circ$ and favor the solution $\theta\approx -58^\circ$. Though the decays $D^0\to \bar K_1^0\pi^0$ are color suppressed, they are comparable to and even larger than the color-allowed counterparts: $\bar K_1^0(1270)\pi^0\sim K_1^-(1270)\pi^+$ and $\bar K_1^0(1400)\pi^0> K_1^-(1400)\pi^+$. The finite width effect of the axial-vector resonance is examined. It becomes important for $a_1(1260)$ in particular when its width is near 600 MeV.Comment: 19 page

Flavor SU(3) symmetry and QCD factorization in B→PPB \to PP and PVPV decays

Using flavor SU(3) symmetry, we perform a model-independent analysis of charmless $\bar B_{u,d} (\bar B_s) \to PP, ~PV$ decays. All the relevant topological diagrams, including the presumably subleading diagrams, such as the QCD- and EW-penguin exchange diagrams and flavor-singlet weak annihilation ones, are introduced. Indeed, the QCD-penguin exchange diagram turns out to be important in understanding the data for penguin-dominated decay modes. In this work we make efforts to bridge the (model-independent but less quantitative) topological diagram or flavor SU(3) approach and the (quantitative but somewhat model-dependent) QCD factorization (QCDF) approach in these decays, by explicitly showing how to translate each flavor SU(3) amplitude into the corresponding terms in the QCDF framework. After estimating each flavor SU(3) amplitude numerically using QCDF, we discuss various physical consequences, including SU(3) breaking effects and some useful SU(3) relations among decay amplitudes of $\bar B_s \to PV$ and $\bar B_d \to PV$.Comment: 47 pages, 3 figures, 28 table

Charmless Two-body Baryonic B Decays

We study charmless two-body baryonic B decays in a diagramatic approach. Relations on decay amplitudes are obtained. In general there are more than one tree and more than one penguin amplitudes. The number of independent amplitudes can be reduced in the large m_B limit. It leads to more predictive results. Some prominent modes for experimental searches are pointed out.Comment: 15 pages, 2 figures. To appear in Phys. Rev.

A Cellular Automaton Model for Diffusive and Dissipative Systems

We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added onto a site. Whenever the local energy content of a site reaches a fixed threshold $E_{c1}$, energy will be dissipated. Dissipation of energy propagates to the neighboring sites provided that the energy contents of those sites are greater than or equal to another fixed threshold $E_{c2} (\leq E_{c1})$. Under such dynamics, the system evolves into three different types of states depending on the values of $E_{c1}$ and $E_{c2}$ as reflected in their dissipation size distributions, namely: localized peaks, power laws, or exponential laws. This model is able to describe the behaviors of various physical systems including the statistics of burst sizes and burst rates in type-I X-ray bursters. Comparisons between our model and the famous forest-fire model (FFM) are made.Comment: in REVTEX 3.0. Figures available on request. Extensively revised. Accepted by Phys.Rev.

Nonresonant Three-body Decays of D and B Mesons

Nonresonant three-body decays of D and B mesons are studied. It is pointed out that if heavy meson chiral perturbation theory (HMChPT) is applied to the heavy-light strong and weak vertices and assumed to be valid over the whole kinematic region, then the predicted decay rates for nonresonant charmless 3-body B decays will be too large and especially B^- --> pi^- K^+ K^- greatly exceeds the current experimental limit. This can be understood as chiral symmetry has been applied there twice beyond its region of validity. If HMChPT is applied only to the strong vertex and the weak transition is accounted for by the form factors, the dominant B^* pole contribution to the tree-dominated direct three-body B decays will become small and the branching ratio will be of order 10^{-6}. The decay modes B^- --> (K^- h^+ h^-)_{NR} and bar{B}^0 --> (bar{K}^0 h^+h^-)_{NR} for h = pi, K are penguin dominated. We apply HMChPT in two different cases to study the direct 3-body D decays and compare the results with experiment. Theoretical uncertainties are discussed.Comment: 24 pages, 2 figures. New experimental results of direct 3-body D decays as Reported at ICHEP2002 are included. To appear in Phys. Re