Available online at www.sciencedirect.com Physics Reports 389 (2004) 61–117 www.elsevier.com/locate/physrep Mesons beyond the naive quark model Claude Amslera;∗, Nils A. T,ornqvistb aPhysik-Institut der Universitat Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland bDepartment of Physical Sciences, University of Helsinki, P.O.Box 64, Fin-00014, Helsinki, Finland Accepted 1 September 2003 editor: J.V. Allaby Abstract We discuss theoretical predictions for the existence of exotic (non-quark-model) mesons and review promi- nent experimental candidates. These are especially the f0(1500) and f0(1710) mesons for the scalar glueball, fJ (2220) for the tensor glueball, Á(1410) for the pseudoscalar glueball, f0(600);f0(980);a0(980), the still 2 2 to be ÿrmly established Ä(800) and the f2(1565) for q q8 or two-meson states, and 1(1400);1(1600) for hybrid states. We conclude that some of these states exist, o9er our views and discuss crucial issues that need to be investigated both theoretically and experimentally. c 2003 Elsevier B.V. All rights reserved. PACS: 12.39.Mk; 12.39.Jh; 13.25.Jx; 14.40.Cs Keywords: Quark model; QCD; Scalar mesons; 4-quark states; Deuteronlike states; Gluonium; Hybride Contents 1. Introduction ........................................................................................ 62 1.1. The light meson spectrum ....................................................................... 63 2. Four-quark mesons .................................................................................. 66 2.1. Ja9e’s four-quark states ......................................................................... 66 2.2. Deuteronlike meson–meson bound states (or deusons) ............................................... 70 2.2.1. One-pion exchange ....................................................................... 70 2.2.2. Predictions for deuteronlike meson–meson bound states ....................................... 72 3. Are the scalars below 1 GeV non-qq8 states? ............................................................ 74 3.1. The hadronic widths of the a0(980) and f0(980) mesons ............................................ 75 3.1.1. widths of the a0(980) and f0(980) mesons ............................................... 76 ∗ Corresponding author. E-mail addresses: [email protected] (C. Amsler), nils.tornqvist@helsinki.ÿ (N.A. T,ornqvist). URL: http://unizh.web.cern.ch/unizh/ 0370-1573/$ - see front matter c 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2003.09.003 62 C. Amsler, N.A. Tornqvist / Physics Reports 389 (2004) 61–117 3.1.2. Radiative widths of the (1020) to a0(980) and f0(980) ................................... 76 3.1.3. The f0(980) produced in Ds → 3 ........................................................ 79 3.2. A possible interpretation of the nature of a0(980) and f0(980) ....................................... 80 3.3. Is the f0(600) a non-qq8 state and does the Ä(800) exist?............................................ 81 3.3.1. The f0(600) (or ) ...................................................................... 81 3.3.2. The Ä(800) ............................................................................. 84 ∗ 3.4. Observation of a charm-strange state DsJ (2317) .................................................... 85 3.5. Do we have a complete scalar nonet below 1 GeV? ................................................ 87 4. Glueballs ........................................................................................... 88 4.1. Theoretical predictions .......................................................................... 88 4.2. Is the f0(1500) meson the ground state scalar glueball? ............................................. 90 4.2.1. Hadronic decay width .................................................................... 92 4.2.2. 2 -decay width .......................................................................... 95 4.2.3. Mixing with qq8 states .................................................................... 96 4.3. The tensor glueball ............................................................................. 97 4.4. The pseudoscalar glueball ....................................................................... 99 5. Hybrid mesons ...................................................................................... 102 5.1. Theoretical predictions .......................................................................... 102 −+ 5.2. A 1 exotic meson, the 1(1400) ............................................................... 104 −+ 5.3. Another 1 exotic meson, the 1(1600) .......................................................... 108 5.3.1. Other hybrid candidates .................................................................. 110 6. Conclusions and outlook ............................................................................. 111 Acknowledgements ..................................................................................... 113 References ............................................................................................ 113 1. Introduction The nearly 40 years old naive or constituent quark model (NQM), including many generalizations, has been since the pioneering work of Gell-Mann and Zweig [1,2] the basic framework within which most of the hadronic states could be understood, at least qualitatively. The NQMwas very successful in describing the observed spectrum, especially for the heavy (c and b) Navour sector. As expected, 3 1 there are very well established heavy quark–antiquark S-wave vector ( S1) and pseudoscalar ( S0) 3 3 3 1 mesons, as well as P-wave states ( P2; P1; P0 and P1) which can be identiÿed in the observed spectrum without ambiguities. No clearly superNuous and well established heavy meson state has been reported. The success of the NQMcan be understood within QCD from the fact that the bound system is approximately non-relativistic for heavy constituents, and from the fact that the e9ective couplings become suOciently small, so that higher order or non-perturbative e9ects can be neglected as a ÿrst approximation. 8 3 In particular, the scalar cc8 and bb states behave as expected for P0 states, whose axial and tensor 3 3 siblings are the heavy P1;2 mesons. Their production in radiative transitions from the 2 S1 states 3 and decays into 1 S1 or light hadrons are as expected. Nothing appears to be “exotic” (suggesting a composition di9erent from qq8) for these heavy scalar mesons. However, the situation is quite di9erent both theoretically and experimentally for the light meson spectrum. Since the e9ective coupling within QCD becomes large, higher order graphs cannot be C. Amsler, N.A. Tornqvist / Physics Reports 389 (2004) 61–117 63 neglected and there may be non-perturbative e9ects which cannot be described within the NQMnor by tree graphs within a phenomenological e9ective Lagrangian. The quark model has to be unitarized, requiring from the formalism the right analytic properties. Also, crossing symmetry should be at least approximately imposed. In addition, the qq8 system becomes inherently non-relativistic and one should allow the amplitudes and the spectrum to be consistent with the (almost exact) chiral symmetry of QCD for the light u and d quarks. All this clashes with the NQMassumptions, and one should not a priori believe any simple results from the NQMwithout criticism. From the experimental side one should devote most e9orts to look for states that cannot be described within the NQM, but which are consistent with QCD and conÿnement, such as gluonium (composed of only glue), multiquark states (such as qqq8 q8), hybrid states (gqq8, composed of qq8 and a constituent gluon), or meson–meson bound states. Such states are expected especially among the light hadrons, where the NQMmust eventually break down. For most of the ground state light NQM qq8 nonets one can, with reasonable Navour symmetry breaking and binding assumptions, easily associate well established experimental candidates [3]. This 3 is remarkable indeed. The main exception is the scalar ( P0) nonet, for which there are too many observed candidates. On the other hand, if mesons with “exotic” quantum numbers (that do not couple to qq8 and therefore cannot appear in the qq8 NQM) were observed, this would give clues as to how the NQMshould be generalized. The light scalar mesons stand out as singular and their nature has been controversial for over thirty years. There is still no universal agreement as to which states are mainly qq8,astohowa glueball would appear among the light scalars, and whether some of the too numerous scalars are multiquark, or meson–meson states, such as KK8 bound states. Since the NQMperforms rather well for heavy constituents, the predicted mass spectrum of heavy mesons might be more reliable, hence non-qq8 states are easier to identify. For example, the recently ∗ discovered (presumably scalar) DsJ (2317) [4], the mass of which lies far below predictions, is likely to throw new light also on the light scalar sector. These are fundamental questions of great importance in particle physics. In particular, the scalar mesons have vacuum quantum numbers and are crucial for a full understanding of the symmetry breaking mechanisms in QCD, and presumably also for conÿnement. The structure of this review is as follows. In the next section we brieNy review the current status of the qq8 spectrum. For a recent comprehensive review on light quark spectroscopy we refer to Ref. [5]. We then discuss the theoretical