Search

Abstract In 2021, a new charm-strange meson, $$D_{s0}(2590)^+$$ D s 0 ( 2590 ) + , was discovered, which is believed to be the $$D_s^+(2^1S_0)$$ D s + ( 2 1 S 0 ) . However, its low mass and wide width are challenged by theoretical results. Given the small branching ratio of the current production channel, resulting in a small number of events and large errors, we suggest searching for the $$D_{s0}(2590)^+$$ D s 0 ( 2590 ) + in the B meson nonleptonic decays, $$B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+$$ B q → D q ( ∗ ) D s 0 ( 2590 ) + ( $$q=u,d$$ q = u , d ), followed by $$D_{s0}(2590)^+\rightarrow D^*K$$ D s 0 ( 2590 ) + → D ∗ K . We find that $$Br(B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+)\times Br(D_{s0}(2590)^+\rightarrow D^{*}K)=(2.16\sim 2.82)\times 10^{-3}$$ B r ( B q → D q ( ∗ ) D s 0 ( 2590 ) + ) × B r ( D s 0 ( 2590 ) + → D ∗ K ) = ( 2.16 ∼ 2.82 ) × 10 - 3 is very large, and the result is not sensitive to the mass of $$D_{s0}(2590)^+$$ D s 0 ( 2590 ) + . Due to the large branching ratio, numerous $$D_{s0}(2590)^+$$ D s 0 ( 2590 ) + events are expected. This study is based on the framework of the instantaneous Bethe–Salpeter equation, and the relativistic wave functions used for mesons contain different partial waves. The contributions of the different partial waves are also studied.

Abstract Using an almost complete relativistic method based on the Bethe–Salpeter equation, we study the mixing angle $$\theta $$ θ , the mass splitting $$\bigtriangleup M$$ △ M , the strong decay widths $$\Gamma (D^{({\prime })}_1)$$ Γ ( D 1 ( ′ ) ) and the weak production rates $$Br(B\rightarrow D^{({\prime })}_1\ell \nu _{\ell })$$ B r ( B → D 1 ( ′ ) ℓ ν ℓ ) of the $$D_1(2420)$$ D 1 ( 2420 ) and $$D_1^{\prime }(2430)$$ D 1 ′ ( 2430 ) . We find there is the strong cancellation between the $$^1P_1$$ 1 P 1 and $$^3P_1$$ 3 P 1 partial waves in $$D_1^{\prime }(2430)$$ D 1 ′ ( 2430 ) with $$\theta \sim -\,35.3^{\circ }$$ θ ∼ - 35 . 3 ∘ , which leads to the ‘1/2 vs 3/2’ puzzle. The puzzle can not be overcome by adding only relativistic corrections since in a large parameter range where $$\bigtriangleup M$$ △ M is linear varying and not small, the $$\theta $$ θ , $$\Gamma (D^{({\prime })}_1)$$ Γ ( D 1 ( ′ ) ) and $$Br(B\rightarrow D^{({\prime })}_1\ell \nu _{\ell })$$ B r ( B → D 1 ( ′ ) ℓ ν ℓ ) remain almost unchanged but conflict with data. While in a special range around the mass inverse point where $$\bigtriangleup M=0$$ △ M = 0 and $$\theta =\pm \, 90^{\circ }$$ θ = ± 90 ∘ , they change rapidly but we find the windows where $$\bigtriangleup M$$ △ M , $$\Gamma (D^{({\prime })}_1)$$ Γ ( D 1 ( ′ ) ) and $$Br(B\rightarrow D^{({\prime })}_1\ell \nu _{\ell })$$ B r ( B → D 1 ( ′ ) ℓ ν ℓ ) are all consistent with data. The small $$\bigtriangleup M$$ △ M confirmed by experiment, is crucial to solve the ‘1/2 vs 3/2’ puzzle.

Abstract The relativistic Bethe–Salpeter method is adopted to study the OZI-allowed strong decays of the $$2^+$$ 2 + state $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 5747 ) 0 , with emphasis on the relativistic corrections. We first study the partial waves in the wave functions used and find that there are P, D, and F partial waves in the $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 5747 ) 0 meson, with ratios of $$P/D/F=1:0.421:0.051$$ P / D / F = 1 : 0.421 : 0.051 . We also find that $$S/P/D=1:0.354:0.046$$ S / P / D = 1 : 0.354 : 0.046 for $$B^*$$ B ∗ , and $$S/P=1:0.343$$ S / P = 1 : 0.343 for the B meson. The large components of the D wave in $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 5747 ) 0 and the P wave in $$B^{(*)}$$ B ( ∗ ) mean that large relativistic effects exist in these states. Second, we calculate the strong decays, and the total decay width $$\Gamma (B^{*}_{2}(5747)^{0})=25.9$$ Γ ( B 2 ∗ ( 5747 ) 0 ) = 25.9 MeV and the branching fraction $$\Gamma (B^{*}_{2}(5747)^{0} \rightarrow B^{*}\pi )$$ Γ ( B 2 ∗ ( 5747 ) 0 → B ∗ π ) / $$\Gamma (B^{*}_{2}(5747)^{0} \rightarrow B\pi )=0.96$$ Γ ( B 2 ∗ ( 5747 ) 0 → B π ) = 0.96 obtained are consistent with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, and find that the relativistic effects are about $$15\%$$ 15 % and $$11\%$$ 11 % for $$B^{*}_{2}(5747)^{0} \rightarrow B\pi $$ B 2 ∗ ( 5747 ) 0 → B π and $$B^{*}_{2}(5747)^{0} \rightarrow B^{*}\pi $$ B 2 ∗ ( 5747 ) 0 → B ∗ π , respectively, which are much smaller than our expected effects, showing that the relativistic corrections cancel each other in these decays.

Abstract We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the S matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $$D^*(2010)\rightarrow D\pi $$ D ∗ ( 2010 ) → D π , we study the newly observed $$D_{s0}(2590)^{+}$$ D s 0 ( 2590 ) + with supposing it to be the state $$D_s(2^1S_0)^+$$ D s ( 2 1 S 0 ) + , we find its decay width $$\Gamma $$ Γ is highly sensitive to the $$D_{s0}(2590)^{+}$$ D s 0 ( 2590 ) + mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we studied the overlap integral over the wave functions of initial and final states, here we parameterized it as X which is model-independent, and the ratio $$\Gamma /{|{\mathbf {P}_f}|^3}$$ Γ / | P f | 3 , both are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $$X_{D_s(2S) \rightarrow D^*K}=0.25\sim 0.41$$ X D s ( 2 S ) → D ∗ K = 0.25 ∼ 0.41 and $$\Gamma /{|{\mathbf {P}_f}|^3}=0.81\sim 1.77$$ Γ / | P f | 3 = 0.81 ∼ 1.77 $$\hbox {MeV}^{-2}$$ MeV - 2 are smaller than experimental data $$0.585^{+0.015}_{-0.035}$$ 0 . 585 - 0.035 + 0.015 and $$4.54^{+0.25}_{-0.52}$$ 4 . 54 - 0.52 + 0.25 $$\hbox {MeV}^{-2}$$ MeV - 2 . Further compared with $$X^{ex}_{D^*(2010) \rightarrow D\pi }=0.540\pm 0.009$$ X D ∗ ( 2010 ) → D π ex = 0.540 ± 0.009 , the current data $$X^{ex}_{D_s(2S) \rightarrow D^*K}=0.585^{+0.015}_{-0.035}$$ X D s ( 2 S ) → D ∗ K ex = 0 . 585 - 0.035 + 0.015 is too big to be an reasonable value, so it is early to say $$D_{s0}(2590)^{+}$$ D s 0 ( 2590 ) + is the conventional $$D_s(2^1S_0)^+$$ D s ( 2 1 S 0 ) + meson.

Abstract Mass spectra and wave functions of the $$J^P=\frac{1}{2}^+$$ J P = 1 2 + (bcq) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the $$1^+$$ 1 + and $$0^+$$ 0 + (bc)-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the $$0^+$$ 0 + diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the (bc)-diquark. Considering the obtained diquark form factors, the (bcq) baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the $$0^+$$ 0 + and $$1^+$$ 1 + diquarks. The general wave function of the $$\frac{1}{2}^+$$ 1 2 + (bcq) baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between $$\Xi _{bc}(\Omega _{bc})$$ Ξ bc ( Ω bc ) and $$\Xi _{bc}'(\Omega '_{bc})$$ Ξ bc ′ ( Ω bc ′ ) in ground states are computed and determined to be small ( $$\sim \!1\%$$ ∼ 1 % ). The numerical results indicate that it is a good choice to take $$\Xi _{bc}$$ Ξ bc and $$\Xi '_{bc}$$ Ξ bc ′ as the baryon states with the inside (bc)-diquarks occupying the definite spin.

Abstract In this paper, we study the FCNC decay processes of B and $$B_c$$ 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 between 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 $$B_c$$ B c decays, which are of the order of $$10^{-6}$$ 10 - 6 or $$10^{-5}$$ 10 - 5 when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when $$m_\chi \approx 3.5$$ m χ ≈ 3.5 –4 GeV, where $$m_\chi $$ m χ is the mass of the invisible particle.

Abstract We study the CP violation in two-body nonleptonic decays of $$B_c$$ 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: $$B_c\rightarrow c{\bar{c}}(2S, 2P)+{\bar{c}}q(1S, 1P)$$ B c → c c ¯ ( 2 S , 2 P ) + c ¯ q ( 1 S , 1 P ) , $$B_c\rightarrow c{\bar{c}}(1S)+{\bar{c}}q(2S, 2P)$$ B c → c c ¯ ( 1 S ) + c ¯ q ( 2 S , 2 P ) , $$B_c\rightarrow c{\bar{c}}(1P)+{\bar{c}}q(2S)$$ B c → c c ¯ ( 1 P ) + c ¯ q ( 2 S ) , $$B_c\rightarrow c{\bar{c}}(1D)+{\bar{c}}q(1S, 1P)$$ B c → c c ¯ ( 1 D ) + c ¯ q ( 1 S , 1 P ) , and $$B_c\rightarrow c{\bar{c}}(3S)+{\bar{c}}q(1S)$$ B c → c c ¯ ( 3 S ) + c ¯ q ( 1 S ) . 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 $$10^{-3}$$ 10 - 3 . The CP violation effect in $$B_c \rightarrow \eta _c(1S)+D(2S)$$ B c → η c ( 1 S ) + D ( 2 S ) , $$B_c \rightarrow \eta _c(1S)+D_0^{*}(2P)$$ B c → η c ( 1 S ) + D 0 ∗ ( 2 P ) , and $$B_c \rightarrow J/\psi +D^{*}(2S)$$ B c → J / ψ + D ∗ ( 2 S ) are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $$3\sigma $$ 3 σ level, at least $$10^7$$ 10 7 $$B_c$$ B c events are needed.

Abstract Considering Z(3930) and X(4160) as $$\chi _{c2}(2P)$$ χc2(2P) and $$\chi _{c2}(3P)$$ χc2(3P) states, the semileptonic and nonleptonic of $$B_c$$ Bc 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 $$B_c$$ Bc weak decays to Z(3930) and X(4160) are predicted. Some of the branching ratios are: $$Br(B_c^+\rightarrow Z(3930)e^+\nu _e)=(3.03^{+0.09}_{-0.16})\times 10^{-4}$$ Br(Bc+→Z(3930)e+νe)=(3.03-0.16+0.09)×10-4 and $$Br(B_c^+\rightarrow X(4160)e^+\nu _e)=(3.55^{+0.83}_{-0.35})\times 10^{-6}$$ Br(Bc+→X(4160)e+νe)=(3.55-0.35+0.83)×10-6 . These results may provide useful information to discover Z(3930) and X(4160) and the necessary information for the phenomenological study of $$B_c$$ Bc physics.

Abstract We solved the instantaneous Bethe–Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. Since we cannot give a complete QCD-based calculation, the results are gauge dependent. We compared the obtained mass spectra of heavy pseudoscalars between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge.

Abstract In this paper, the dilepton electromagnetic decays $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$ χcJ(1P)→J/ψe+e- and $$\chi _{cJ}(1P) \rightarrow J\psi \mu ^+\mu ^-$$ χcJ(1P)→Jψμ+μ- , where $$\chi _{cJ}$$ χcJ denotes $$\chi _{c0}$$ χc0 , $$\chi _{c1}$$ χc1 and $$\chi _{c2}$$ χc2 , 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 $$e^+e^-$$ e+e- , the gauge invariance is decisive and should be considered carefully. For the processes of $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$ χcJ(1P)→J/ψe+e- , the branching fraction are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi e^+e^-]=1.06^{+0.16}_{-0.18} \times 10^{-4}$$ B[χc0(1P)→J/ψe+e-]=1.06-0.18+0.16×10-4 , $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi e^+e^-]=2.88^{+0.50}_{-0.53} \times 10^{-3}$$ B[χc1(1P)→J/ψe+e-]=2.88-0.53+0.50×10-3 , and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi e^+e^-]=1.74^{+0.22}_{-0.21} \times 10^{-3}$$ B[χc2(1P)→J/ψe+e-]=1.74-0.21+0.22×10-3 . The calculated branching fractions of $$\chi _{cJ}(1P)\rightarrow J/\psi \mu ^+\mu ^-$$ χcJ(1P)→J/ψμ+μ- channels are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=3.80^{+0.59}_{-0.64} \times 10^{-6}$$ B[χc0(1P)→J/ψμ+μ-]=3.80-0.64+0.59×10-6 , $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=2.04^{+0.36}_{-0.38} \times 10^{-4}$$ B[χc1(1P)→J/ψμ+μ-]=2.04-0.38+0.36×10-4 , and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=1.66^{+0.19}_{-0.19} \times 10^{-4}$$ B[χc2(1P)→J/ψμ+μ-]=1.66-0.19+0.19×10-4 .

Abstract In this paper, we use the instantaneous Bethe–Salpeter method to calculate the semi-leptonic and non-leptonic production of the orbitally excited scalar $$ D_0^* $$ D0∗ in B meson decays. When the final state is 1P state $$ D_0^*(2400) $$ D0∗(2400) , our theoretical decay rate is consistent with experimental data. For $$ D_J^*(3000) $$ DJ∗(3000) final state, which was observed by LHCb collaboration recently and here treated as the orbitally excited scalar $$D^{*}_{0}(2P)$$ D0∗(2P) , its rate is in the order of $$ 10^{-4} \sim 10^{-6}$$ 10-4∼10-6 . We find the special node structure of $$D^{*}_{0}(2P)$$ D0∗(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 $$ 10^{-5}$$ 10-5 .

Abstract We calculate the two-body strong decays of the orbitally excited scalar mesons $$D_0^*(2400)$$ D0∗(2400) and $$D_J^*(3000)$$ DJ∗(3000) by using the relativistic Bethe–Salpeter (BS) method. $$D_J^*(3000)$$ DJ∗(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 $$0^+(2P)$$ 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 $$D_0^*(2400)^{0}$$ D0∗(2400)0 and $$ D_0^*(2400)^+$$ D0∗(2400)+ are 226 and 246 MeV, respectively. With the assumption of $$0^+(2P)$$ 0+(2P) state, the widths of $$D_J^*(3000)^0$$ DJ∗(3000)0 and $$D_J^*(3000)^+$$ DJ∗(3000)+ are both about 131 MeV, which is close to the present experimental data. Therefore, $$D_J^*(3000)$$ DJ∗(3000) is a strong candidate for the $$2^3P_0$$ 23P0 state.

Abstract We give a systematical study on the recently reported excited charm and charm–strange mesons with potential $$1^-$$ 1 - spin–parity, including the $$D^*_{s1}(2700)^+$$ D s 1 ∗ ( 2700 ) + , $$D^*_{s1}(2860)^+$$ D s 1 ∗ ( 2860 ) + , $$D^*(2600)^0$$ D ∗ ( 2600 ) 0 , $$D^*(2650)^0$$ D ∗ ( 2650 ) 0 , $$D^*_1(2680)^0$$ D 1 ∗ ( 2680 ) 0 and $$D^*_1(2760)^0$$ D 1 ∗ ( 2760 ) 0 . The main strong decay properties are obtained in the framework of Bethe–Salpeter (BS) methods. Our results reveal that the two $$1^-$$ 1 - charm–strange mesons can be well described by the further $$2^3\!S_1$$ 2 3 S 1 – $$1^3\!D_1$$ 1 3 D 1 mixing scheme with a mixing angle of $$(8.7^{+3.9}_{-3.2})^\circ $$ ( 8 . 7 - 3.2 + 3.9 ) ∘ . The predicted decay ratio $$\frac{\mathcal {B}(D^*K)}{\mathcal {B}(D~K)}$$ B ( D ∗ K ) B ( D K ) for $$D^*_{s1}(2860)$$ D s 1 ∗ ( 2860 ) is $$0.62^{+0.22}_{-0.12}$$ 0 . 62 - 0.12 + 0.22 . $$D^*(2600)^0$$ D ∗ ( 2600 ) 0 can also be explained as the $$2^3\!S_1$$ 2 3 S 1 predominant state with a mixing angle of $$-(7.5^{+4.0}_{-3.3})^\circ $$ - ( 7 . 5 - 3.3 + 4.0 ) ∘ . Considering the mass range, $$D^*(2650)^0$$ D ∗ ( 2650 ) 0 and $$D^*_1(2680)^0$$ D 1 ∗ ( 2680 ) 0 are more likely to be the $$2^3\!S_1$$ 2 3 S 1 predominant states, although the total widths under the two $$2^3\!S_1$$ 2 3 S 1 and $$1^3\!D_1$$ 1 3 D 1 assignments have no great conflict with the current experimental data. The calculated width for the LHCb $$D^*_1(2760)^0$$ D 1 ∗ ( 2760 ) 0 seems to be about 100 MeV larger than the experimental measurement if taking it as $$1^3\!D_1$$ 1 3 D 1 or $$1^3\!D_1$$ 1 3 D 1 dominant state $$c\bar{u}$$ c u ¯ . The comparisons with other calculations and several important decay ratios are also presented. For the identification of these $$1^-$$ 1 - charm mesons, further experimental information, such as $$\frac{\mathcal {B}(D\pi )}{\mathcal {B}(D^*\pi )}$$ B ( D π ) B ( D ∗ π ) , is necessary.