In this paper we study the semileptonic decays of B * , B s *, and B c * by using the Bethe-Salpeter method with instantaneous approximation. Both the V Pl l n -¯and V Vl l n -¯cases are considered. The largest partial width of
* n-¯channels have the largest branching ratio, which is of the order of 10 −6 .
Recently, the deviation of the ratios [Formula: see text], [Formula: see text] and [Formula: see text] have been found between experimental data and the Standard Model predictions, which may be the hint of new physics. In this work, we calculate these ratios within the Standard Model by using the improved instantaneous Bethe–Salpeter method. The emphasis is pad to the relativistic correction of the form factors. The results are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which are consistent with predictions of other models and the experimental data. The semileptonic decay rates and corresponding form factors at zero recoil are also given.
In this paper, we systematically calculate two-body strong decays of newly observed D J ð3000Þ and D sJ ð3040Þ with 2Pð1 þ Þ and 2Pð1 þ0 Þ assignments in an instantaneous approximation of the Bethe-Salpeter equation method. Our results show that both resonances can be explained as the 2Pð1 þ 0 Þ with broad width . For D sJ ð3040Þ, the total width is 157.4 MeV in our calculation, close to the lower limit of experimental data, and the dominant channels are D Ã K and D Ã K Ã . 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.
Relativistic effects are important in the rigorous study of heavy quarks. In this paper, we study the relativistic corrections of semileptonic B c decays to charmonium with the instantaneous Bethe-Salpeter method. Within the Bethe-Salpeter framework, we use two methods to study the relativistic effects. One of them is to expand the transition amplitude in powers of q which is the relative momentum between the quark and antiquark, and the other is to expand the amplitude base on the wave functions. In the level of decay width, the results show that, for the transition of B c → η c , the relativistic correction is about 22%; for B c → J/ψ, it is about 19%; the relativistic effects of 1P final states are about 14 ∼ 46% larger than those of 1S final states; for 2S final states, they are about 19 ∼ 28% larger than those of 1S final states; for 3S final states, they are about 12 ∼ 13% larger than those of 2S final states; for 2P final states, they are about 10 ∼ 14% larger than those of 1P final states; for 3P final states, they are about 7 ∼ 12% larger than those of 2P final states. We conclude that the relativistic corrections of the B c decays to the orbitally or radially excited charmonium (2S, 3S, 1P, 2P, 3P) are quite large.
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 2 3 P 0 state.
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