New data on theKK¯threshold region and the nature of thef0(

Abstract

We combine new data on fo(S*) production in J/+ and D, decays with earlier information on central production and elastic PP, KK processes to make a fresh examination of the f o ( S * ) resonance. The key feature of our amplitude analysis is its strict enforcement of unitarity. This allows the good energy resolution of the new J/+-&T~P(KE) data to play its full role in delineating the fo(S* ) resonance structure that experiment demands. This enables us to distinguish alternative resonance mechanisms that have been proposed: we conclude that fo(S* ) is most probably not a KE molecule, nor an amalgam of two resonances, but a conventional Breit-Wigner-like structure. In this preferred description, the fo(S* ) has rather a narrow width (To-52 MeV) and comparable couplings to av and KZ. Possible spectroscopic interpretations are considered. PACS number(s): 14.40.Cs, 13.20.Fc, 13.20.Gd, 13.25. + m D. MORGAN AND M. R. PENNINGTON 48 ture on the continued scattering amplitudes. This sheet structure arises because the functional form of the scattering amplitude, in fact, depends upon the c.m. momentum of the opening channel.The paradigm case is the simple Breit-Wigner resonance with For narrow resonances remote from relevant thresholds the various partial widths r, can be well approximated by constants; in general, unitarity requires energydependent partial widths-for S-wave channels typically of the form r, =k, y, , with k, the corresponding channel c.m. momentum and the reduced width y, roughly constant. Since k, and -k, correspond to the same energy, yet give different values for the continued scattering amplitude, Eq. (1.1), we need to distinguish these. It is this specification of the signs of the momenta that defines the sheet structure of the energy plane. In the present discussion we are mainly concerned with two channels, n-n-and KC and we label their corresponding c.m. channel mo-

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

“…The analysis in ref. [5,6,7] favours this latter interpretation, but in ref. [21] the first interpretation is advocated, since the pole found in the IV sheet is far from threshold.…”

“…However, the f 0 (980) (also called S * , I G (J P C ) = 0 + (0 ++ )), and the a 0 (980) (also called δ, I G (J P C ) = 1 − (0 ++ )) mesonic states are well established experimentally, although there is still debate around their decay widths and particularly about their nature. Following the discovery of the f 0 [1], and a 0 [2], several proposals were made about the nature of these states: qq states [3][4][5][6][7][8][9][10], multiquark states [11,12] or KK molecules [13,14,15,16]. Other works argue against the qq nature of the states [17].…”

“…Coming back to the meson-meson interaction in the scalar sector, a large fraction of the work done consists in a parametrization of the amplitudes respecting general principles [4,5,6,7,21] while some other works use models inspired in QCD [11,12,13,14,15] or phenomenological ones based on the exchange of mesons [16].…”

“…The different approaches which are successful in reproducing the meson-meson scattering amplitudes rely upon a relatively high number of parameters which are adjusted to the data, and vary between around 25 in [4,5,6,7,21] and 5-6 in [8,15].…”

Structure of $f_0(980)$ from a coupled channel analysis of $S$ -wave $\pi\pi$ scattering

“…A complicated interplay between S-matrix poles and the KK threshold structure was shown in [10] to play an important role and obscure conventional simple correspondence between the poles and resonances. The phenomenological analysis in the K-matrix framework favoured for a long time a conventional Breight-Wigner resonance interpretation (contrary to a KK state) [11,12,13,14]. A quasi-bound KK state was found in the coupled channel models [15,16,17] and in the meson exchange interaction model [18,19].…”