1. 1 Collaborators Johan Durand, CEA - Saclay Jun He, CEA - Saclay Zhenping Li, Univ. of Maryland Qiang Zhao, IHEP - Beijing PLAN:  Motivations  Chiral constituent quark approach  Results for  p → ηp ; E  Lab ≈ 0.7 to 3.0 GeV  W ≈ 1.5 to 2.6 GeV  M N*  Role of N*s: “known” and “New”  Summary & concluding remarks NSTAR2007, Bonn, Sept. 5, ’07 Chiral constituent quark model study of the process  p → ηp Bijan Saghai CEA – Saclay

2. 2 New generation of data for  p  ηp Lab / Collaboration Observable (GeV) # of data points Reference MAMI / TAPS dσ / dΩ0.716 – 0.790100 B. Krusche et al., PRL 74, 3736 (1995) ELSA/ PHOENICS T0.717 – 1.10550 A. Bock et al., PRL 81, 534 (1998) JLab / CLAS dσ / dΩ0.775 – 1.925190 M. Dugger et al., PRL 89, 222002 (2002) ELSA / CB dσ / dΩ0.775 – 2.900631 V. Credé et al., PRL 94, 012004 (2005) LNS dσ / dΩ0.718 – 1.142180 T. Nakabayashi et al.,PR C74, 035202 (2006) GRAAL dσ / dΩ Σ 0.714 – 1.477 0.724 – 1.472 487 150 O. Bartalini et al., EPJ A (2007) [PRL 81, 1797 (1998); PL B528, 215 (2002)] ELSA / CB-TAPS Σ0.843 – 1.34534 D. Elsner et al., nucl-ex/0702032

3. 3 What do we learn from those data? Need a formalism robust enough to  Allow embodying all known N*s (i.e. PDG, one to four star resonances)  Introduce new resonances reported by several authors S 11, P 11, P 13, D 13, D 15 & H 1,11  Build a model with “reasonable” number of adjustable parameters

4. 4. 3 rd S 11 M [Γ] (MeV) APPROACHREF. 1945Constituent quark model (CQM)Capstick & Roberts, PRD 49 (1994) 1712 [184]KY quasi-bound stateLi & Workman, PRC 53 (1996) 1792 [360] Coupled channel analysis N → N, ηN & ηN → ηN Batinic et al., nucl-th/9703023 1780 [280] Constituent quark model (CQM) p → ηp Saghai & Li, EPJ A11 (2001) ; nucl-th/0305004 (N* 2002) 1861Hypercentral CQMGiannini et al.,nucl-th/0111073 1846 Coupled channel analysis  N →  N & γ N →  N G.-Y. Chen et al., NP A723 (2003) 1945Reggeized isobar model γ p → η′pW.T. Chiang et al., PRC 68 (2003) 1825 [160]Isobar model γ p → ηpV.A. Trasuchev, EPJ A22 (2004) 1806 [300]Coupled-channel & CQM γ p → K + ΛB. Juliá-Díaz et al., PRC 73 (2006)

5. 5 3 rd P 13 M [Γ] (MeV) APPROACHREF. 1870, 1910, 1950, 2030 Constituent quark modelCapstick & Roberts, PRD 49 (1994) 1816, 1894, 1939 Hypercentral CQMGiannini et al., nucl-th/0111073 2068 [165] BES Collaboration Data J/ψ → π + n, π - p Ablikim et al., PRL 97 (2006); Fang et al., Int. J. Mod. Phys. A21 (2006) 1893 [204] Coupled-channel & CQM p → K + Λ B. Juliá-Díaz et al, PRC 73 (2006) 3 rd D 13 1960Constituent quark modelCapstick & Roberts, PRD 49 (1994) 1895 Isobar model γ p → K + Λ Mart & Bennhold, PRC 61 (1999) 1875 [80] Isobar model γ p → N, ηN, K + Λ, K + Σ°, K ° Σ + Anisovich et al. EPJ A25 (2005); Sarantsev et al., EPJ A25 (2005) 1954 [249] Coupled-channel & CQM  p → K + Λ B. Juliá-Díaz et al., PRC 73 (2006)

6. 6 Additional P 11, D 15 & H 1,11 resonances?  Anisovich et al., EPJ A 25 (2005) 427 ; Isobar model, γp  πN, ηN: P 11 (1840), D 15 (1875) ↔ D 15 (2200) in PDG?  Sarantsev et al., EPJ A 25 (2005) 441 ; Isobar model, γ p  Κ + Λ, Κ + Σ°, Κ°Σ + : P 11 (1840)  Corthals et al., PRC 73 (2006) 045207 ; Regge + Resonance Approach, γ p  Κ + Λ: P 11 (1900)  Arndt et al., PRC 74 (2006) 045205, EPWA, πN  πN, ηN: H 1,11 (2247)

7. 7 Present approach p → ηp Chiral Constituent Quark Model Starting point: low energy QCD Lagrangian derived by Manohar & Georgi, Nucl. Phys. B234 (1984), which ensures that the meson-baryon interaction is invariant under the chiral transformation

8. 8 Chiral Constituent Quark Model

9. 9 SU(6)  O(3) symmetry predicts: C 2 N* = 0 or 1 e.g. C 2 N* = 1 for S 11 (1535) & D 13 (1520) C 2 N* = 0 for S 11 (1650) & D 13 (1700) SU(6)  O(3) symmetry is broken due to the configuration mixings caused by one- gluon exchange (Isgur, Karl & Koniuk, PRL 1978) Configuration mixings between two SU(6)  O(3) states with the total quark spin 1/2 or 3/2: S11: N( 2 P M ) 1/2 - N( 4 P M ) 1/2 - D13: N( 2 P M ) 3/2 - N( 4 P M ) 3/2 -

10. 10 Configuration mixing │S 11 (1535)  = │N( 2 P M ) 1/2 -  cosθ S - │N( 4 P M ) 1/2 -  sinθ S │S 11 (1650)  = │N( 2 P M ) 1/2 -  sinθ S + │N( 4 P M ) 1/2 -  cosθ S  Transition amplitudes: A N*   N│H m (│N *   N * │H e │N  A S11   N│H m ( cosθ S │N( 2 P M ) 1/2 -  - sinθ S │N( 4 P M ) 1/2 -  ) (cos θ S  N( 2 P M ) 1/2 - │- sinθ S  N( 4 P M ) 1/2 - │) H e │N   N( 4 P M ) 1/2 - │ H e │ N  = 0, due to Moorhouse selection rule (PRL 1966) A S11  ( cos 2 θ S – R sinθ S cosθ S )  N│H m │N( 2 P M ) 1/2 -   N( 2 P M ) 1/2 - │ H e │N  R S = [  N│H m │N( 4 P M ) 1/2 -  ] / [  N│H m │N( 2 P M ) 1/2 -  ] SU(6)  O(3)  R S = -1 & R D = 1 / √10, for p → ηp C S11(1535) = cosθ S ( cosθ S – sinθ S ) C D13(1520) = cosθ D ( cosθ D – sinθ D / √10 ) C S11(1650) = - sinθ S ( cosθ S + sinθ S ) C D13(1700) = sinθ D ( cosθ D / √10 + sinθ D )

11. 11 Ingredients s-channel: all known I=1/2 N*s & 6 “new” ones u-channel: nucleon Born term + N*s t-channel:  & ω exchanges Previous study (E γ lab ≤ 2 GeV) B. Saghai & Z. Li, EPJ A11 (2001); Limited to n ≤ 2 shell & no t-channel n = 1: 2 S 11, 2 D 13, 1 D 15 n = 2: 2 P 11, 2 P 13, 2 F 15, 1 F 17 Present work: besides t-channel embodies also: n = 3: S 11, D 13, D 15, G 17, G 19 n = 4: P 11, H 19 Degenerate n=5: I 1,11 n=6: K 1,13

12. 12 All I=1/2 PDG N* + 6 new ones. PDG Star N* PDG Star N* PDG Star N* 4S 11 (1535)4D 13 (1520)4G 17 (2190) 4S 11 (1650)3D 13 (1700)4G 19 (2250) 1S 11 (2090)2D 13 (2080) NS 11 (1730)ND 13 (1850) 4P 11 (1440)4D 15 (1675)4H 19 (2220) 3P 11 (1710)2D 15 (2200)NH 1,11 (2200) 1P 11 (2100)ND 15 (1950) NP 11 (1810)3I 1,11 (2600) 4P 13 (1720)4F 15 (1680)2K 1,13 (2700) 2P 13 (1900)2F 15 (2000) NP 13 (2170)2F 17 (1990)

13. 13 Full model  21 known N*s  6 new N*s  Fitted on 1822 data points  χ 2 = 1.81  Mixing angles: θ S ≈ - 35° ; θ D ≈ 15° (in good agreement with findings by Isgur, Karl, Chizma, Capstick…)

14. 14 Differential cross-section

15. 15 Polarization observables

16. 16 Removing one resonance. PDG Star N* PDG Star N* PDG Star N* 4S 11 (1535)4D 13 (1520)4G 17 (2190) 4S 11 (1650)3D 13 (1700)4G 19 (2250) 1S 11 (2090)2D 13 (2080) NS 11 (1730)ND 13 (1850) 4P 11 (1440)4D 15 (1675)4H 19 (2220) 3P 11 (1710)2D 15 (2200)NH 1,11 (2200) 1P 11 (2100)ND 15 (1950) NP 11 (1810)3I 1,11 (2600) 4P 13 (1720)4F 15 (1680)2K 1,13 (2700) 2P 13 (1900)2F 15 (2000) NP 13 (2170)2F 17 (1990) χ 2 variation δχ 2 < 5%5% ≤ δχ 2 ≤ 15% Nb of N*s153

17. 17 “Reduced” model  Remove ALL 18 N*s (δχ 2 ≤ 15%)  Then, re-fit the data with remaining 9 N*s χ 2 =1,81 → 2,12

18. 18 Schematic presentation of the role played by the most relevant resonances in the process  p → η p Switched-off N*   d.o.f (Full Model:   =2.1) S 11 (1535)39.2 D 13 (1520)9.0 S 11 (2090)2.3 S 11 (1724)2.3 S 11 (1650)2.2 F 15 (1680)2.2 P 13 (1520)2.1 P 13 (1900)2.1 D 13 (1700)2.1

19. 19 Polarization observables

20. 20 Differential cross-section

21. 21 Summary & Concluding remarks (I) Direct channel formalism for  p →ηp, within a chiral constituent quark approach. All data for d  /dΩ, Σ & T are well reproduced.  All 21 Known N*s and 6 new ones included in the model.  Rather few and severely constrained adjustable parameters.  Reaction mechanism dominated by 6N*. HOWEVER, Direct channel investigations: mandatory, but  No strong conclusions!

22. 22 Summary & Concluding remarks (II) To go further, two directions:  Experimental: polarization asymmetries, especially with polarized target  Theoretical: coupled-channel approach (cf. talk by Harry Lee):  Already investigated by our collaboration (Argonne, Barcelona, Pittsburgh, Saclay)  p → [  N ;  N ; KY ] → K + Λ W.-T. Chiang, B. Saghai, F. Tabakin, T.-S.H. Lee, PRC 69, 065208 (2004). B. Juliá-Díaz, B. Saghai, T.-S.H. Lee, F. Tabakin, PRC 73, 055204 (2006).  In progress J. Durand, J. He, B. Juliá-Díaz, T.-S.H. Lee, T. Sato, B. Saghai, N. Suzuki  p → [  N ;  ;  N ;  N ; ηN] → ηp