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

Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

Factorial Moments in a Generalized Lattice Gas Model

We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which depends on the species involved. This model is capable of reproducing the relations between factorial moments observed in high--energy scattering experiments for moderate values of $D$. The factorial moments of the negative binomial distribution can be obtained exactly in the limit as $D$ becomes large, and two suitable prescriptions involving randomly drawn nearest neighbor interactions are given. These results indicate the need for considerable care in any attempt to extract information regarding possible critical phenomena from empirical factorial moments.Comment: 15 pages + 1 figure (appended as postscript file), REVTEX 3.0, NORDITA preprint 93/4

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

Dynamics of a suspended nanowire driven by an ac Josephson current in an inhomogeneous magnetic field

We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak-link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement present different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic and chaotic. Transitions between these regimes are also discussed.Comment: 7 pages, 5 figure

Nonleptonic Two-Body Decays of D Mesons in Broken SU(3)

Decays of the D mesons to two pseudoscalars, to two vectors, and to pseudoscalar plus vector are discussed in the context of broken flavor SU(3). A few assumptions are used to reduce the number of parameters. Amplitudes are fit to the available data, and predictions of branching ratios for unmeasured modes are made.Comment: LaTeX, 24 page

Cabibbo-allowed nonleptonic weak decays of charmed baryons

Cabibbo-allowed nonleptonic weak decays of charmed baryons \lamc,~\xin,~\xip and $\Omega_c^0$ into an octet baryon and a pseudoscalar meson are analyzed. The nonfactorizable contributions are evaluated under pole approximation, and it turns out that the $s$-wave amplitudes are dominated by the low-lying \halfm resonances, while $p$-wave ones governed by the ground-state \halfp poles. The MIT bag model is employed to calculate the coupling constants, form factors and baryon matrix elements. Our conclusions are: (i) $s$ waves are no longer dominated by commutator terms; the current-algebra method is certainly not applicable to parity-violating amplitudes, (ii) nonfactorizable $W$ exchange effects are generally important; they can be comparable to and somtimes even dominate over factorizable contributions, depending on the decay modes under consideration, (iii) large-$N_c$ approximation for factorizable amplitudes also works in the heavy baryon sector and it accounts for the color nonsuppression of \lamc\ri p\bar{K}^0 relative to \lamc\ri\Lambda\pi^+, (iv) a measurement of the decay rate and the sign of the $\alpha$ asymmetry parameter of certain proposed decay modes will help discern various models; especially the sign of $\alpha$ in \lamc\ri\Sigma\pi decays can be used to unambiguously differentiate recent theoretical schemes from current algebra, and (v) $p$ waves are the dominant contributions to the decays \lamc\ri\Xi^0 K^+ and \xin\ri\Sigma^+ K^-, but they are subject to a large cancellation; this renders present theoretical predictions on these two channels unreliable.Comment: PHYZZX, 31 pages, 3 tables, IP-ASTP-10-93, ITP-SB-93-2

Implications of Recent Bˉ0→D(∗)0X0\bar{B}^0\to D^{(*)0}X^0 Measurements

The recent measurements of the color-suppressed modes $\bar B^0\to D^{(*)0}\pi^0$ imply non-vanishing relative final-state interaction (FSI) phases among various $\bar B\to D\pi$ decay amplitudes. Depending on whether or not FSIs are implemented in the topological quark-diagram amplitudes, two solutions for the parameters $a_1$ and $a_2$ are extracted from data using various form-factor models. It is found that $a_2$ is not universal: $|a_2(D\pi)|= 0.40-0.55$ and $|a_2(D^*\pi)|= 0.25-0.35$ with a relative phase of order $(50-55)^\circ$ between $a_1$ and $a_2$. If FSIs are not included in quark-diagram amplitudes from the outset, $a_2^{eff}/a_1^{eff}$ and $a_2^{eff}$ will become smaller. The large value of $|a_2(D\pi)|$ compared to $|a_2^{eff}(D\pi)|$ or naive expectation implies the importance of long-distance FSI contributions to color-suppressed internal $W$-emission via final-state rescatterings of the color-allowed tree amplitude.Comment: 17 pages. The Introduction is substantially revised and the order of the presentation in Sec. 2 is rearranged. To appear in Phys. Re

Final-State Phases in Charmed Meson Two-Body Nonleptonic Decays

Observed decay rates indicate large phase differences among the amplitudes for the charge states in $D \to \bar K \pi$ and $D \to \bar K^* \pi$ but relatively real amplitudes in the charge states for $D \to \bar K \rho$. This feature is traced using an SU(3) flavor analysis to a sign flip in the contribution of one of the amplitudes contributing to the latter processes in comparison with its contribution to the other two sets. This amplitude may be regarded as an effect of rescattering and is found to be of magnitude comparable to others contributing to charmed particle two-body nonleptonic decays.Comment: 19 pages, latex, 4 figures, to be submitted to Phys. Rev.

A Continuum Model for Soil-Pile-Structure Interactions Under Earthquake Excitation

An exact analytical method for the interaction analysis of a fully coupled soil-pile-structure system under seismic excitation is investigated in this paper. Only horizontal shaking induced by harmonic SH waves was considered. The soil mass, pile and building were all considered as elastic with hysteretic type damping. Geometrically, the soil is modeled as an elastic isotropic homogeneous continuum, and both pile and structures are simplified as beam models. The structure and piles are coupled through a rigid foundation at the ground level. Buildings of various heights in Hong Kong designed to withstand wind load were analyzed using the present model. Only the shaking at the ground level is considered in this study. It was discovered that the maximum shaking of the piled-structures at ground level is generally larger than that of a free field ground shaking except near the first natural frequency of the coupled soil-pile-structure system. This first resonant frequency depends strongly on the natural frequency of the structure