B(*)B¯(*)intermediate states contribution to

H. W. Ke

¹

,

Xue–Qian Li

²

,

Xiang Liu

³

Abstract

In this work, we investigate the rescattering effects in the radiative decay Çð5SÞ ! b þ , which were suggested to be crucially important for understanding the anomalous largeness of the branching ratios BðÇð5SÞ ! Çð1SÞ þ Þ and BðÇð5SÞ ! Çð1SÞ þ Þ. Our calculations show that the rescattering effects may enhance ÀðÇð10860Þ ! b þ Þ by four orders, but the tetraquark structure does not. Recently the BABAR and CLEO collaborations have measured the mass of b and the branching ratios BðÇð2SÞ ! b þ Þ, BðÇð3SÞ ! b þ Þ. We hope that very soon, Çð10860Þ ! b þ will be measured and it would be an ideal opportunity for testing whether the rescattering or the tetraquark structure is responsible for the anomaly of BðÇð5SÞ ! ÇðnSÞ þ À ðn ¼ 1; 2; 3ÞÞ, i.e., the future measurements on the radiative decays of Çð5SÞ might be a touchstone of the two mechanisms.

Importance of confinement in instanton induced potential for bottomonium spectroscopy

“…Looking to the advances in the experimental side, it is necessary to review earlier theoretical attempts to understand the quarkonia systems. Although there are many different approaches like Lattice QCD methods [26][27][28][29], NRQCD methods [30][31][32], Light front quark model [33][34][35][36], various coupled channel quark models [37][38][39], Effective Lagrangian approach [40] etc., employed to study them, still there exist no consensus and discrepancy persist in the predictions. For instance, authors [41] have used nonrelativistic constituent quark model wherein the lowest lying bottomonium states Υ (1S) and η b (1S) are about 50 MeV higher than the PDG [43] data but the same model give fine agreement for the higher excited state Υ (6S) while the relativized quark model [42] provides very good description of the low-lying states but higher excited Υ (6S) is overestimated by 100 MeV.…”

A natural interpretation on the data of $Λ_c\toΣπ$

“…In terms of the effective interaction, the corresponding coupling constants the first step of the sequential Λ c decays could be formulated according to the scenario presented in the literature. The re-scattering mechanism has been successfully applied to explain some anomalies existing in low energy experiments, such as the decays of Υ and bottomed mesons [18][19][20][21], thus we have a full confidence that the mechanism also works well here.…”

“…However the pion in Λ c → Σπ is far from being soft so it is not natural to explain the data by using the current algebra. Following the approach in the references [18][19][20][21] we suggest that a final state interaction (or re-scattering) in the decays of Λ c can contribute to the observed Λ c → Σπ. In terms of the effective interactions, coupling constants we calculate the contribution of the subprocess Λ c → Λρ → Σπ to the observed Λ c → Σπ.…”

“…In some Refs. [19,21] the form factor is parameterized as Λ 1 = λΛ QCD + m P with Λ QCD ≈ 220 MeV and the dimensionless parameter λ is of order of unit.…”

Cabibbo-favored $Λ^+_c\toΛa_{0}(980)^+$ decay in the final state interaction

“…The cutoff parameter c Λ is not well controlled. The estimation presents that c Λ = λΛ QCD + m π , where Λ QCD = 0.22 GeV, and λ is a free parameter [13,18,21]. On the other hand, c Λ can be taken as an empirical parameter, determined by the data.…”