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

2 SU(6)xO(3) Classification of Baryons D 13 (1520) S 11 (1535) Roper P 11 (1440)

3 The Roper Resonance – what are the issues?  Poorly understood in nrCQMs - Wrong mass ordering (~ 1700 MeV) - nrCQM gives A 1/2 (Q 2 =0) > 0, in contrast to experiment which finds A 1/2 (Q 2 =0) < 0.  Alternative models: - Light front kinematics (many predictions) - Hybrid baryon with gluonic excitation |q 3 G> (prediction) - Quark core with large meson cloud |q 3 m> (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 P 11 (1440), S 11 (1535) F. Lee, N*2004 Masses of both states are well reproduced in quenched LQCD with 3 valence quarks. C. Gattringer, N*2007

5 UIM & DR Fit at low & high Q 2 ObservableData points UIMDR # data points:> 50,000, E e = 1.515, 1.645, 5.75 GeV

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

7  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). P 33 (1232) amplitudes found by solving integral equations.  Integrals over high energy region are calculated through π,ρ,ω,b 1,a 1 Regge poles. However these contributions were found negligible for W < 1.7 GeV  For η channel, contributions of Roper P 11 (1440) and S 11 (1535) to unphysical region s<(m η +m N ) 2 of dispersion integral included. Dispersion Relations

8 Fits for ep  enπ +

9 W = 1.53 GeV Q 2 =0.4 GeV 2 UIMDR UIM vs DR Fits for ep → enπ +

10 ep → enπ + Q 2 =0.4 GeV 2 UIM Fit to Structure Functions UIM Fit

11 Unpolarized structure function –Amplify small resonance multipole by an interfering larger resonance multipole Power of Interference II Polarized structure function –Amplify resonance multipole by a large background amplitude  LT ~ Re(L*T) = Re(L)Re(T) + Im(L)Im(T)  LT’ ~ Im(L*T) = Re(L)Im(T) + Im(L)Re(T) Large Small P 33 (1232) Im(S 1+ ) Im(M 1+ ) Bkg P 11 (1440) Resonance Im(S 1- ) Re(E 0+ )

12 UIM Fits for ep  enπ + A e Polarized beam beam helicity Ae=Ae= +--+-- ++-++- UIM Fit

13 Sensitivity of σ LT ’ to P 11 (1440) strength Shift in S 1/2 Shift in A 1/2 Polarized structure function are sensitive to imaginary part of P 11 (1440) through interference with real Born background. ep → eπ + n

14 Examples of diff. cross sections at Q 2 =2.05 GeV 2 W-dependence φ-dependence at W=1.43 GeV DR UIM DR w/o P11

15 Legendre moments for σ T +ε σ L DR UIM Q 2 = 2.05 GeV 2 ~cosθ~(1 + bcos 2 θ) ~ const. DR w/o P 11 (1440)

16 Multipole amplitudes for γ * p → π + n Q 2 =0 Q 2 =2.05 GeV 2 Im Re_UIM Re_DR  At Q 2 = , resonance behavior is seen in these amplitudes more clearly than at Q 2 =0  DR and UIM give close results for real parts of multipole amplitudes

17 Helicity amplitudes for the γp → P 11 (1440) transition DR UIM RPP Nπ, Nππ Model uncertainties due to N, π, ρ(ω) → πγ form factors NπNπ CLAS

18 Comparison with LF quark model predictions P 11 (1440) ≡ [56,0 + ] r LF CQM predictions have common features, which agree with data: Sign of A 1/2 at Q 2 =0 is negative A 1/2 changes sign at small Q 2 Sign of S 1/2 is positive 1.Weber, PR C41(1990) Capstick..PRD51(1995) Simula…PL B397 (1997)13 4. Riska..PRC69(2004) Aznauryan, PRC76(2007) Cano PL B431(1998)270

19 Is the P 11 (1440) a hybrid baryon? Suppression of S 1/2 has its origin in the form of vertex γq→qG. It is practically independent of relativistic effects Z.P. Li, V. Burkert, Zh. Li, PRD46 (1992) 70  G q3q3 In a nonrelativistic approximation A 1/2 (Q 2 ) and S 1/2 (Q 2 ) behave like the γ*NΔ(1232) amplitudes. previous data

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 Q 2 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 A 1/2 (Q 2 ).  Other models need to predict transition form factors as a sensitive test of internal structure.  The Q 2 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 2 nd N* Region S 11 (1535) Hard form factor (slow fall off with Q 2 ) Not a quark resonance, but KΣ dynamical system? D 13 (1520) - CQM: Change of helicity structure with increasing Q 2 from Λ=3/2 dominance to Λ=1/2 dominance, predicted in nrCQMs, pQCD. Measure Q 2 dependence of Transition F.F.

22 The S 11 (1535) This state has traditionally studied in the S 11 (1535) → pη channel, which is the dominant decay: S 11 (1535) → 55% (pη) ; pη selects isospin I=1/2 S 11 (1535) → 35% (Nπ) ; Nπ sensitive to I=1/2, 3/2 Nearby states, especially D 13 (1520) have very small coupling to pη channel, making the S 11 (1535) a rather isolated resonance in in this channel.

23 Q 2 =0 The S 11 (1535) – an isolated resonance S 11 → pη (~55%) Resonance remains prominent up to highest Q 2

24 Response Functions and Legendre Polynomials Expansion in terms of Legendre Polynomials Sample differential cross sections for Q 2 =0.8 GeV 2, and selected W bins. Solid line: CLAS fit, dashed line: η-MAID. A 0 → E 0+ → A 1/2 (S 11 )

25 S 11 (1535) in pη and Nπ pηpη CLAS 2007 CLAS 2002 previous results CLAS

26 Examples of Fits with UIM to CLAS data on Nπ l    multipoles W, GeV Q 2 =0 Q 2 =3 GeV 2

27 S 11 (1535) in pη and Nπ pηpη pπ0pπ0 nπ+nπ+ pπ0pπ0 nπ+nπ+ pηpη CLAS 2007 CLAS 2002 previous results New CLAS results A 1/2 from pη and Nπ are consistent CLAS PDG (2006): S 11 → πN (35-55)% → ηN (45-60)%

28 A new P 11 (1650) in γ*p → ηp ? CLAS 4 resonance fit gives reasonable description including S 11 (1535), S 11 (1650), P 11 (1710), D 13 (1520) A 0 → E 0+ → A 1/2 (S 11 ) A 1 /A 0 shows a sharp structure near 1.65 GeV. The observation is consistent with a rapid change in the relative phase of the E 0+ and M 1- multipoles because one of them is passing through resonance. No new P 11 resonance needed as long as P 11 (1710) mass, width, BR(pη) are not better determined

29 l    multipoles The D 13 (1520)

30 Transition amplitudes γpD 13 (1520) A 1/2 A 3/2 Q 2, GeV 2 CLAS Previous pπ 0 based data pπ0pπ0 nπ+nπ+ Nπ, pπ + π - nπ+nπ+ pπ0pπ0 preliminary nrCQM predictions: A 1/2 dominance with increasing Q 2.

31 Helicity Asymmetry for γpD 13 D 13 (1520) A hel CQMs and pQCD A hel → +1 at Q 2 →∞ A hel = A 2 1/2 – A 2 3/2 A 2 1/2 + A 2 3/2 Helicity structure of transition changes rapidly with Q 2 from helicity 3/2 (A hel = - 1) to helicity 1/2 (A hel = +1) dominance! CLAS

32 What have we learned about the S 11 (15350 and D 13 (1520) resonances ? Nπ + and pη give consistent results for A 1/2 (Q 2 ) of S 11 (1535) New nπ+ data largely consistent with analysis of previous pπ 0 data for A 1/2 and A 3/2 of D 13 (1520) D 13 (1520) shows rapid change of helicity structure from A 3/2 to A 1/2 dominance. Both states appear consistent with 3-quark model orbital excitation in [70,1 - ]

33 Test prediction of helicity conservation Q 3 A 1/2 Q 5 A 3/2 S 11 P 11 F 15 D 13 No scaling seen for helicity non-conserving amplitude A 3/2 F 15 D 13 Helicity conserving amplitude A 1/2 appears to approach scaling → Expect approach to flat behavior at high Q 2

34 Single Quark Transition Model EM transitions between all members of two SU(6)xO(3) multiplets expressed as 4 reduced matrix elements A,B,C,D. Fit A,B,C to D 13 (1535) and S 11 (1520) A 3/2, A 1/2 A,B,C,D SU(6) Clebsch- Gordon Example:(D=0) Predicts 16 amplitudes of same supermultiplet orbit flip spin flip spin-orbit A B C

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 Neutron SQTM Predictions for [56,0 + ] → [70,1 - ] Transitions A 1/2 =A 3/2 = 0 for D 15 (1675) on protons

38 End of Part III

39 Analysis of  +  - p single differential cross-sections. Full calculations  p  -  ++ p+0p+0 pppp  p  - P (1600)  p  + F 0 15 (1685) direct 2  production  p  + D 13 (1520) Combined fit of various 1-diff. cross-sections allowed to establish all significant mechanisms. Isobar Model JM05

40 Test of JM05 program on well known states. D 13 (1520) ep → ep     (A 1/2 2 +S 1/2 2 ) 1/2, GeV -1/2 A 3/2, GeV -1/2 Q 2 GeV 2 → JM05 works well for states with significant Npp couplings.

41 First consistent amplitudes for A 1/2 (Q 2 ), A 3/2 (Q 2 ) of D 33 (1700) D 33 (1700) ep → ep     State has dominant coupling to N 