Some problems in heavy-quarkonium decays

Abstract

Problems proposed by the present authors for studies at c-τ, b, super-c-τ, and super-b factories are formulated. First, a comparison of the mechanisms of light-scalar-meson production in the process \(D_s^ + \to s\bar se^ + \nu \to [\sigma (600) + f_0 (980)]e^ + \nu \to \pi ^ + \pi ^ - e^ + \nu\) with the mechanisms of light-pseudoscalar-meson production in the process \(D_s^ + \to s\bar se^ + \nu \to (\eta /\eta ')e^ + \nu\) reveals that the transition \(s\bar s \to \sigma (600)\) is negligible in relation to the transition \(s\bar s \to f_0 (980)\). As for f0(980), \(s\bar s \to f_0 (980)\) is not more than 30% of \(s\bar s \to \eta _s (\eta _s = s\bar s)\). It is proposed to study light scalar mesons in the semileptonic decays of D+(D−) \(D^0 (\bar D^0 )\), B+(B−), and \(B^0 (\bar B^0 )\). Second, interference phenomena observed in the ψ(3770)-resonance region in the reaction \(e^ + e^ - \to D\bar D\) are described on the basis of models satisfying the elastic-unitarity requirement. As a model, we propose the model of mixed ψ(3770) and ψ(2S) resonances. In order to select theoretical models, it is proposed to employ non-\(D\bar D\) decay channels such as e+e− → ψ(3770) → γχc0, J/ψη, and ϕη. Third, branching ratios are calculated for ψ(3770) and ϒ(10580) decays proceeding to light (non-\(D\bar D\) and non-\(B\bar B\)) hadrons owing to the contributions of real \(D\bar D\) and \(B\bar B\) intermediate states. The predictions obtained for these branching ratios lie in the range of 1% ≲ BR ≲ 15%. The lower boundary of this range is ten times higher than the branching ratio for annihilation to three gluons.