The nature of the Roper P 11 (1440), S 11 (1535), D 13 (1520), and beyond.

1. The nature of the Roper P11(1440), S11(1535), D13(1520), and beyond.

2. SU(6)xO(3) Classification of Baryons D13(1520) S11(1535) Roper P11(1440)

3. The Roper Resonance – what are the issues? • Poorly understood in nrCQMs • - Wrong mass ordering (~ 1700 MeV) • - nrCQM gives A1/2(Q2=0) > 0, in contrast to experiment which finds A1/2(Q2=0) < 0. • Alternative models: • - Light front kinematics (many predictions) • - Hybrid baryon with gluonic excitation |q3G> (prediction) • - Quark core with large meson cloud |q3m> (prediction) • - Nucleon-sigma molecule |Nm> (no predictions) • - Dynamically generated resonance (no predictions) • Lattice QCD gives conflicting results • - Roper is consistent with 3-quark excitation (F. Lee, N*2004) • - Roper is not found as state (C. Gattringer, N*2007)

4. Lattice calculations of P11(1440), S11(1535) C. Gattringer, N*2007 F. Lee, N*2004 Masses of both states are well reproduced in quenched LQCD with 3 valence quarks.

5. UIM & DR Fit at low & high Q2 # data points:> 50,000 , Ee = 1.515, 1.645, 5.75 GeV

6. Fixed-t Dispersion Relations for invariant Ball amplitudes γ*p→Nπ Dispersion relations for 6 invariant Ball amplitudes: Unsubtracted Dispersion Relations (i=1,2,4,5,6) Subtracted Dispersion Relation

7. Dispersion Relations • Causality, analyticity constrain real and imaginary amplitudes: • Born term is nucleon pole in s- and u-channels and meson-exchange in t-channel. • Integrals over resonance region saturated by known resonances (Breit-Wigner). P33(1232) amplitudes found by solving integral equations. • Integrals over high energy region are calculated through π,ρ,ω,b1,a1 Regge poles. However these contributions were found negligible for W < 1.7 GeV • For η channel, contributions of Roper P11(1440) and S11(1535) to unphysical region s<(mη+mN)2 of dispersion integral included.

8. Fits for ep enπ+

9. UIM DR UIM vs DR Fits for ep →enπ+ Q2=0.4 GeV2 W = 1.53 GeV

10. ep → enπ+ UIM Fit to Structure Functions UIM Fit Q2=0.4 GeV2

11. Power of Interference II Im(S1+)Im(M1+) Large P33(1232) Small Im(S1-)Re(E0+) Bkg P11(1440) Resonance • Unpolarized structure function • Amplify small resonance multipole by an interfering larger resonance multipole sLT ~ Re(L*T) = Re(L)Re(T) + Im(L)Im(T) • Polarized structure function • Amplify resonance multipole by a large background amplitude sLT’ ~ Im(L*T) = Re(L)Im(T) + Im(L)Re(T)

12. UIM Fits for ep enπ+ s+-s- Ae= s++s- Ae Polarized beam beam helicity UIM Fit

13. Sensitivity of σLT’ to P11(1440) strength ep → eπ+n Polarized structure function are sensitive to imaginary part of P11(1440) through interference with real Born background. Shift in S1/2 Shift in A1/2

14. Examples of diff. cross sections at Q2=2.05 GeV2 DR DR w/o P11 UIM • φ-dependence • at W=1.43 GeV • W-dependence

15. Legendre moments forσT+ε σL Q2 = 2.05 GeV2 DR w/o P11(1440) ~cosθ ~(1 + bcos2θ) ~ const. DR UIM

16. Multipole amplitudes forγ*p→π+n Q2 =2.05 GeV2 Q2 =0 • At Q2=1.7-4.2, resonance behavior is seen in these amplitudes more clearly than at Q2 =0 • DR and UIM give close results for real parts of multipole amplitudes Im Re_UIM Re_DR

17. Helicity amplitudes for the γp→ P11(1440) transition CLAS Nπ, Nππ Nπ RPP Model uncertainties due to N, π, ρ(ω) → πγ form factors DRUIM

18. Comparison with LF quark model predictionsP11(1440)≡[56,0+]r • LF CQM predictions have common features, which agree with data: • Sign of A1/2 at Q2=0 is negative • A1/2 changes • sign at small Q2 • Sign of S1/2 is • positive • 1.Weber, PR C41(1990)2783 2.Capstick..PRD51(1995)3598 • 3.Simula…PL B397 (1997)13 4.Riska..PRC69(2004)035212 • 5.Aznauryan, PRC76(2007)025212 6.Cano PL B431(1998)270

19. Is the P11(1440) a hybrid baryon? previous data previous data g q3 G Suppression of S1/2 has its origin in the form of vertexγq→qG. It is practically independent of relativistic effects Z.P. Li, V. Burkert, Zh. Li, PRD46 (1992) 70 In a nonrelativistic approximation A1/2(Q2) and S1/2(Q2)behave like the γ*NΔ(1232) amplitudes.

20. So what have we learned about the Roper resonance? • LQCD shows a 3-quark component. Does it exclude a meson-nucleon resonance? • Roper resonance transition formfactors not described in non-relativistic CQM. If relativity (LC) is included the description is improved. • Overall best description at low Q2 in model with large meson cloud and quark core. • Gluonic excitation, i.e. a hybrid baryon, ruled out due to strong longitudinal coupling and the lack of a zero-crossing predicted for A1/2(Q2). • Other models need to predict transition form factors as a sensitive test of internal structure. • The Q2 dependence seems qualitatively consistent with the Roper as a radial excitation of a 3 quark system, may require quark form factors.

21. Negative Parity States in 2nd N* Region - • Hard form factor (slow fall off with Q2) • Not a quark resonance, but KΣ dynamical system? S11(1535) Change of helicity structure with increasing Q2 from Λ=3/2 dominance to Λ=1/2 dominance, predicted in nrCQMs, pQCD. D13(1520) CQM: Measure Q2 dependence of Transition F.F.

22. The S11(1535) • This state has traditionally studied in the S11(1535)→pη channel, which is the dominant decay: S11(1535) → 55% (pη) ; pη selects isospin I=1/2 S11(1535) → 35% (Nπ); Nπ sensitive to I=1/2, 3/2 • Nearby states, especially D13(1520) have very small coupling to pη channel, making the S11(1535) a rather isolated resonance in in this channel.

23. The S11(1535) – an isolated resonance S11→ pη (~55%) Q2=0 Resonance remains prominent up to highest Q2

24. Response Functions and Legendre Polynomials Expansion in terms of Legendre Polynomials A0 → E0+ → A1/2(S11) Sample differential cross sections for Q2=0.8 GeV2, and selected W bins. Solid line: CLAS fit, dashed line: η-MAID.

25. S11(1535) in pη and Nπ CLAS CLAS 2007 CLAS 2002 previous results pη

26. Examples of Fits with UIM to CLAS data on Nπ lp= 0+multipoles Q2=0 Q2=3 GeV2 W, GeV W, GeV

27. S11(1535) in pη and Nπ CLAS New CLAS results CLAS 2007 pπ0 nπ+ CLAS 2002 previous results pη nπ+ pπ0 pη PDG (2006): S11→πN (35-55)% → ηN (45-60)% A1/2 from pη and Nπ are consistent

28. A new P11(1650) in γ*p→ηp ? CLAS 4 resonance fit gives reasonable description including S11(1535), S11(1650), P11(1710), D13(1520) A0 → E0+ → A1/2(S11) A1/A0 shows a sharp structure near 1.65 GeV. The observation is consistent with a rapid change in the relative phase of the E0+ and M1- multipoles because one of them is passing through resonance. No new P11 resonance needed as long as P11(1710) mass, width, BR(pη) are not better determined

29. The D13(1520) lp= 2- multipoles

30. Transition amplitudes γpD13(1520) CLAS A3/2 Previous pπ0 based data preliminary preliminary A1/2 Q2, GeV2 Q2, GeV2 nrCQM predictions: A1/2 dominance with increasing Q2. Nπ, pπ+π- nπ+ nπ+ pπ0 pπ0

31. Helicity Asymmetry for γpD13 A21/2 – A23/2 Ahel = A21/2 + A23/2 Ahel D13(1520) CLAS CQMs and pQCD Ahel→ +1 at Q2→∞ Helicity structure of transition changes rapidly with Q2 from helicity 3/2 (Ahel= -1) to helicity 1/2 (Ahel= +1) dominance!

32. What have we learned about the S11(15350 and D13(1520) resonances ? • Nπ+ and pη give consistent results for A1/2(Q2) of S11(1535) • New nπ+ data largely consistent with analysis of previous pπ0 data for A1/2 and A3/2 of D13(1520) • D13(1520) shows rapid change of helicity structure from A3/2 to A1/2 dominance. • Both states appear consistent with 3-quark model orbital excitation in [70,1-]

33. Test prediction of helicity conservation → Expect approach to flat behavior at high Q2 Q3A1/2 S11 D13 Q5A3/2 P11 F15 F15 D13 Helicity conserving amplitude A1/2 appears to approach scaling No scaling seen for helicity non-conserving amplitude A3/2

34. Single Quark Transition Model A orbit flip spin flip B spin-orbit C EM transitions between all members of two SU(6)xO(3) multiplets expressed as 4 reduced matrix elements A,B,C,D. Example: (D=0) Fit A,B,C to D13(1535) and S11(1520) SU(6) Clebsch-Gordon A3/2, A1/2 A,B,C,D Predicts 16 amplitudes of same supermultiplet

35. Single Quark Transition Model Photocoupling amplitudes SQTM amplitudes (C-G coefficients and mixing angles)

36. SQTM Predictions for [56,0+]→[70,1-] Transitions Proton

37. SQTM Predictions for [56,0+]→[70,1-] Transitions Neutron A1/2=A3/2= 0 for D15(1675)on protons

38. End of Part III

39. Analysis of p+p-p single differential cross-sections. Isobar Model JM05 Full calculations gpp-D++ gpp+D0 gpp+D13(1520) gprp gpp-P++33(1600) gpp+F015(1685) direct2p production Combined fit of various 1-diff. cross-sections allowed to establish all significant mechanisms.

40. Test of JM05 program on well known states. ep → epp+p- A3/2,GeV-1/2 (A1/22+S1/22)1/2, GeV-1/2 D13(1520) Q2 GeV2 Q2 GeV2 → JM05 works well for states with significant Npp couplings.

41. First consistent amplitudes for A1/2(Q2), A3/2(Q2) of D33(1700) State has dominant coupling to Npp ep → epp+p- D33(1700)