Narrow Results

Motivated by the heavy-flavor experiments at running Large Hadron Collider (LHC) and upgrading SuperKEKB, which provide abundant $\mathrm{{\rm Y}}$ data samples, the tree-dominated $\mathrm{{\rm Y}}(nS)\to B_c\rho$ and $B_c{K}^{\ast }$ (n =1, 2, 3) weak decays are studied within the framework of quantum chromodynamics (QCD) factorization. The QCD corrections to the longitudinal and transverse amplitudes are evaluated at next-to-leading order, and the branching fractions and polarization fractions are predicted. Numerically, the $\mathrm{{\rm Y}}(nS)\to B_c\rho$ decays have relatively large branching fractions at the order of ${𝒪}(10^{-10})$ and are in the scope of the LHC and SuperKEKB/Belle-II experiments.

Within the effective quark model with chiral U(3) × U(3) symmetry we calculate the S-wave and P-wave amplitudes and the partial widths of the nonleptonic decays of the Λ⁰-hyperon, Λ⁰ → pπ^- and Λ⁰ → nπ⁰. The theoretical results agree well with the experimental data. The angular distributions of the decay rates in dependence on the polarizations of baryons are analyzed both in the laboratory frame and in the rest frame of the Λ⁰-hyperon.

Motivated by the recent measurements on nonleptonic J/ψ weak decays at BESIII and the potential prospects of J/ψ meson at the high-luminosity heavy-flavor experiments, the branching ratios of the two-body nonleptonic J/ψ → DP, DV decays are estimated quantitatively by considering the QCD radiative corrections to hadronic matrix elements with the QCD factorization approach. It is found that the Cabibbo favored , , decays have branching ratios ≳ 10^-10, which might be promisingly detectable in the near future.

Motivated by the experiments of heavy flavor physics at running LHC and upgrading SuperKEKB/Belle-II in the future, the nonleptonic $B_{(s)}^{\ast }\to M_1{M}_2$$(M=D,D_s,\pi ,K)$ weak decays are studied in this paper. The amplitudes are calculated with factorization approach, and the transition form factors $A_0^{B_{(s)}^{\ast }\to M_1}(0)$ are evaluated within BSW model. With the reasonable approximation ${\Gamma }_{\mathrm{\text{tot}}}\left(\right.B_{(s)}^{\ast }\left)\right.\simeq \Gamma \left(\right.B_{(s)}^{\ast }\to B_{(s)}\gamma \left)\right.$, our predictions of branching fractions are presented. Numerically, the CKM-favored tree-dominated ${\bar{B}}^{\ast 0}\to D^{+}{D}_s^{-}$ and ${\bar{B}}_s^{\ast 0}\to D_s^{+}{D}_s^{-}$ decays have the largest branching fractions of the order $\sim {𝒪}(10^{-8})$, and hence will be firstly observed by forthcoming Belle-II experiment. However, most of the other decay modes have the branching fractions $<{𝒪}(10^{-9})$ and thus are hardly to be observed soon. Besides, for the possible detectable $B_{(s)}^{\ast }$ decays with branching fractions $\gtrsim {𝒪}(10^{-9})$, some useful ratios, such as $R_D$, etc. are presented and discussed in detail.

The $\mathrm{{\rm Y}}(1S)\to B_c{D}_s^{\ast }$ weak decay is studied with the perturbative QCD approach firstly. It is found that (1) main contributions to branching ratio come from the longitudinal and parallel helicity amplitudes, (2) branching ratio, longitudinal and parallel polarization fractions are sensitive to the wave functions of the $\mathrm{{\rm Y}}(1S)$ meson, (3) branching ratio for the $\mathrm{{\rm Y}}(1S)\to B_c{D}_s^{\ast }$ decay can reach up to $10^{-9}$, which might be promisingly measured by the future experiments.

The $\mathrm{{\rm Y}}(nS)\to B_c^{\ast }D$ weak decays $(n=1,2,3)$ are investigated with perturbative QCD approach. It is found that the CKM-favored $\mathrm{{\rm Y}}(nS)\to B_c^{\ast }{D}_s$ decays have branching ratio of ${𝒪}(10^{-10})$, which might be potentially accessible to the future LHC and SuperKEKB experiments.

Inspired by the recent measurements on two-body nonleptonic $J/\psi$ weak decay at BESIII, the charm-changing $J/\psi \to D_{s,d}V$ weak decays are studied with perturbative QCD approach, where $V$ denotes $\rho$ and $K^{\ast }$ vector mesons. It is found that branching ratio for $J/\psi \to D_s\rho$ decay can reach up to ${𝒪}(10^{-9})$, which is within the potential measurement capability of the future high-luminosity experiments.

Inspired by the potential prospects of high-luminosity dedicated colliders and the high enthusiasms in searching for new physics in the flavor sector at the intensity frontier, the $\mathrm{{\rm Y}}(1S)\to D^{-}{\pi }^{+}$, ${\bar{D}}^0{\pi }^0$ and $D_s^{-}{K}^{+}$ weak decays are studied with the perturbative QCD approach. It is found within the standard model that the branching ratios for the concerned processes are tiny, about ${𝒪}(10^{-18})$, and far beyond the detective ability of current experiments unless there exists some significant enhancements from a novel interaction.

This paper establishes the weak controllability of solutions in terms of energy norms for a class of nonlinear functions using an energy perturbation method, in order to tackle the problem of poor stability control for a class of quasilinear wave equations with weak attenuation. We demonstrate the weak controllability with the assistance of differential inequalities by estimating the relationship between energy inequalities and the attenuating property of weak solutions.