Meson dynamics beyond the quark model: Study of final-state interactions

Abstract

A scalar glueball is predicted in the 1-GeV mass region. The present analysis is concerned with experimental evidence for such a state. It has been proposed that glueballs should be preferentially produced in supposedly glue-rich processes such as I ) decay and double-Pomeron exchange. However, any meson of such a mass and quantum number has very restricted decay channels availableessentially only nn and, if the mass allows, Ki?. In this case, any production process is very tightly correlated to elastic reactions, na-an and TI--KK, by unitarity. Novel processes cannot then reveal effects that could not be seen in these elastic reactions. Nevertheless, they can valuably supplement this standard information where it lacks precision. Recent high-statistics results on central dimeson production at the CERN ISR enable us to perform an extensive new coupled-channel analysis of Z=0 S-wave nn and KE final states. This unambiguously reveals three resonances in the 1-GeV region, S1(991), S2(988), and ~(900), where the naive quark model expects just two. We discuss in detail these new features and how they may be confirmed experimentally, and give their present interpretation. The S1(991) is a plausible candidate for the scalar glueball. We examine other production reactions (heavy-flavor decays and y y reactions) leading to the same final states, and discuss how, with future precision, these can probe fine details.

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

“…(11,12), as shown in Fig.3. The sheets of the complex s-plane are distinguished by the signs of the imaginary parts of the channel momenta k 1 and k 2 , with the standard notation given in Table 2.…”

“…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].…”

Zweig rule violation in the scalar sector and values of low-energy constants

“…[31] leads to the least pronounced effect. The two other models [32,33] lead to a higher f 0 (980) peak, a larger value for Π(0), and a smaller value for X(3). The range for X(3) is much narrower for large values of r, and can be even reduced to one value in the case of Ref.…”

“…(65) for s < s 1 . Three different models of T -matrix have been used [32,33,31]. The central element is the shape of the f 0 (980) peak.…”

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

“…For instance, in ref. [18] a glueball state at 992 MeV (S 1 (991)) is predicted in addition to the f 0 (980) and the σ which have another nature. In ref.…”