1. Light quark spectroscopy Gomel, 25.07.2007 A.Zaitsev, Protvino

2. Content π π at threshold Scalars Higher excitations Exotics

3. π π at threshold Spontaneous chiral symmetry breaking is most important happening in light quark spectroscopy In Chiral perturbation theory some values are calculated with precision of few % π π scattering length at kr<<1 S=exp(iδ I ) I=0, 2 - isospin δ I =ka I a I -scattering length Predictions: a 0 m π+ = 7m 2 π+ /16 π f 2 π = 0.159 Weinberg (1966) a 2 m π+ = -m 2 π+ /8 π f 2 π = - 0.045 a 0 m π+ = 0.220 ± 0.005 Colangelo, Gasser, Leutwyler a 2 m π+ = - 0.0444 ± 0.0010 (2001) (a 0 - a 2 )m π+ = 0.265 ± 0.004 χPT two loops π π π π π

4. Recent experiments Form-factors in the decay K + →π + π - e + ν BNL E865 (2003) 4 · 10 5 events a 0 m π = 0.216±0.013(stat) ±0.002(syst) ±0.002(theor) NA48/2 (2006) 3.7 · 10 5 events (preliminary) a 0 m π = 0.256±0.008(stat) ±0.007(syst) ±0.018(theor) Pionium lifetime CERN DIRAC (2005) τ =40 · (a 0 - a 2 ) 2 · 10 -15 s τ = [2.91 +0.49 -0.62 ] · 10 -15 s |a 0 - a 2 | m π = 0.264 +0.033 -0.020 p p π+π-π+π- π0π0π0π0

5. NA48/2 CERN NA48/2 (2005) 2.3 · 10 7 K ± →π ± π 0 π 0 decays The cusp at m 2π0 =2m π+ is clearly seen. It stimulated some theoretical works Cabibbo (2004), Cabibbo, Isidory (2005) M ∞ a 0 - a 2 The best fit is obtained with the two loops calculations + pionium (a 0 - a 2 ) m π+ = =0.268±0.010(stat)±0.004(syst) 2π 0 invarint mass square

6. Experimental results on π π scattering length are self consistent. They agree with χPT NNLO calculations with ≈7% precision Higher order corrections are clearly seen These facts can be considered as the proof of principles for χPT M π 2 =1/F π 2 · (m u +m d ) · | | + … More than 94% of the pion mass must stem from the quark condensate Colangelo (2001)

7. Pion polarisabilities γγ→π + π - Polarizabilities: H eff ~α 1 Ē 2 + β 1 Ħ 2 Experiments (in 10 -4 fm 3 ) : Protvino, 1983, π - Z→π - γZ α 1 = 6.8±1.4±1.2 → α 1 - β 1 =13.6± 6 Lebedev, 1984, γp →γ π + n α 1 = 20 ± 12 → α 1 - β 1 =40± 28 MAMI, 2005, γp →γ π + n α 1 - β 1 =11.6 ±1.5 stat ±3.0 syst ±0.5 mod Fil’kov et al, 2005, γ γ →π + π - Dispersion relations α 1 - β 1 =13.0 +2.6 -1.9 χPT (Gasser et al,2006) α 1 - β 1 =5.7 ± 1 This result is at variance with the experiments New COMPASS result moves α 1 - β 1 in right direction

8. Scalars “ σ ” plays a role of Higgs boson in QCD ( “ σ ” - light scalar I G J PC =0 + 0 ++ ) For last two decades the existence of this object was questioned The problems: - in low energy ππ scattering the phase δ 0 0 moves very slowly - the bump at M≈ 900 MeV appears as a result of “ destructive interference ” of very broad signal with f 0 (980) due to unitarity of the amplitude - “ Adler zero ” at S≈m π 2 /2 suppresses the amplitude near the threshold In case of “ other than ππ ” source of S-wave ππ - unitarity is less restrictive - “ Adler zero ” is less obligatory - it could lead to more clear signal Zhu (1996)

9. “σ”“σ” The “ σ ” bump is clearly seen in decays J/ψ→ωππ with very high statistics BES(2004) The pole position is determined to be (541±39) - i (252±42) MeV The results on D-decays definitely point to the “ σ ” with the same parameters D + →π + π + π - E791(2001), CLEO(2006) D 0 →K 0 π + π - CLEO(2002), Belle(2003), BaBar(2004) The analysis of old data (Crystal Ball, 1990) on γγ→π + π - with dispersion relations (Pennington, 2006) confirms the existence of the “ σ ” pole with very high branching σ→γγ Γ (σ→γγ) = (4.1 ± 0.3) keV BES, J/ψ→ωππ

10. “σ” ! Experimental results on low energy ππ S- wave are self-consistent. The existence of the “ σ ” should be taken for granted As “ σ ”– pole is far from physical region its position is model dependent. With the Roy equations the existence of the pole can be proven without any model assumptions and parameters of this pole can be determined with high precision (Caprini,Colangelo,Leutwyler, 2005): M σ = 441 +16 -8 MeV, Γ σ = 544 +18 -25 MeV What is the nature – t-channel exchanges, qq̃, [qq][q̃q̃], G … ?

11. “κ”“κ” The overall situation with Kπ (S-wave, I=1/2) scattering resembles that with π π. The pole, if it exists, is far from physical region and hardly seen in data. At the same time the signal is seen in D + →K - π + π + (E791, 2002) J/ψ→ K + K - π + π + (BES, 2005) It was shown (Bugg,2005) that all these data definitely require the pole at (760±20(stat)±40(syst))-i(420±45(stat)±60(syst)) MeV The analysis of Kπ scattering with Roy-Steiner equations gives the pole at (658±13) –i(228±12) MeV (Descotes-Genon, Moussalam, 2006)

12. f 0 (…) Too many f 0 (…) f 0 (1790) - very unusual signal was observed recently at BES J/ψ→ ω f 0 (1790) K̃K, φ f 0 (1790) K̃K - suppressed J/ψ→ φ f 0 (1790) ππ – clearly seen J/ψ→ γ f 0 (1810) ωφ – clearly seen I=1/2I=1I=0 K* 0 (700)a 0 (980)f 0 (600) f 0 (980) K* 0 (1430)a 0 (1490)f 0 (1370) f 0 (1500) f 0 (1710) K* 0 (1950)f 0 (1790) f 0 (2100) f 0 (2300)

13. SU(3) multiplets If first K* 0, a 0, f 0 compose SU(3) multiplet – it can not be normal q̃q. Inverted ordering of the states looks as if all these states are mainly [qq][̃q̃q] [qq] – “ good ” diquarks: S=0, {̃3} c {̃3} f a + =[su][̃s̃d] f 0 =1/√2([su][̃s̃ũ]+[sd][̃s̃d] σ=[ud][ũ̃d] κ=[ud][̃s̃d] Second multiplet is very unusual as well. It is inverted, flatten and has near extra state M(a 0 (1490)) > M(K*(1420)) ? Maiani et al, 2004

14. f 0 -G mixing Experimental results on scalars were fitted by various models leading to very different compositions of scalars Few examples: 1. {8}+{1} [qq] [q̃ ̃ q ̃ ], {8}+{1} [q̃q] + {1}G 2. {8}+{1} [qq][q̃q ̃ ], {8}+{1} [qq][q̃q̃] + {1}G 3. {8}+{1}[qq] [q̃q̃] + {8}+{1} [qq ̃ ] + {1}G 4. f 0 (1710) - f 0 (1790) - f 0 (1810) ≈ G 1 2 3 4 σ 980 1370 1500 1710 1790

15. Higher states In last few years the quantity of meson states was significantly increased mainly due to the PWA of Crystal Barrel data on p̃p→various final states in flight at nine momenta from 600 MeV/c to 1940 MeV/c (1962 MeV<M<2409 MeV). (Rutherford-Queen Mary-PNPI) Now we have sufficient supply (≈100 states with I=0, 1 out of ≈150 states expected at M <2.4 GeV) These states tend to form equidistant clasters in M 2 ; Δ M 2 ≈ 1.15 GeV 2 (all states but s̃s or J=0 are plotted) This effect is known in baryon spectroscopy with smaller statistics

16. Striking regularities At high M 2 and J: Trajectories are linear in (M 2,J) plane Trajectories are linear in (M 2,n) plane Trajectories are parallel The states I G J PC =0 + 0 ++ are overpopulated The states I G J PC =0 + 2 ++ are overpopulated Some states are suspicious: π 2 (1880), η 2 (1870) – candidates to hybrids (Anisovich, Bugg, 2004) ≈30 states are missed

17. Chiral symmetry restoration The momenta of valence quarks could increase at large hadron excitation energies and could then decouple from the chiral condensates of the QCD vacuum. As a consequence, the dynamical quark mass is reduced. Asymptotically, the states may approach a regime where their properties are determined by the underlying unbroken chiral symmetry. In this case hadrons should form new multiplets SU(2)L×SU(2)R. In the usual potential model classification I; J PC, chiral symmetry restoration leads to the following mass relations: The U A (1) symmetry connects opposite-parity states of the same isospin but from different SU(2)L×SU(2)R multiplets, for example 1; 0-+ ↔ 1; 0++. Chiral symmetry restoration requires a doubling of some of the radial and angular Regge trajectories for J > 0. At large excitations, some of the ρ- mesons have a1 mesons as their chiral partners, while the other ρ -meson excitations are chiral partners of h1 mesons. The n+l degeneracy has been interpreted as evidence for restoration of chiral symmetry in highly excited mesons. A new QCD scale Λ CSR = 2.5 GeV is suggested at which chiral symmetry is restored. The string model and the conjectured restoration of chiral symmetry thus both lead to a n+l degeneracy of excited states. The two models make however different predictions for ‘stretched’ states, for states with J = l+s. The string model predicts no parity partners for a2(1320)–f2(1270), ρ3(1690)– ω 3(1670), a4(2040)–f4(2050), ρ5(2350)– ω 5, a6(2450)–f6(2510). On the contrary, there is no reason why these isospin doublets should not be accompanied by chiral partners, if chiral symmetry would be restored in highly excited mesons. Experimentally, there are no chiral partner for any of these 10 states. Hence data do not support the hypothesis of chiral symmetry restoration.

18. π(1870) The evidence for π(1870) (f 2 π - D-wave) was found by ACCMOR(1981) with PWA of the reaction π - p→π + π + π - p and confirmed by VES(1996) One more evidence was observed with PWA of the reaction p̃p→ η η π 0 π 0 (Anisovich, 2001) The resonance is strongly required by PWA of the reaction π - N→ η π + π - π - N (VES, 2006) M=(1870±10) MeV Γ=(140±12) MeV (preliminary) The PWA model perfectly fits experimental data. There is no place for this state among q̃q mesons

19. X(1835) A signal in M(π + π - η ’ ) is observed in radiative decay J/ψ→ γ π + π - η ’ (BES, 2005) M=1833.7±6.1(stat)±2.7(syst) MeV Γ=67.7±20.3(stat)±7.7(syst)MeV B(J/ψ→ γX) · B(X→π + π - η ’ )= (2.2±0.4(stat)±0.4(syst)) · 10 -4 An anomalous enhancement near the threshold of p̃p mass spectrum is observed at BES II X(1835) could be the same structure as p̃p mass threshold enhancement It could be a p̃p bound state

20. The structure in e + e   (1020) f 0 (980) Analysis of low energy e + e   K + K      and e + e   K + K   0  0 has been performed at BaBar using ISR Final states    ,  0  0 and  f 0 (980) (f 0     ,  0  0 ) are selected A structure with m ~ 2.175 GeV and  ~ 0.06-0.08 GeV with J PC = 1   has been observed in e + e    (1020) f 0 (980) (f 0     ,  0  0 ) reactions with < 10 -3 probability to be a statistical fluctuation. Structure at 2.175 can be interpreted as a “ strange ” partner of Y(4260) with c-quark replaced by s-quark. Or it is a ss̃s̃̃s -state? Λ ̃Λ ? The confirmation is needed. e e Hadrons

21. J PC = 1 -+ Exotic J PC = 1 -+ signals were observed by VES(1993) in two channels: ηπ at M≈1.4 GeV and η`π at M≈1.7 GeV in π - N interactions at p π =37 GeV/c These two channels as well as others 1 -+ like f1π, b1π, ρπ were studied in different reactions, most extensively by BNL E852 and by VES,Protvino π 1 (1400) The existence of this resonance was suggested by E852. It was found that phase motion and intensity of P-wave ηπ- signal can be fitted by BW resonance. Recent reanalysis of the same data (Indiana, 2003) demonstrated that phase motion is moderate and these data can be fitted without resonance. This resonance, if exists, belongs to {10} f (P-wave in two {8} f ), it can not be a hybrid. This decuplet includes also K - π - state where P-wave is very small at M<1.7 GeV.

22. π 1 (1600) Possible decays are: π 1 (1600)) → η π, η` π, f 1 π, b 1 π, ρπ Clear signal is seen in η`π channel ( VES, E852). Its shape points to possible resonance at M=1.6÷1.9 GeV Narrow ρπ signal was observed by E852 at M≈1.6 GeV. It is not seen in VES data. The absence of π 1 (1600) in charge exchange reaction π-p → π 1 (1600) n (ρ-exchange) leads to strong upper limit on π 1 (1600)) →ρπ branching New analysis of E852 data on π→3π reactions does not confirm narrow ρπ signal. It is good news for hybrid, its decays to ρπ are suppressed in various models In other channels - f 1 π, b 1 π the situation is not stabilized yet. The results of VES and E852 on these channels are different

23. θ + observation θ + - supposed baryon with positive strangeness First experimental evidence on the existence of narrow θ + was observed in the reaction γC→K + K - X at low energy (LEPS, 2002) The existence of this signal was confirmed by ≈10 experiments in different reactions: γd→K + K - p n; γp→K + K - n; γp→π + K + K - n; νA →K 0 p X; K + Xe →K 0 pX; e + d →K 0 p X; pp →K 0 p Σ + ; pA →K 0 p X Λ(1520)θ+θ+ Dzierba et al, 2005)

24. The best signal Statistics in these experiments is not very high. Statistical significance of the signal was estimated as 4÷5 σ. More conservative estimate leads to 2÷4 σ. The mass of the signal varies from 1520 MeV to 1555 MeV. The visible width is compatible with resolution. The most statistically significant signal is seen in the reaction γp→ π + K + K - n (CLAS, 2004) “ No obvious structure is seen in this spectrum. ” “ A peak appears most clearly when requiring cosθ* π+ >0.8 “ CLAS, 2004

25. K + D total crossection The K + n resonance has to be seen in K + D scattering. Experimental data on K + D total crossection disagree significantly at p K+ <700 MeV The analysis of available data (Gibbs, 2004) points to possible K + n resonance at: M=(1.559±0.003) GeV (for J P =1/2 + ) M=(1.547±0.002) GeV (for J P =1/2 - ) Γ=0.9±0.3 MeV ↓ Γ<1.5 MeV ?

26. θ + negative searches in various reactions In last two years the experiments on the θ + search as a rule do not see the signal The ratio R(θ + /Λ*)=(σ(θ + )/ σ(Λ(1520)) can be used to quantify relative sensitivities of the experiments R(θ + /Λ*)=0.05÷2 in experiments which claim the evidence of θ + R(θ + /Λ*)<0.005÷0.02 in experiments which do not see θ +

27. θ + negative searches in h N reactions R(θ + /Λ*) HERA-B pA→ θ + X <0.02 HyperCP (π+,K+,p)Cu → θ + <0.003 K 0 p CDF ̃pp→θ + X <0.03 PHENIX AuAu →θ + X SELEX (π,p,Σ) p →θ + X SPHINX pC→θ + K 0 C <0.1 WA89 Σ - N →θ + X E690 pp→ θ + X <0.005 WA89 HyperCP

28. θ + negative and positive searches in high energy γ(*) N reactions FOCUS Eγ > 25 GeV R(θ + /Σ*(1385))<0.023 BaBar e (9 GeV) ZEUS e(27.6GeV) p(820-960GeV) L=121 pbn -1 At Q 2 >20GeV 2 the θ + signal is seen at ~5 σ σ=125±27 +36 -28 pbn (prel.) H1 L= 74 pbn -1 σ<72pb (90% CL) H1 does not confirm the ZEUS result FOCUS BaBar

29. θ + negative searches in various reactions BES J/ψ → θ ̃θ <1.1 · 10 -5 BaBar Υ(4s) → K 0 p X < 1.0 · 10 -4 Belle Υ(4s) → K 0 p̃p X <2.3 · 10 -7 LEP Z → K 0 p X <0.07×Λ* NOMAD (blind analysis) N<2.13 · 10 -3 / interaction

30. θ + negative searches in low energy γ N reactions High statistics searches of θ + in different reactions do not confirm the signal at M≈1540 MeV. In particular it is not seen in γp and γd reactions at Jlab. Early evidence is explained as combination of statistical fluctuation and background underestimation. Within the models the upper limit on θ + production cross section can be transformed to the limit on Г θ+ In bulk of the models it leads to Г θ+ <0.3 MeV for J p =1/2 + In conservative models Г θ+ <3 MeV CLAS, 2003 CLAS, 2006 5.92 CLAS, 2006 θ+ ? Λ(1520) SAPHIR, 2003

31. Positive claims Two more experiments claim evidence for θ + DIANA K + Xe → θ + X (K + n →K 0 p) M=(1537 ± 2) GeV Γ=(0.36 ± 0.11) MeV SVD p A →p K 0 s X M=(1523 ± 2(stat) ± 3(syst)) GeV R(θ + /Λ*) ≈ 0.1 DIANA SVD

32. {10} Model independent upper limit on the width Г θ+ <0.64 MeV (BELLE, 2006) Other members of suggested antidecuplet: The NA49 claim for evidence of double strange pentaquark Ξ — (1862)→Ξ - π - was not supported by a number of experiments Lessons ….. BELLE BURKERT, 2005

33. Conclusion Agreement of experimental data on  scattering lengths with high precision calculations in χPT “ σ ” and “ κ ” are there Unbelievably regular pattern of meson states at high  and J The experimental data on J PC =1 -+ hybrids tend to converge Cusps/resonances at baryon-antibaryon thresholds No θ + at Γ < 0.7 MeV No convincing evidence for θ +