1. Yu. Guz (IHEP Protvino) Light exotic mesons in hadronic collisions

2. LL J PC =0 –+, 1 +–, 2 –+, … J PC =0 ++, 1 – –, 1 ++, 2 ++, … Some combinations are impossible (exotic): 0 – –, 0 +–, 1 –+, 2 +–, 3 –+,... In multiquark or hybrid states all J PC combinations can be reached Conventional mesons are bound states of quark and antiquark P=(-1) L+1, C=(-1) L+S Hybrid mesons are quark-antiquark states with excited gluonic degrees of freedom. (Jaffe, Johnson 1976; Vainshtein, Okun 1976) flux tube model lattice calculations... There are many approaches to describe meson spectra and decays: sum rules potential models bag models

3. Flux tube model: excitation of a massive string (flux tube) (Isgur, Paton 1985; Close, Page 1995) Bag model: an extra (constituent) gluon in the bag (Chanowitz, Sharpe 1983; Barnes et al 1983) Potential models: a linear attraction potential between gluon and each quark (Horn, Mandula 1978)) Conventional meson Hybrid meson

4. Lightest hybrid states: in the bag model, J PC =1 – –, (0,1,2) –+ Predictions for masses: bag model 1.3÷1.4 GeV flux tube 1.8÷2.0 GeV sum rules 1.7÷1.9 GeV lattice QCD 1.8÷2.3 GeV Theoretical predictions for hybrid mesons Decays: flux tube + 3 P 0 model: Feature: suppression of the decays into two S-wave mesons: 1 –+  ηπ, η’π, ρπ; 0 –+  ρπ, ωρ;... Prediction for decay widths of 1.8 GeV 1 –+ in the flux tube model (Close, Page 1995): b1πb1πf1πf1πρπf2πf2πη(η’)πη(η’)π 170605÷2000÷10MeV

5. Exotic quantum numbers (1 –+ ): no problem of mixing with conventional states. Non-exotic quantum numbers: production and decay properties may be used as indication. Hybrid mesons with light quarks can be produced in diffraction-like reactions (Pomeron exchange) in pion beam. The 0 –+ and 1 –+ will be discussed here, based mainly on the results of the VES experiment (IHEP Protvino). Partial-wave analysis of many final states (ηπ 0, ηπ –, η’π –, f 1 π –, b 1 π – ) shows significant 1 –+ wave. In addition, there are 0 –+ and 2 –+ states having unusual decay patterns.

6. The VES experiment Fixed target, π – (K – ) beam 23–47 GeV π – (K – ) A → (n π(K) + m γ) A’ Trigger condition: n≥2. Total of ~10 9 events accumulated Studied (PWA) final states: π + π –, π + π – π 0, π + π – η, ηπ 0, η’π 0, ωπ 0, π + π – π –, π + π – π – η, ηπ –, η’π –, ωπ –, η’ηπ –, ηηπ –, ωπ – π 0, ωω, η’η’, π – K + K –, K – π + π –, … VES

7. Experimental studies of 1 –+ VES diffraction, charge exchg π – beam 28, 37, 43 GeV/с ηπ –, η’π –, ρπ, f 1 π –, b 1 π –, η’π 0 BENKEI (KEK) diffraction π – beam 6.3 GeV/с ηπ – Crystal Barrel ppbar annihilation Dalitz plot analysis of ηπ + π –, ηπ 0 π 0, η’π + π – ηπ ±, ηπ 0, η’π ± GAMS / NA12 charge exchange π – beam 32, 38, GeV/с ηπ 0 E852 (BNL) diffraction, charge exchg π – beam 18 GeV/с ηπ –, η’π –, ρπ, f 1 π –, b 1 π –, ηπ 0

8. 1 –+ in π – A→ηπ – A (Beladidze 1993; Dorofeev @ HADRON 2001) Partial waves with unnatural parity exchange are negligible. The D+ wave (L=2, J PC =2 ++ ) is dominant, with a 2 (1320) peak. The intensity in 2 ++ at M>1.5 GeV can be represented either as non-resonant background or as production of the (not well established) resonance a 2 (1750). The P+ wave, (L=1, J PC =1 –+ ) is significant: ~4% of the a 2 peak. Its spectrum can be described as either non- resonant background or exotic resonance π 1 (1400), in any assumption on the nature of the D+ wave at M>1.5 GeV. Confirmed by E852; the π 1 (1400) was also seen by Crystal Barrel as an isobar in ηππ Dalitz-plot analysis. KEK: different result --- resonance in 1 –+ with the same parameters as a 2 --- leakage from a 2 ?

9. Completely different situation: here the exotic wave is dominant. Waves with unnatural parity exchange negligible Like in ηπ –, the D+ signal at M>1.6 GeV can come either from a 2 (1750) or from nonresonant background. The resonant interpretation of the signal in the exotic wave is possible in both cases. Confirmed by E852 and Crystal Barrel 1 –+ in π – A→η’π – A (Beladidze 1993; Dorofeev @ HADRON 2001)

10. 1 –+ in ηπ – и η’π – Beladidze et al 1993 Comparison of matrix elements squared of 1 –+ in ηπ – and η’π – supports its mainly “hybrid” nature at M>1.4 GeV. The hybrid decays into ηπ (η’π) through OZI breaking, i.e. into SU(3) octet (π) and singlet (η 0 ). (Close, Lipkin, 1987) Cannot be described within the 3 P 0 model. η (η’) π π P-wave states in η 8 π and η 0 π are different in their SU(3) properties: η 0 π belongs to an octet, while η 8 π – to So only π 1 (1600) can be a hybrid (S.U.Chung et al, 2002); the π 1 (1400) (if it is a resonance) has to be a multiquark state. Experimental searches for the K + π + P-wave production in K-beam (SU(3) partner of π 1 (1400) ) gave negative result. (Estabrooks et al 1978)

11. This signal at 1.6 GeV is observed in 1 –+ b 1 (1235)π. The phase difference of 1 –+ and 2 ++ requires a resonance in 1 –+ at any hypothesis on the origin of the peak in 2 ++. The combined fit of the 1 –+ spectra in b 1 π and η’π with a resonance and non-coherent background gives M≈1.56±0.06 GeV, Γ≈0.34±0.06 GeV 2 ++ ωρ 1 -+ b 1 π 1 –+ in b 1 π (π – A→ωπ – π 0 A) (Dorofeev @ HADRON 2001)

12. 1 –+ in f 1 π – (π – A→ηπ + π – π – A) The 1 –+ f 1 (1285)π spectrum is similar to that in η’π: M≈1.64±0.03 GeV, Γ≈0.24±0.06 GeV. No signal at 1.9-2.1 GeV (in contradiction with E852 results, Kuhn et al 2004). The relative phase of 1 –+ f 1 π with respect to 1 ++ f 1 π allows resonance interpretation only in case if the 1 ++ signal comes from a 1 (1640); this is not a well established resonance. 1–+1–+ 1 ++ Arg(1 –+ –1 ++ ) f 1 π –

13. π + π – π –, total intensity 1 –+ ρπ, “tight” model 1 –+ ρπ, “loose” model 1 –+ in ρπ – (π – A→π + π – π – A) The 1 –+ wave is present in ρπ, at ~2-3% of full π + π – π – intensity. There is a peak in its spectrum at M~1.6 GeV, which resembles π 1 (1600) (Adams et al 1998 ). In the analysis of VES data it was proven that the height of this peak depends on the PWA model: it is maximal in the assumption of full coherence of waves (“tight model”) and significantly reduced in case of using spin-density matrix of arbitrary rank (“loose model”). Therefore the direct search of 1 –+ in ρπ does not produce reliable results; (most part of) the peak at 1.6 GeV can be a leakage from π 2 (1670). (Zaitsev @ HADRON 1997)

14. π – p → η’π 0 n (Amelin et al, 2004) M(η’π 0 )M(ηπ 0 ) The positive exchange naturality waves 1 –+ and 2 ++ are produced mainly through ρ-exchange. The a 2 signal in ηπ 0 is a monitor of intensity of ρ-exchange. The π 1 (1600) signal is present in η’π – and absent in η’π 0 ═> π 1 (1600) is not produced in ρ-exchange. A (model dependent) constraint can be obtained: BR(π 1 (1600)→ρπ)<3%, or Γ(π 1 (1600)→ρπ)<10 MeV The η’π 0 and η’π – spectra

15. First studied by GAMS/NA12, then confirmed by VES and E852. The 1 –+ is large (~20% of the a 2 peak) and allows both resonant Alde et al 1999) and non-resonant (S.Sadovsky et al 1999) interpretation (additional uncertainty from several nontrivially different PWA solutions). Produced in ρ-exchange, but not seen in ρπ ??? π–p→ηπ0nπ–p→ηπ0n D.Alde et al, Phys.Atom.Nucl. 62 (1999) S.Sadovsky et al, NP A665 (1999)

16. The J PC =1 –+ wave was searched for in several experiments in the final states ηπ –, η’π –, π + π – π –, ηπ + π – π –, ωπ – π 0, K + K – π –, ηπ 0, η’π 0. π 1 (1400) A broad peak at mass M~1.4 GeV and width Γ≈350 MeV, which can be interpreted either as an exotic resonance π 1 (1400) or non-resonant background, was observed in ηπ – and ηπ 0. From SU(3) considerations, it can belong only to decuplet-antidecuplet representation and therefore can be only a multiquark state and not a hybrid. Its SU(3) partner is not found in K + π + ; it is produced in ρ-exchange, but not seen in ρπ: not a resonance??? 1 -+ summary

17. π 1 (1600) Another broad peak, at mass M~1.6 GeV and width Γ≈300 MeV, which can be interpreted as an exotic resonance π 1 (1600), was observed in η’π –, b 1 (1235)π – и f 1 (1285)π –. This peak is absent in the final states ρπ, f 2 (1270)π and K * K (the peak at 1.6 GeV in the 1 –+ ρπ P-wave seems to be an analysis artifact, most probably leakage from π 2 (1670) ). Strictly speaking, one cannot draw unambiguous conclusion on resonant nature of this peak: the phase of the exotic wave can be measured only with respect to the J PC =1 ++ and 2 ++ waves, which contain in this mass region the resonances a 1 (1640) and a 2 (1750); these resonances are not well established. 1 -+ summary

18. Assuming that the 1 –+ peaks at M~1.6 GeV in η’π –, b 1 π – и f 1 π – come from the decays of exotic resonance π 1 (1600), we can compare their properties with theoretical predictions. Its mass (1.6 GeV) agrees with the bag model predictions and is somewhat lower than predicted by FTM. The branching ratios of π 1 (1600) Experiment: b 1 π : f 1 π : ρπ : η’π = 1.0±0.3 : 1.1±0.3 : <0.03 : 1. FTM predictions: b 1 π : f 1 π : ρπ : η’π = 170 : 60 : 5÷20 : 0÷10 (Close, Page 1995) The largest discrepancy with FTM predictions is η’π: may be because the OZI-suppressed processes are not taken into account. The decay width into η’π could be as high as ~1 GeV if the coupling of η’ to two gluons through the anomaly is included into the model (Frere, Titard, 1988). Similar effect was observed in decays of π(1800) with J PC =0 –+, which is a well established resonance. 1 -+ summary

19. Theoretical predictions for higher 0 –+ states (Barnes et al 1997) Both hybrid (π H ) and radially excited (3S) states are expected at M~1.8÷2.0 GeV FTM predictions for their decay widths : ρπρωρ (1450)πf 0 (1300)πf2πf2πK*KK*Ktotal π(3S)30745662936231MeV πHπH 30÷50010÷5040÷1703÷85÷15240MeV Main decay mode for the hybrid state – f 0 (1300)π; for the conventional state – ρω

20. π(1800) First observed by the Dubna-Milan spectrometer (U70, IHEP Protvino) (Bellini et al, 1982) extensively studied by VES: decay modes f 0 (980)π, f 0 (1300)π, f 0 (1500)π, a 0 (980)η, (Kπ) S K were observed in final states π + π – π –, K + K – π –, ηηπ –, η’ηπ –. NOT observed in ρπ, K * K, f 2 π. The peak in 0 –+ was also seen in ρω, however at significantly lower mass. its decay modes f 0 (980)π, f 0 (1300)π were observed in E852 in π + π – π – final state

21. π(1800) в эксперименте ВЕС: ηηπ – (Bityukov et al 1991; Amelin et al 1996) π(1800) is dominant in the ηηπ – mass spectrum Mainly a 0 η, with some fraction of f 0 (1500)π. M≈1840±10(stat)±10(syst) MeV Г≈210±30(stat)±30(syst) MeV Events/10 MeV

22. π(1800) in π + π – π – (Amelin et al, 1995) π(1800) is present in f 0 (980)π, f 0 (1300)π, f 0 (1500)π NO ACTIVITY in ρπ at 1.8 GeV. This is in contradiction with theoretical predictions for both π H and π 3S states. The phase behaviour proves that π(1800) is a resonance. Its parameters are: M≈1775±7(stat)±10(syst) MeV Г≈190±15(stat)±15(syst) MeV

23. π(1800) in K + K – π – (Amelin et al, 1994) π(1800) peak can be seen in the KKπ mass spectrum of events with M(KK)<1.1 GeV. Partial-wave analysis: the π(1800) peak is present in f 0 (980)π and κK (κ=(Kπ) S-wave ). M≈1790 ±14 MeV, Г ≈210 ±70 MeV, Not seen in K * K

24. π(1800) in K + K – π – (Dorofeev et al, 1998) A peak in 0 –+ ρω was observed : M≈1737±5 MeV, Г≈259±19 MeV The phase behavior proves the resonant interpretation. The mass value is incompatible with π(1800) in other channels May be interpreted as π(3S) ?

25. π(1800): combined analysis final statedecay channelpartial width π–π+π–π–π+π– f 0 (1300) π+π– π – f 0 (980) π+π– π – f 0 (1500) π+π– π – ρ(770)π – 1 1.1±0.1 0.44±0.15 0.11±0.05 <0.02 K + K – π – K*(892)K – 0.29±0.10 <0.03 ηηπ – a 0 (980) ηπ– η f 0 (1500) ηη π – 0.15±0.06 0.13±0.06 0.012±0.005 η’ηπ – f 0 (1500) η’η π – 0.026±0.010 (Nikolaenko @ HADRON 2003) ρω channel excluded

26. π(1800) summary The mass and width of π(1800) are close to those expected for the lowest 0 –+ hybrid. Its main decay modes are f 0 (1300)π, f 0 (980)π and f 0 (1500)π; the decay probabilities into ρπ and K * K are negligible. High probability of the decay into f 0 (1300)π supports its interpretation as a hybrid state. However its decay pattern is more complicated than theoretically predicted. It decays also into f 0 (980)π and f 0 (1500)π. The f 0 (1300) is considered to be a state, while f 0 (980) is mainly, and f 0 (1500) is believed to contain substantial glueball component. Therefore the OZI rule is significantly violated in the π(1800) decays: the main decay mode is emission of an SU(3) singlet state. It was shown in lattice calculations that decays of this kind are important for heavy quark hybrid mesons (McNeile et al, 2002), so their contribution may also be large for light hybrids. On the other hand, it can be a common feature of higher excitations.

27. Conclusion The status of three states, the π(1800) with J PC =0 –+ and π 1 (1400) and π 1 (1600) with J PC =1 –+, is considered. π(1800) is a well established resonance seen in the final states π + π – π –, ηηπ –, η’ηπ –, K + K – π – in the decay modes f 0 (980)π –, f 0 (1300)π –, f 0 (1500)π –, a 0 (980)η. π 1 (1400) was observed ηπ – and ηπ 0 in several experiments. It allows both resonant and non- resonant interpretation. From SU(3) considerations, it can be only a multiquark state and not a hybrid. Produced in ρ-exchange, but not seen in ρπ; its SU(3) partner is not found in K + π + π 1 (1600) peak was observed in η’π, b 1 π, f 1 π by two independent experiments. Its resonant interpretation is very likely, however the lack of model-independent ways to measure its phase prevents us from drawing the unambiguous conclusion. The properties π 1 (1600) and π(1800) agree in general with the predictions for lightest 1 –+ и 0 –+ hybrid mesons. The discrepancies can be explained by significant contribution from OZI- suppressed decay modes. } not a resonance?