Structure of

The a0(980), a0(1450) and scalar decay constants and the isovector scalar spectrum

“…Such bound states occur naturally in the quark model treatment of Ref. [4], as well as several coupled channel treatments using model meson-meson interactions with parameters fit to experimental data [5][6][7][8]. The picture predicts γγ decay widths [17,18,7] compatible with experiment [15,16], and considerably smaller than those expected, at least in the simplest version of the quark model, for 3 P 0 qq mesons.…”

“…Interpretations still advocated in the literature include (1) the q 2q2 ("four-quark") cryptoexotic interpretation originally proposed by Jaffe [1] (see Refs. [2,3]); (2) the KK bound state, or "molecule", picture [4][5][6][7][8]; (3) the unitarized quark model picture [9][10][11][12][13]8]; and (4) the "minion" picture of Gribov [14].…”

“…Second, existing experimental data are apparently insufficient to distinguish between the molecule and UQM pictures, since coupled channel models exist, both with and without an underlying conventional quark model state, which provide good fits to existing data in the coupled ππ, KK and πη, KK channels, once the data has been used to fit the free parameters of the models. Third, although the method for distinguishing conventional resonances from bound states posited by Morgan and Pennington [11] (a conventional resonance having poles near the physical region on both the second and third sheets, a bound state having such a pole on only the second sheet) is frequently borne out in existing coupled channel calculations [4][5][6][7][8], this is not universally the case [8]. In particular, a situation in which there are two nearby poles, one on the second and one on the third sheet, can arise in a model which provides a good fit to existing data, but for which one of the nearby poles is most naturally thought of as the coupled-channel remnant of a KK bound state (in the sense that, as the channel coupling is dialed up towards its final fitted value, what was a KK bound state in the absence of channel coupling moves continuously to become one of the two final nearby poles) [8].…”

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

“…In the infinite volume, this model is very successful, and reproduces well the ππ/πη and KK data up to 1200 MeV. The resonances f 0 (600), f 0 (980), a 0 (980) are generated dynamically from the coupled channel interaction [26,27,28,29]. In this paper, we consider the same model in a finite volume to produce the volume-dependent discrete energy spectrum.…”

“…[26,29,49]). Recently, its existence has been rigorously proved by using ChPT combined with Roy equations [54].…”