On lower scalar quark-antiquark nonets

Abstract

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, KK, ηη in the channel with I G J P C = 0 + 0 ++ are carried out and discussed. In a modelindependent approach, confirmation of the σ-meson below 1 GeV and definite indications of the QCD nature of other f0 resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.

Nature of the scalar-isoscalar mesons in the uniformizing-variable method based on analyticity and unitarity

“…The former is just observed in the processes of decay and production of mesons. An indication about nature of the latter follows from the fact that the f 0 (1500) is coupled with the approximately equal strength with the ππ, KK and ηη systems [25,26,30,[37][38][39] and from the arguments of Ref. [14] on the glueball width.…”

“…[68]. We have used a "model-independent" method [27,30,37,39,40] based on the first principles (analyticity and unitarity) directly applied to the analysis of experimental data. This approach permits us to omit a theoretical prejudice in extracting the resonance parameters.…”

“…Unlike in the previous three-channel analysis of the above processes [25][26][27]39], in this work we used a new uniformizing variable in which we took into account the left-hand branch-point at s = 0 related to the thresholds of the ππ scattering in crossed channels, in addition to the right-hand branch-points related to the thresholds of the analyzed processes. This should diminish considerably dependence of the extracted parameters of resonances on the background because the elastic part of the ππ background is stipulated mainly by the contribution of the left-hand cuts.…”

Effect of theηηchannel and interference phenomena in the two-pion transitions of charmonia and bottomonia

“…In whereas masses and total widths are very model-dependent for wide resonances [16]. The masses, widths, and the coupling constants of resonances should be calculated using the poles on sheets II, IV and VIII, because only on these sheets the analytic continuations have the forms (see table 1 respectively, i.e., the pole positions of resonances are at the same points of the complex-energy plane, as the resonance zeros on the physical sheet, and are not shifted due to the coupling of channels.…”

“…This fact confirms, first, the existence of the f 0 (1370) (up to now there is no firm conviction if it exists or not). Second, that the exciting role of this meson in making the threshold bell-shaped form of the di-pion spectra can be explained as follows: the f 0 (1370), being predominantly the ss state [3] and practically not contributing to the ππ-scattering amplitude, influences noticeably the KK scattering; e.g., it was shown that the KK-scattering length is very sensitive to whether this state does exist or not [16]. The interference of contributions of the ππ-scattering amplitude and the analytically-continued ππ → KK and ππ → ηη amplitudes lead to the observed results.…”