The weak decay $B_c$ to $Z(3930)$ and $X(4160)$ by Bethe-Salpeter method

Considering $Z(3930)$ and $X(4160)$ as $chi_{c2}(2P)$ and $chi_{c2}(3P)$ states, the semileptonic and nonleptonic of $B_c$ decays to $Z(3930)$ and $X(4160)$ are studied by the improved Bethe-Salpeter(B-S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of $B_c$ weak decays to $Z(3930)$ and $X(4160)$ are predicted. Some of the branching ratios are: $Br(B_c^+to Z(3930)e^+ u_e)$$=(3.03^{+0.09}_{-0.16})times 10^{-4}$ and $Br(B_c^+to X(4160)e^+ u_e)$$=(3.55^{+0.83}_{-0.35})times 10^{-6}$. These results may provide useful information to discover $Z(3930)$ and $X(4160)$ and the necessary information for the phenomenological study of $B_c$ physics.

The Strong Decays of $P-$wave Mixing Heavy-Light $1^+$ States

Many $P-$wave mixing heavy-light $1^+$ states have not been discovered by experiment, some of them have been discovered but without the information of width, or with large uncertainty widths. In this paper, we study the strong decays of $P-$wave mixing heavy-light $1^+$ states $D^0$, $D^pm$, $D_s^pm$, $B^0$, $B^pm$ and $B_s$ by the improved Bethe-Salpeter(B-S) method in two conditions of mixing angle $theta$: one is $theta=35.3^circ$; another is considering the correction to mixing angle $theta=35.3^circ+theta_1$. And we get some valuable predictions of the strong decay widths: $Gamma(D_1^{prime0})=232$ MeV, $Gamma(D_1^0)=21.5$ MeV, $Gamma(D_1^{primepm})=232$ MeV, $Gamma(D_1^pm)=21.5$ MeV, $Gamma(D_{s1}^{primepm})=0.0101$ MeV, $Gamma(D_{s1}^{pm})=0.950$ MeV, $Gamma(B_1^{primepm})=263$ MeV, $Gamma(B_1^{pm})=16.8$ MeV, $Gamma(B_{s1}^{prime})=0.01987$ MeV and $Gamma(B_{s1})=0.412$ MeV. We find that the decay widths of $D_{s1}^{pm}$ and $B_{s1}$ are very sensitive to the mixing angle. And our results will provide the theoretical assistance by the future experiments.

Doubly-charged scalar in rare decays of $B_c$ meson

In this paper, we study the lepton number violation processes of $B_c$ meson induced by possible doubly-charged scalars. Both the three-body decay channels and the four-body decay channels are considered. For the former, $Brtimesleft(frac{s_Delta h_{ij}}{M_Delta^2}right)^{-2}$ is of the order of $10^{-7}sim 10^{-9}$, and for the later channels, $Brtimesleft(frac{s_Delta h_{ij}}{M_Delta^2}right)^{-2}$ is of the order of $10^{-12}sim 10^{-20}$, where $s_Delta$, $h_{ij}$, $M_Delta$ are the constants related to the doubly-charged boson.

Strong decays of $D_{3}^{ast}(2760)$, $D_{s3}^{ast}(2860)$, $B_{3}^{ast}$, and $B_{s3}^{ast}$

In this paper, we study the OZI-allowed two-body strong decays of $3^-$ heavy-light mesons. Experimentally the charmed $D_{3}^{ast}(2760)$ and the charm-strange $D_{s3}^{ast}(2860)$ states with these quantum numbers have been discovered. For the bottomed $B(5970)$ state, which was found by the CDF Collaboration recently, its quantum number has not been decided yet and we assume its a $3^-$ meson in this paper. The theoretical prediction for the strong decays of bottom-strange state $B_{s3}^ast$ is also given. The relativistic wave functions of $3^-$ heavy mesons are constructed and their numerical values are obtained by solving the corresponding Bethe-Salpeter equation with instantaneous approximation. The transition matrix is calculated by using the PCAC and low energy theorem, following which, the decay widths are obtained. For $D_{3}^ast(2760)$ and $D_{s3}^ast(2860)$, the total strong decay widths are 72.6 MeV and 47.6 MeV, respectively. For $B_3^ast$ with $M=5978$ MeV and $B_{s3}^ast$ with $M=6178$ MeV, their strong decay widths are 22.9 MeV and 40.8 MeV, respectively.

The Strong Decays of X(3940) and X(4160)

The new mesons $X(3940)$ and $X(4160)$ have been found by Belle Collaboration in the processes $e^+e^-to J/psi D^{(*)}bar D^{(*)}$. Considering $X(3940)$ and $X(4160)$ as $eta_c(3S)$ and $eta_c(4S)$ states, the two-body open charm OZI-allowed strong decay of $eta_c(3S)$ and $eta_c(4S)$ are studied by the improved Bethe-Salpeter method combine with the $^3P_0$ model. The strong decay width of $eta_c(3S)$ is $Gamma_{eta_c(3S)}=(33.5^{+18.4}_{-15.3})$ MeV, which is closed to the result of $X(3940)$, therefore, $eta_c(3S)$ is a good candidate of $X(3940)$. The strong decay width of $eta_c(4S)$ is $Gamma_{eta_c(4S)}=(69.9^{+22.4}_{-21.1})$ MeV, considering the errors of the results, its closed to the lower limit of $X(4160)$. But the ratio of the decay width $frac{Gamma(Dbar D^*)}{Gamma (D^*bar D^*)}$ of $eta_c(4S)$ is larger than the experimental data of $X(4160)$. According to the above analysis, $eta_c(4S)$ is not the candidate of $X(4160)$, and more investigations of $X(4160)$ is needed.

The Production of $X(3940)$ and $X(4160)$ in $B_c$ decays

Considering $X(3940)$ and $X(4160)$ as $eta_c(3S)$ and $eta_c(4S)$, we study the productions of $X(3940)$ and $X(4160)$ in exclusive weak decays of $B_c$ meson by the improved Bethe-Salpeter(B-S) Method. Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+to X(3940)e^+ u_e)$$=1.0times10^{-4}$ and $Br(B_c^+to X(4160)e^+ u_e)=2.4times10^{-5}$. That will provide us a new way to observe the $X(3940)$ and $X(4160)$ in the future, as well as to improve the knowledge of $B_c$ meson decay.

General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows

In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reactions. Furthermore, based on the theoretical modelling of the second order shear and heat transfer terms in Burnett equations, a modified analogy is derived in the near continuum regime by considering the rarefied gas effects. And a bridge function is also constructed to describe the nonlinear analogy in the transition flow regime. At last, the direct simulation Monte Carlo method is used to validate the theoretical results. The general analogy, beyond the classical Reynolds analogy, is applicable to both flat plates and blunt-nosed bodies, in either continuous or rarefied hypersonic flows.

Coherence loss and recovery of an electron spin coupled inhomogeneously to a one-dimensional interacting spin bath: an adaptive t-DMRG study

Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, is studied using the adaptive time dependent density matrix renormalization group (t-DMRG) method. It is found that the interplay of the coupling inhomogeneity and the transverse intra-bath interactions results in two qualitatively different coherence evolutions, namely, a coherence preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron spin flip at time $tau$ exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at $sqrt 2 tau$ for the decoherence evolution, respectively. With the diagonal intra-bath interaction included, the specific feature of the periodic regime is kept, while the $sqrt 2tau$-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of $tau$ is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.

Classification of the Super-conducting order parameters under the point group symmetry for a multi-band system: application to LaOFeAs

All the possible super-conducting order parameters for the LaOFeAs system are classified by their transformation under the complete crystal symmetry. The general forms of the super-conducting gap functions for each class are discussed. We find that the gap functions in such a multi-band system belong to three types, full gap, nodal type and finite {}``Fermi arc type. Possible physical consequences caused by different types of gap functions are also discussed.