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We study the wave functions and purely leptonic decays of $b$-flavored mesons (pseudoscalars, vector mesons, and higher excited states that are well established in experiment) in the relativistic potential model based on our previous works. The wave functions are obtained by solving the wave equation including the spin-spin and spin-orbit corrections in the effective potential. The decay constants of $B$, $B^*$ and some of their excited states that have been found in experiment are calculated with these wave functions. Then the branching fractions of the purely leptonic decay modes of these bottom mesons are studied. Our results are in well agreement with experiment data for decay modes that have been measured in experiments. We also provide predictions for some yet unmeasured channels, which are useful for experimental test in the future., Comment: 14 pages, 4 figures, 5 tables

Using measured branching fraction of the decay $J/\psi \rightarrow\eta Y(2175))\rightarrow\eta\phi f_0(980)\rightarrow\eta\phi\pi^+\pi^{-}$ from the BESIII experiment, we estimate branching fraction of $J/\psi \rightarrow\eta Y(2175))\rightarrow\eta\phi f_0(980)\rightarrow\eta\phi\eta\pi^{0}$ decay, which proceeds via the $f_0(980)$-$a_0^0(980)$ mixing and the $\pi^0$-$\eta$ mixing. The branching fraction is predicted to be about $O(10^{-6})$, which can be accessed with $10^{10}$ $J/\psi$ events collected at the BESIII. The decay is dominated by the contribution from $f_0(980)$-$a_0^0(980)$ mixing. We find that the interference between the amplitudes due to $f_0(980)$-$a_0^0(980)$ mixing and that due to $\pi^0$-$\eta$ mixing is destructive. The branching fraction can be decreased by about $10\%$ owing to the interference effect. We also study the $\eta\pi^0$ mass squared spectrum, and find that a narrow peak due to the $f_0(980)$-$a_0^0(980)$ mixing in the $\eta\pi^0$ mass squared spectrum should be observed. The observation of this decay in experiment will be helpful to determine the $f_0(980)$-$a_0^0(980)$ mixing intensity and get information about the structures of the light scalar mesons., Comment: 16 pages, 3 figures

We employ an atomic-scale theory within the framework of nonaffine lattice dynamics to uncover the origin of the Johari-Goldstein (JG) $\beta$-relaxation in metallic glasses (MGs). Combining simulation and experimental data with our theoretical approach, we reveal that the large mass asymmetry between the elements in a La$_{60}$Ni$_{15}$Al$_{25}$ MG leads to a clear separation in the respective relaxation time scales, giving strong evidence that JG relaxation is controlled by the lightest atomic species present. Moreover, we show that only qualitative features of the vibrational density of states determine the overall observed mechanical response of the glass, paving the way for a possible unified theory of secondary relaxations in glasses.

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional constrained ADP framework, the optimal control issearched via a policy iteration algorithm, where the value under a constrainedcontrol is solved from a Hamilton-Jacobi-Bellman (HJB) equation while theconstrained control policy is improved based on the current estimated value.This concise and applicable method has been widely-used. However, the con-vergence of the existing policy iteration algorithm may possesses a theoreticaldifficulty, which might be caused by forcibly evaluating the same trajectoryeven though the control policy has already changed. This problem will beexplored in this paper., Comment: The theoretical difficulty talked in this paper is too minor. It does not affect the final result in the original paper. And, my presentation is also problematic. Sorry for that

Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear Hamilton-Jacobi-Bellman equation, whose solution is often to difficult to determine but is needed to determine the optimal control policy. ADP methods usually employ a policy iteration algorithm that evaluates and improves a value function at every step to find the optimal control policy. Previous works in ADP have been lacking a stronger condition that ensures the convergence of the policy iteration algorithm. This paper provides a sufficient but not necessary condition that guarantees the convergence of an ADP algorithm. This condition may provide a more solid theoretical framework for ADP-based control algorithm design for nonlinear dynamical systems., Comment: My derivation in this paper was wrong, which was misled by some other paper. I would like to withdraw it as it may mislead other readers. Sorry for that

Within the QCD light-cone sum rule (LCSR) approach, we investigate the transition form factors of $D\rightarrow a_0(980)$ up to the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar meson $a_0(980)$ in the two-quark picture. Using these form factors, we calculate the differential decay widths and branching ratios of the $D\rightarrow a_0(980) e^+ \nu_e$ semileptonic decays. We obtain ${\mathcal B}(D^0\rightarrow a_0^- (980) e^+ \nu_e)=(4.08^{+1.37}_{-1.22})\times 10^{-4}$ and ${\mathcal B}(D^+\rightarrow a_0^0 (980) e^+ \nu_e)=(5.40^{+1.78}_{-1.59})\times 10^{-4}$. The results are sensitive to the $a_0(980)$ inner structure. These decays can be searched for at BESIII experiment, and any experimental observations will be useful to identify internal quark contents of the $a_0(980)$ meson, which will shed light on understanding theoretical models., Comment: 19 pages,5 figures

In this work we study the decay constants of $B$ and $B_s$ mesons based on the wave function obtained in the relativistic potential model. Our results are in good agreement with experimental data which enables us to apply this method to the investigation of $B$-meson distribution amplitudes. A very compact form of the distribution amplitude is obtained. We also investigate the one-loop QCD corrections to the pure leptonic decays of $B$ mesons. We find that, after subtracting the infrared divergence in the one-loop corrections using the factorization method, the QCD one-loop corrections to the hard amplitude of leptonic decay will be zero., Comment: 26 pages, 8 figures, 2 tables. Comments are welcomed; version to appear in Phys.Rev.D

In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons using factorization approach. Factorization is proved to be valid explicitly at 1-loop level at any order of $O(\Lambda_{\rm QCD}\left/m_Q\right.)$. We consider the contribution in the soft photon region that $E_{\gamma} \sim \left. \Lambda^2_{\rm QCD} /\right. m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to \gamma e\nu_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma}\sim m_Q$. And for the case of $D\to \gamma e\nu_e$, the result of the branching ratio is $1.92\times 10^{-5}$., Comment: arXiv admin note: text overlap with arXiv:1409.0358

In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons in the standard model and the two-Higgs-doublet-model type II. The results are obtained using the factorization procedure, and the contribution of the order $O(\Lambda _{\rm QCD}\left/m_Q\right.)$ is included. The numerical results are calculated using the wave-function obtained in relativistic potential model. As a result, the decay mode $B\to \gamma \tau \nu_{\tau}$ is found to be sensitive to the effect of the charged Higgs boson. Using the constraint on the free parameters of the two Higgs doublet model given in previous works, we find the contribution of the charged Higgs boson in the decay mode $B\to \gamma \tau \nu_{\tau}$ can be as large as about $13\%$., Comment: 17 pages, 7 figures

We study the heavy-light mesons in a relativistic model, which is derived from the instantaneous Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation on the heavy quark. The kernel we choose is based on scalar confining and vector Coulomb potentials, the transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of $D$, $D_s$, $B$, $B_s$ meson states are obtained. The spectra are calculated up to the order of $1/m_Q$, and wave functions are treated to leading order., Comment: 14 pages, 1 figure

Strong spin-orbital coupling (SOC) was found previously to lead to dramatic effects in quantum materials, such as those found in topological insulators. It was shown theoretically that local noncentrosymmetricity resulting from the rotation of RuO$_6$ octahedral in Sr$_3$Ru$_2$O$_7$ will also give rise to an effective SOC\cite{SocSr327,MicroscopicnematicSr327}. In the presence of a magnetic field applied along a specific in-plane direction, the Fermi surface was predicted to undergo a reconstruction. Here we report results of our in-plane magnetoresistivity and magnetothermopower measurements on single crystals of Sr$_3$Ru$_2$O$_7$ with an electrical or a thermal current applied along specific crystalline directions and a magnetic field rotating in the $ab$ plane (Fig. 1a), showing a minimal value for field directions predicted by the local noncentrosymmetricity theory. Furthermore, the thermopower, and therefore, the electron entropy, were found to be suppressed as the field was applied perpendicular to the thermal current, which suggests that the spin and the momentum in Sr$_3$Ru$_2$O$_7$ are locked over substantial parts of the Fermi surface, likely originating from local noncentrosymmetricity as well.

We study the masses and wave functions of heavy-light quark-antiquark system in the relativistic potential model, where we focus on the higher excited states of $B$ and $D$ mesons. The resonances of $D_J(2740)$, $D_J^*(2760)$, $D_J^*(3000)$ and $D_{sJ}^*(2860)$ recently observed in experiments are considered. We find that the four resonances can be identified as the $|1^{1,3}D_2\rangle$, $|1^3D_3\rangle$, $|1^{1,3}F_3\rangle$ and $|1^3D_3\rangle$ states due to the prediction to the states with $l=2$ and $l=3$ in the potential-model calculation. The masses of $n=2$ excited states are also calculated. All the observed mesons can be accommodated successfully in the potential model., Comment: 12 pages, 1 figure and 4 tables. arXiv admin note: text overlap with arXiv:1307.4636