Isospin breaking exposed in f 0 ( 980 ) − a 0 ( 980 ) mixing

We suggest that mixing between the f0(980) and a0(980), due to their dynamical interaction with the nearby KK̄ thresholds, can give rise to a significantly enhanced production rate of a0(980) relative to a2(1320) in pp → ps(ηπ)pf as xF → 0. The peaking of the cross section as φ → 0 should also occur. We show that such effects are seen in data and deduce that the f0(980) − a0(980) mixing intensity is 8 ± 3 %. e-mail: [email protected] e-mail: [email protected] The enigma of the scalar mesons may be boiled down to an essential question: what are the f0(980) and a0(980)? Do they have a common origin and, if so, what is it? Understanding the f0(980) in particular is a central problem for identifying the dynamics associated with the long sought scalar glueball. There have even been suggestions that the f0(980) itself may be the eponymous glueball, perhaps mixed with qq̄; in such a case the mass degeneracy with the a0(980) would be somewhat accidental and the two mesons not clearly related. An interpretation of the f0(980) as a qq̄ state is still consistent with the present data (see for example ref. [1]). By contrast, there is a large body of work drawing on the observation that the f0(980) and a0(980) are very close to the KK̄ threshold, and that the KK̄ channel drives the dynamics [2]. As an extreme, there is the possibility that these mesons are truly bound states of KK̄ [3]. Traditionally in strong interactions isospin is believed to be a nearly exact symmetry, broken only by the slightly different masses of the u and d quarks and/or electroweak effects. The small difference in mass between K andK is a particular example. However, the mass gaps between the f0(980)/a0(980) and the K K and KK thresholds are substantially different with the result that the dynamics of bound KK̄ states can be described better in a basis specified by mass eigenstates. Such dynamics would give rise to a violation of isospin and lead to mixing of states with different G-parities. The possibility of such an effect was suggested long ago in ref. [4]. In ref. [5] a study was performed of the production of the a0(980) in the reaction π π → ηπ which due to G parity is forbidden and can only occur through f0(980)− a0(980) mixing. This showed that (6–33)% of the a0(980) cross section in π p reactions could be due to f0(980)− a0(980) mixing. Further discussions along this line have been made by ref. [6] who have specifically drawn attention to the relation between the existence of KK̄ molecular bound states and large violations of isospin. Very recently, attention has been drawn to such mixings having observable effects in threshold photoproduction, such as at CEBAF [7]. These papers have all concentrated on the production of the f0(980)/a0(980) by flavoured mesons or photons; in this paper we propose that their production by gluonic systems, such as the IP (Pomeron)-induced production in the central region at high energy: pp → pp + f0(980)/a0(980), may provide rather clean tests of the mixing. Furthermore, we shall suggest that new data from the WA102 collaboration at CERN [8] are already consistent with a significant mixing. We shall consider alternative interpretations and suggest ways of eliminating these in future experiments. These data potentially may help to elucidate the nature of the f0(980)/a0(980) states. Our hypothesis is based on recent breakthroughs in understanding the dynamics and topology (momentum and spatial distributions) of meson production in the central region of rapidity, pp → pMp [9, 10]. In particular, we shall focus on the description of the observed φ dependences [10], where φ is the angle between the pT vectors of the two outgoing protons. In such processes at high energy, where IPIP fusion dominates the meson production, C = +, I = 0 resonances such as the f0(980) are very strongly produced [11] whereas in general isospin 1 states are suppressed [12]. Even at the energies of the WA102 data, there is considerable evidence that IPIP fusion is an important part of the production dynamics [12]. It is tantalising therefore that recent data from the WA102 collaboration on the centrally produced ηπ final state [8] show interesting effects in that they are in accord with substantial f0(980)− a0(980) mixing.