The σ-Meson Production in Excited ϒ Decay Processes

Abstract

We analyze the ππ production amplitudes in the excited Υ decay processes, Υ (2S) → Υ (1S)π + π − , Υ (3S) → Υ (1S)π + π − and Υ (3S) → Υ (2S)π + π − , and the ππ and KK production amplitudes in the charmonium decay processes, ψ(2S) → J/ψπ + π − and J/ψ → φπ + π − , φK + K − , including the possible effect of light σ production. The amplitudes are parametrized by the sum of Breit-Wigner amplitudes for the σ and the other relevant particles and of the direct 2π-production amplitude, following the VMW method. All the ππ (and KK) mass spectra are reproduced well with the obtained values of σ-parameters, mσ = 526 +48 −37 MeV and Γσ = 301 +145 −100 MeV, which is almost consistent with the values in our previous phase shift analyses. §1. IntroductionWhether the light σ-meson really exists or does not is an important problem in hadron physics. For many years, its existence had been neglected phenomenologically mainly due to the negative result of the analyses of I = 0 S-wave ππ scattering phase shift.In many ππ-production experiments, a large event concentration or a bump structure in the spectra of ππ invariant mass m ππ around 500 MeV had been observed, however, conventionally it was not regarded as σ-resonance, but as a mere ππ-background, under influence of the so callled "universality argument." 1) In this argument, it is stated that because of the unitarity of S-matrix and of the analyticity of the amplitudes, the ππ production amplitude F takes the form F = α(s)T (T being the ππ scattering amplitude), with a slowly varying real function α(s). The pole position of S-matrix is determined solely through the analysis of T , which was believed to have no light σ-pole at that time.Recently the data of ππ-scattering phase shift had been reanalyzed by many groups 2) including ours and the existence of light σ(450 ∼ 600) was strongly suggested. The result of no σ-existence in the conventional analyses was pointed out 3) to be due to the lack of consideration on the cancellation mechanism guaranteed by chiral symmetry, and shown to be not correct. Furthermore, we have pointed out that the "universality argument" should be revised, taking into account the quark physical picture of hadrons 4) : The essential point is that the strong interaction is a residual interaction of QCD among all color-neutral bound states of quarks, anti-

Chiral Mass Splitting for cs̄ and cn̄ Mesons in the Ũ(12)-Classification Scheme of Hadrons

“…We accept the existence of these vector mesons as true [7]. The resulting assignments, though some of them are ambiguous, are shown in Table 1.…”