[en] In this paper, the dilepton electromagnetic decays χ${}_{cJ}$(1P)→J/ψe${}^{+}$e${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$ and χ${}_{cJ}$(1P)→Jψμ${}^{+}$μ${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$, where χ${}_{cJ}$ denotes χ${}_{c0}$, χ${}_{c1}$ and χ${}_{c2}$, 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${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$, the gauge invariance is decisive and should be considered carefully. For the processes of χ${}_{cJ}$(1P)→J/ψe${}^{+}$e${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$, the branching fraction are: B[χ${}_{c0}$(1P)→J/ψe${}^{+}$e${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=1.06${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.18}^{+0.16}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}4}$, B[χ${}_{c1}$(1P)→J/ψe${}^{+}$e${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=2.88${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.53}^{+0.50}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}3}$, and B[χ${}_{c2}$(1P)→J/ψe${}^{+}$e${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=1.74${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.21}^{+0.22}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}3}$. The calculated branching fractions of χ${}_{cJ}$(1P)→J/ψμ${}^{+}$μ${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$ channels are: B[χ${}_{c0}$(1P)→J/ψμ${}^{+}$μ${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=3.80${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.64}^{+0.59}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}6}$, B[χ${}_{c1}$(1P)→J/ψμ${}^{+}$μ${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=2.04${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.38}^{+0.36}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}4}$, and B[χ${}_{c2}$(1P)→J/ψμ${}^{+}$μ${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}$]=1.66${}_{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}0.19}^{+0.19}$×10${}^{\text{â<!-- ?? -->}\text{ˆ<!-- ?? -->}\text{’<!-- ??? -->}4}$.

[en] In this paper, we use the instantaneous Bethe–Salpeter method to calculate the semi-leptonic and non-leptonic production of the orbitally excited scalar D${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}{\text{—<!-- ??? -->}}_0$ in B meson decays. When the final state is 1P state D${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}{\text{—<!-- ??? -->}}_0$(2400), our theoretical decay rate is consistent with experimental data. For D${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}{\text{—<!-- ??? -->}}_J$(3000) final state, which was observed by LHCb collaboration recently and here treated as the orbitally excited scalar D${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}{\text{—<!-- ??? -->}}_0$(2P), its rate is in the order of 10${}^{-<!--\; ???\; -->4}$∼10${}^{-<!--\; ???\; -->6}$. We find the special node structure of D${}^{\text{â<!-- ?? -->}}\text{ˆ<!-- ?? -->}{\text{—<!-- ??? -->}}_0$(2P) wave function possibly results in the suppression of its branching ratio and the abnormal uncertainty. The 3P states production rate is in the order of 10${}^{-<!--\; ???\; -->5}$.

[en] In this paper we study the semileptonic decays of B*, $B_s^{\ast <!--\; ???\; -->}$, and $B_c^{\ast <!--\; ???\; -->}$ by using the Bethe–Salpeter method with instantaneous approximation. Both the $V\to <!--\; ???\; -->{Pl}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_l$ and $V\to <!--\; ???\; -->{Vl}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_l$ cases are considered. The largest partial width of these channels is of the order of 10⁻¹⁴ GeV. The branching ratios of these semileptonic decays are also estimated by using the partial width of the one photon decay channel to approximate the total width. For $B^{\ast <!--\; ???\; -->-<!--\; ???\; -->}\to <!--\; ???\; -->D^{(\ast <!--\; ???\; -->)0}{e}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e$ and $B_s^{\ast <!--\; ???\; -->0}\to <!--\; ???\; -->D_s^{(\ast <!--\; ???\; -->)+}{e}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e$, the branching ratios are of the order of 10⁻⁸ and 10⁻⁷, respectively. For $B_c^{\ast <!--\; ???\; -->-<!--\; ???\; -->}$, the $J/\mathrm{\psi <!--\; ??\; -->}{e}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e$ and $B_s^{\ast <!--\; ???\; -->0}{e}^{-<!--\; ???\; -->}{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e$ channels have the largest branching ratio, which is of the order of 10⁻⁶. (paper)

[en] In this paper, we study the light scalar and pseudoscalar invisible particles in the flavor changing neutral current processes of the B_c meson. Effective operators are introduced to describe the couplings between quarks and light invisible particles. The Wilson coefficients are extracted from the experimental results of the B and D mesons, which are used to predict the upper limits of the branching fractions of the similar decay processes for the B_c meson. The hadronic transition matrix element is calculated with the instantaneously approximated Bethe-Salpeter method. The upper limits of the branching fractions when m_χ taking different values are presented. It is found that at some region of m_χ, the channel B_c → D_s^(*)χχ has the largest upper limit which is of the order of 10⁻⁶, and for B_c → D_s^*χχ^†, the largest value of the upper limits can achieve the order of 10⁻⁵. Other decay modes, such as B_c → D^(*)χχ^(†) and B_c → B^(*)χχ^(†), are also considered.

[en] 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 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 2³P₀ state. (orig.)