Masses, branching ratios, and full widths of heavy ρ′, ρ″ and ω′, ω″ resonances

Abstract

Based on the previous and recent fits of multiple data on the reactions of e + e − annihilation, τ lepton decay, and the reaction K − p → π + π − Λ, the magnitude of the branching ratios and total widths of the isovector ρ ′ , ρ ′′ , and the isoscalar ω ′ , ω ′′ resonances are calculated. Some topics on the spectroscopy of the ρ(1450) and ω (1420) , with isospin zero is still far from being clear. Although the characteristic peaks corresponding to these resonances were observed in a number of channels of the one-photon e + e − annihilation, τ lepton decays, NN annihilation, photoproduction, etc., the specific masses and branching ratios are not properly established and hence are not given in the Tables [1]. Recently, the present authors undertook an attempt to fit then existing data on e + e − annihilation, τ lepton decays, and the reactionwhere the above heavy resonances were observed, in the framework of the unified approach. The approach is based on the scheme that takes into account both energy dependence of the partial widths and the mixing via common decay modes among the latter and the ground state ρ(770) and ω(782) resonances, in the respective isovector [2] and isoscalar [3] channels. When so doing, the masses and coupling constants of the resonances were taken as free parameters to be determined from the fit. This choice is convenient because, first, it is just these parameters that are essential in identifying the nature of heavy resonances with J CP = 1 −− . Second, the function χ 2 used in obtaining the intervals of the variation of the extracted parameters is represented in this case as the sum of independent contributions, so that the covariance matrix (see the statistics section in Ref.[1]) is diagonal. However, the results of the measurements are often represented in terms of the masses and branching ratios. In view of the excessive size of the publications [2,3] we refrained at that time from the calculation of the partial widths with the parameters found in [2,3]. Here we fill this gap and calculate the branching ratios and total widths of the ρ ′ 1,2 and ω ′ 1,2 resonances using the new data on the cross section of the reactions, and the data on the spectral function v 1 measured in the decays τ. We also comment on the issue of why the resonances with the masses greater than 1400 MeV should be wide in the conventional qq model, and why their bare masses get shifted towards the greater values as compared to the visible peak positions. The latter point, as will be shown below, is of the direct relevance to the hadronic spectroscopy of the ρ(1300) resonance reported by the LASS group [8], and the ω(1200) resonance reported by the SND team [5].First, let us try to understand why the situation with the resonances possessing the masses greater than 1400 MeV is so complicated despite the numerous experiments aimed at the determination of their masses and partial widths. As is known [1], the indications on the existance of the ρ ′ 1,2 and ω ′ 1,2 resonances were obtained, in particular, in th...

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