In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, in which one invisible particle is emitted. Both the spin-0 and spin-1 cases are considered. The model-independent effective Lagrangian is introduced to describe the coupling be
tween the light invisible boson and quarks. The constraints of the coupling coefficients are extracted by experimental upper limits of the missing energy in $B$ meson decays. The bounds are used to predict the upper limits of branching fractions of corresponding $B_c$ decays, which are of the order of $10^{-6}$ or $10^{-5}$ when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when $m_chiapprox3.5- 4$~GeV, where $m_chi$ is the mass of the invisible particle.
We study the CP violation in two-body nonleptonic decays of $B_c$ meson. We concentrate on the decay channels which contain at least one excited heavy meson in the final states. Specifically, the following channels are considered: $B_cto cbar c(2S, 2
P)+bar cq(1S, 1P)$, $B_cto cbar c(1S)+bar cq(2S, 2P)$, $B_cto cbar c(1P)+bar cq(2S)$, $B_cto cbar c(1D)+bar cq(1S, 1P)$, and $B_cto cbar c(3S)+bar cq(1S)$. The improved Bethe-Salpeter method is applied to calculate the hadronic transition matrix element. Our results show that some decay modes have large branching ratios, which is of the order of $10^{-3}$. The CP violation effect in $B_c rightarrow eta_c(1S)+D(2S)$, $B_c rightarrow eta_c(1S)+D_0^{*}(2P)$, and $B_c rightarrow J/psi+D^{*}(2S)$ are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $3sigma$ level, at least $10^7$ $B_c$ events are needed.
In this work, we study the lepton-number-violating processes of $K^pm$ and $D^pm$ mesons. Two quasi-degenerate sterile neutrinos are assumed to induce such processes. Different with the case where only one sterile neutrino involves, here, the CP phas
es of the mixing parameters could give sizable contribution. This, in turn, would affect the absolute values of the mixing parameters determined by the experimental upper limits of the branching fractions. A general function which express the difference of the mixing parameters for two-generation and one-generation is presented. Special cases with specific relations of the parameters are discussed. Besides, we also thoroughly investigate the CP violation effect of such processes. It is shown that generally $mathcal A_{CP}$ is a function of the sterile neutrino mass.
Recently, many new excited states of heavy mesons, especially the radially excited states, are discovered. The study of the production processes of these states from the ground b-flavored mesons is of interest. In this paper, we use the improved Beth
e-Salpeter method to study the semi-leptonic and non-leptonic decays of $B$, $B_s$, and $B_c$ mesons, where the final states are focused on the radial excited $2S$ and $3S$ states. We find that many channels have branching ratios up to $10^{-4}$, which are within the detection accuracy of current experiments.
In this paper, the dilepton electromagnetic decays $chi_{cJ}(1P) to J/psi e^+e^-$ and $chi_{cJ}(1P) to Jpsi mu^+mu^-$, where $chi_{cJ}$ denotes $chi_{c0}$, $chi_{c1}$ and $chi_{c2}$, are calculated systematically in the improved Bethe-Salpeter method
. The numerical results of decay widths and the invariant mass distributions of the final lepton pairs are given. The comparison is made with the recently measured experimental data of BESIII. It is shown that for the cases including $e^+e^-$, the gauge invariance is decisive and should be considered carefully. For the processes of $chi_{cJ}(1P) to J/psi e^+e^-$, the branching fraction are: $mathcal{B}[chi_{c0}(1P) to J/psi e^+e^-]=1.06^{+0.16}_{-0.18} times 10^{-4}$, $mathcal{B}[chi_{c1}(1P) to J/psi e^+e^-]=2.88^{+0.50}_{-0.53} times 10^{-3}$, and $mathcal{B}[chi_{c2}(1P) to J/psi e^+e^-]=1.74^{+0.22}_{-0.21} times 10^{-3}$. The calculated branching fractions of $chi_{cJ}(1P)to J/psi mu^+mu^-$ channels are: $mathcal{B}[chi_{c0}(1P) to J/psi mu^+mu^-]=3.80^{+0.59}_{-0.64} times 10^{-6}$, $mathcal{B}[chi_{c1}(1P) to J/psi mu^+mu^-]=2.04^{+0.36}_{-0.38} times 10^{-4}$, and $mathcal{B}[chi_{c2}(1P) to J/psi mu^+mu^-]=1.66^{+0.19}_{-0.19} times 10^{-4}$.
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.
We calculate the two-body strong decays of the orbitally excited scalar mesons $D_0^*(2400)$ and $D_J^*(3000)$ by using the relativistic Bethe-Salpeter (BS) method. $D_J^*(3000)$ was observed recently by the LHCb Collaboration, the quantum number of
which has not been determined yet. In this paper, we assume that it is the $0^+(2P)$ state and obtain the transition amplitude by using the PCAC relation, low-energy theorem and effective Lagrangian method. For the $1P$ state, the total widths of $D_0^*(2400)^{0}$ and $ D_0^*(2400)^+$ are 226 MeV and 246 MeV, respectively. With the assumption of $0^+(2P)$ state, the widths of $D_J^*(3000)^0$ and $D_J^*(3000)^+$ are both about 131 MeV, which is close to the present experimental data. Therefore, $D_J^*(3000)$ is a strong candidate for the $2^3P_0$ state.
In this paper, we systematically calculate two-body strong decays of newly observed $D_J(3000)$ and $D_{sJ}(3040)$ with 2P$(1^+)$ and 2P$(1^{+prime})$ assignments in an instantaneous approximation of the Bethe-Salpeter equation method. Our results sh
ow that both resonances can be explained as the 2P$(1^{+})$ with broad width via $^3P_1$ and $^1P_1$ mixing in $D$ and $D_s$ families. For $D_J(3000)$, the total width is 229.6 MeV in our calculation, close to the upper limit of experimental data, and the dominant decay channels are $D_2^*pi$, $D^*pi$, and $D^*(2600)pi$. For $D_{sJ}(3040)$, the total width is 157.4 MeV in our calculation, close to the lower limit of experimental data, and the dominant channels are $D^*K$ and $D^*K^*$. These results are consistent with observed channels in experiments. Given the very little information that has been obtained from experiments and the large error bars of the total decay widths, we recommend the detection of dominant channels in our calculation.
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 bott
omed $B(5970)$ 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.
We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constru
cted. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the $3g$ channel are as follows: $Gamma_{^3D_2(cbar c)rightarrow ggg} = 9.24$ keV, $Gamma_{^3D_3(cbar c)rightarrow ggg}=25.0$ keV, $Gamma_{^3D_2(bbar b)rightarrow ggg}= 1.87$ keV, and $Gamma_{^3D_3(bbar b)rightarrow ggg}= 0.815$ keV.
