Covariant quark-diquark model for the N N electromagnetic transitions

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1 Covariant quark-diquark model for the N N electromagnetic transitions Gilberto Ramalho CFTP, Instituto Superior Técnico, Lisbon In collaboration with F. Gross, M.T. Peña and K. Tsushima Nucleon Resonance Structure in Exclusive Electroproduction at High Photon Virtualities with the CLAS 12 Detector Workshop Jlab, Newport News, VA, USA May 16, 211 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

2 1 Motivation 2 Covariant spectator quark model Quark current Baryon wave functions Transition current 3 Results Spin 1/2 resonances N(939), N(144), N(1535) Spin 3/2 resonances (1232), (16) 4 Conclusions Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

3 Nucleon Resonance Structure σ T (1232) P 33 γ p -> n π + N(144) P 11 N(152) D W (MeV) N(1535) S 11 (16) P 33 N(165) S 11 N(168) F 15 N(171) P 11 Q 2 = 1 GeV 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

4 Frameworks to study γn N at high Q 2 Study the N electroproduction (Constituent) Quark Models... Coupled-channels reaction models (Dynamical models) baryon bare core structure (input) with meson dressing (meson-baryon interaction) [EBAC, Sato-Lee, Mainz (DMT), Julich, Bonn,... ] χ-perturbation Theory, χeft Baryons and pions as d.o.f. - low Q 2 regime [Pascalutsa, Vanderhaghen, Gail, Hermert,...] pqcd... very high Q 2 Hybrid models (CBM, soliton,...) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

5 Motivation and goals [γn N ] Challenge: Understand the electromagnetic structure of the Nucleon and Nucleon resonances Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

6 Motivation and goals [γn N ] Challenge: Understand the electromagnetic structure of the Nucleon and Nucleon resonances Low Q 2 [ Q 2 2 GeV 2 ] High Q 2 [ Q GeV 2 ] (not in pqcd regime) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

7 Motivation and goals [γn N ] Challenge: Understand the electromagnetic structure of the Nucleon and Nucleon resonances Low Q 2 [ Q 2 2 GeV 2 ] High Q 2 [ Q GeV 2 ] (not in pqcd regime) What do we know? Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

8 Motivation and goals [γn N ] Challenge: Understand the electromagnetic structure of the Nucleon and Nucleon resonances Low Q 2 [ Q 2 2 GeV 2 ] High Q 2 [ Q GeV 2 ] (not in pqcd regime) What do we know? Theory: Nucleon resonances (baryons): internal structure ruled by QCD Internal degrees of freedom: (light) quarks and gluons Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

9 Motivation and goals [γn N ] Challenge: Understand the electromagnetic structure of the Nucleon and Nucleon resonances Low Q 2 [ Q 2 2 GeV 2 ] High Q 2 [ Q GeV 2 ] (not in pqcd regime) What do we know? Theory: Nucleon resonances (baryons): internal structure ruled by QCD Internal degrees of freedom: (light) quarks and gluons Experiments: We detect baryons and mesons possible decays: πn, ηn, ρn, π,... Effective degrees of freedom: mesons resonant core (N ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

10 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

11 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

12 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

13 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

14 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Why covariant? Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

15 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Why covariant? Relativity fundamental at high Q 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

16 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Why covariant? Relativity fundamental at high Q 2 Ingredients: Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

17 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Why covariant? Relativity fundamental at high Q 2 Ingredients: Wave functions (qqq) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

18 Framework for high Q 2 : Spectator quark model Covariant Spectator Quark Model c - Franz Gross (CST) Why a quark model? N as a qqq system Simple way of describing N quantum numbers: charge, spin, flavor, parity, decays,... Falloff of meson cloud (q q states configuration) high Q 2 Why covariant? Relativity fundamental at high Q 2 Ingredients: Wave functions (qqq) Quark current [constituent quarks e.m. form factors]: [dressing by gluons interactions and some quark-antiquark states] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

19 Program to study γn N reactions Goal: Study Valence Quark content of N structure N = N(939), N(144), N(1535), (1232), (16),... Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

20 Program to study γn N reactions Goal: Study Valence Quark content of N structure N = N(939), N(144), N(1535), (1232), (16),... Input: Nucleon elastic form factor data Lattice QCD data (N = N,,...) Dynamical Model information (valence form factors) Callibration of the model [Quark current & wave functions] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

21 Program to study γn N reactions Goal: Study Valence Quark content of N structure N = N(939), N(144), N(1535), (1232), (16),... Input: Nucleon elastic form factor data Lattice QCD data (N = N,,...) Dynamical Model information (valence form factors) Callibration of the model [Quark current & wave functions] Output: Valence quark contributions for the γn N form factors Dominant at high Q 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

22 Program to study γn N reactions Goal: Study Valence Quark content of N structure N = N(939), N(144), N(1535), (1232), (16),... Input: Nucleon elastic form factor data Lattice QCD data (N = N,,...) Dynamical Model information (valence form factors) Callibration of the model [Quark current & wave functions] Output: Valence quark contributions for the γn N form factors Dominant at high Q 2 Using complementar information: estimate of meson cloud [Low Q 2 data; large-n c relations for meson cloud,...] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

23 Quark structure and electromagnetic interaction (I) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

24 Quark structure and electromagnetic interaction (II) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

25 Quark structure and electromagnetic interaction (II) Not important at high Q 2 [pqcd: supression 1/Q 4 ] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

26 Quark structure and electromagnetic interaction (II) Not important at high Q 2 [pqcd: supression 1/Q 4 ] Assume NO interference with quark dressing processes G X = G B X + G mc X Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

27 Spectator QM: Baryon wave functions Baryon: 3 constituent quark system Covariant Spectator Theory c : wave function Ψ defined in terms of a 3-quark vertex Γ with 2 on-mass-shell quarks «1 Ψ α(p, k 3) = Γ β (P, k 1, k 2) m q k 3 iε αβ Confinement insures that vertex Γ vanishes when the 3 quarks are on-shell [Γ cancels the quark propagator singularity] Stadler, Gross and Frank PRC 56, 2396 (1998); Savkli and Gross PRC 63, 3528 (21) Ψ free of singularities Instead of modulate Γ modulate directly Ψ Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

28 Spectator QM: Baryon wave functions (II) Integrating over the on-mass-shell quark momenta: k = k 1 + k 2, r = 1 2 (k 1 k 2 ); reduce current integrals to the integration in k and s = (k 1 + k 2 ) 2 Gross and Agbakpe, PRC 73, 1523 (26); PRC 77, 1522 (28): d 3 k 1 2E k1 d 3 k 2 = π 2E k2 4 dωˆr + 4m 2 q ds s 4m 2 q s d 3 k 2E k with E k = s + k 2 as the energy of the diquark. Mean value theorem: average in diquark mass s m D d 3 k 1 d 3 k 2 d 3 k 2E k1 2E k2 2 m 2 D + k2 m D =eff. mass; covariant integration in diquark on-shell momentum Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

29 Spectator QM: Baryon wave functions (III) Baryon wave functions: B = diquark quark Combination of diquark (12) and single quark (3) states, using SU(6) O(3): Ψ B = (flavor) (spin) (orbital) ψ B (P, k) }{{} radial Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

30 Spectator QM: Baryon wave functions (III) Baryon wave functions: B = diquark quark Combination of diquark (12) and single quark (3) states, using SU(6) O(3): Ψ B = (flavor) (spin) (orbital) ψ B (P, k) }{{} radial Ψ B in rest frame using quark states Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

31 Spectator QM: Baryon wave functions (III) Baryon wave functions: B = diquark quark Combination of diquark (12) and single quark (3) states, using SU(6) O(3): Ψ B = (flavor) (spin) (orbital) ψ B (P, k) }{{} radial Ψ B in rest frame using quark states Covariant generalization of Ψ B in terms baryon properties Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

32 Spectator QM: Baryon wave functions (III) Baryon wave functions: B = diquark quark Combination of diquark (12) and single quark (3) states, using SU(6) O(3): Ψ B = (flavor) (spin) (orbital) ψ B (P, k) }{{} radial Ψ B in rest frame using quark states Covariant generalization of Ψ B in terms baryon properties Ψ B can be used on any frame and/or Q 2 regime Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

33 Spectator QM: Photon-Quark coupling Quark current [f i± quark form factors] [ j µ 1 I = 6 f ] ) 2 f 1 τ 3 (γ µ qqµ q 2 + [ 1 6 f ] iσ µν 2 f q ν 2 τ 3 2M N Quarks with anomalous magnetic moments κ u, κ d fixed by nucleon magnetic moments: µ p, µ n Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

34 Spectator QM: Photon-Quark coupling Quark current [f i± quark form factors] [ j µ 1 I = 6 f ] ) 2 f 1 τ 3 (γ µ qqµ q 2 + [ 1 6 f ] iσ µν 2 f q ν 2 τ 3 2M N Quarks with anomalous magnetic moments κ u, κ d fixed by nucleon magnetic moments: µ p, µ n Vector meson dominance parameterization: 2 poles: Light vector meson: m v = m ρ Effective heavy meson: M h (=2M N ): 4 adjustable coefficients Nucleon data Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

35 Spectator QM: Transition currents (γn N ) Quark current j µ I Baryon wave function Ψ B J µ Transition current J µ in spectator formalism Franz Gross et al PR 186 (1969); PRC 45, 294 (1992) Relativistic impulse approximation: J µ = 3 λ k Ψ f (P +, k)j µ I Ψ i(p, k) P + N Ψ f k Ψ i P N diquark on-shell q = P + P, P = 1 2 (P + + P ), Q 2 = q 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

36 Spin 1/2 resonances: transition currents Nucleon: [ J µ = ū(p + ) F 1 γ µ iσ µν ] q ν + F 2 u(p ) 2M N γn N(144) (R): J µ = ū R (P + ) γn N(1535) (S): J µ = ū S (P + ) [ F 1 [ F 1 ) (γ µ qqµ q 2 + F2 ) (γ µ qqµ q 2 + F2 iσ µν q ν M R + M N iσ µν q ν M S + M N Form factors - exclusive functions of Q 2 ] u(p ) ] γ 5 u(p ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

37 Spin 1/2 resonances: wave functions Nucleon: S-state approximation (quark-diquark) Ψ N (P, k) = 1 2 [ Φ I Φ S + Φ 1 IΦ 1 S] ψn (P, k) N(144): Ψ R (P, k) = 1 2 [ Φ I Φ S + Φ 1 IΦ 1 S] ψr (P, k) N(1535): Ψ S11 (P, k) = 1 2 [ Φ I X ρ Φ 1 IX λ ] ψs11 (P, k) Φ,1 I : isospin states; Φ,1 S, X ρ, X λ : spin states Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

38 Scalar wave function: Nucleon Scalar wave functions deppendent of (P k) 2 = (quark momentum) 2 χ B = (M B m D ) 2 (P k) 2 M B m D Nucleon scalar wave function: ψ N (P, k) = Position space: NR k2 m 2 D M B = baryon mass; m D = diquark mass N 1 m D (β 1 + χ N )(β 2 + χ N ) = N 1 m D β 2 β NR N 1 m D β 2 β 1 ψ N (P, k) 6 4 FT 1 β 1 + k2 m 2 D e m D β1 r 1 7 β 2 + k2 5 m 2 D " 1 β 1 + χ N e m D β2 r r r β 1, β 2 momentum range parameters; β 2 > β 1 : β 1 long spatial range; β 2 short spatial range 1 β 2 + χ N # Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

39 Nucleon form factors (I) F Gross, GR and MT Peña, PRC 77, 1522 (28) model II Nucleon form factors: G E = F 1 τf 2, G M = F 1 + F 2 ; τ = Q2 4M 2 N G Mp /G D /µ p G Mn /G D /µ n G Ep /G Mp /µ p.5 G En Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

40 Nucleon form factors (II) [PRC 77, 1522 (28)] G Mp /G D /µ p G Mn /G D /µ n G Ep /G Mp /µ p G En Quark current fix 4 parameters; Scalar wave function [2] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

41 Nucleon form factors (II) [PRC 77, 1522 (28)] G Mp /G D /µ p G Mn /G D /µ n G Ep /G Mp /µ p.5 G En Quark current fix 4 parameters; Scalar wave function [2] No pion cloud (explicit)... but VMD Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

42 Nucleon form factors (II) [PRC 77, 1522 (28)] G Mp /G D /µ p G Mn /G D /µ n G Ep /G Mp /µ p.5 G En Quark current fix 4 parameters; Scalar wave function [2] No pion cloud (explicit)... but VMD How can we test the valence quark parametrizarion? Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

43 Nucleon form factors (II) [PRC 77, 1522 (28)] G Mp /G D /µ p G Mn /G D /µ n G Ep /G Mp /µ p.5 G En Quark current fix 4 parameters; Scalar wave function [2] No pion cloud (explicit)... but VMD How can we test the valence quark parametrizarion? Lattice Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

44 Extension of the model for lattice QCD regime GR and MT Peña JPG 36, (29) Quark current: j µ I (M N; m ρ, M h = 2M N ) j µ I (Mlatt N ; mlatt ρ, 2M latt N ) Wave functions: Ψ B ({M B }) Ψ B ({M latt B }) Implicit m π dependence in G X [Form factors] G X include only valence quark (bare) contributions G B X Meson cloud effects suppressed for large m π : Compare G B X with lattice data Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

45 Nucleon form factors on lattice [JPG 36, (29)] G p n X Lattice nucleon form factors v G.6 E.4.2 m π =.646 GeV 4 3 v G M v G.6 E.4.2 m π =.615 GeV 4 3 v G M v G.6 E.4.2 m π =.54 GeV 4 3 v G M Data from Gockeler at al, PRD 71, 3458 (25) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

46 N(144) wave function [N(144) R] (Roper) N(144) is the 1st radial excitation of the nucleon Same spin a isospin structure Ψ R orthogonal to Ψ N Orthogonality given by scalar wave functions ψ R (P +, k)ψ N (P, k) = Q 2 = Wave function: k ( ) (P k) 2 ψ R m D M R excitation {}}{ β (P k)2 3 2 ( ) m = N D M R (P k) 2 1 ψ N m S M R β 1 + 2(P k)2 m D M R β 1 fixed by ψ N; β 3 determined by the orthogonality condition No adjustable parameters predictions Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

47 γn N(144) on lattice [PRD 81, 742 (21)] Lattice Spectator (lattice regime) Spectator (valence) F 1 *(Q 2 ).2 Lattice Spectator (lattice regime) Spectator (valence) F 2 *(Q 2 ) Data: H.W. Lin et al PRD 78, (28) Good agreement with Lattice data GR and K Tsushima, PRD 81, 742 (21) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

48 γn N(144) form factors [PRD 81, 742 (21)].2.15 CLAS data Spectator (valence) MAID.2 F 1 *(Q 2 ).1.5 F 2 *(Q 2 ) CLAS data Spectator (valence) MAID CLAS data - Aznauryan et al PRC 8, 5523 (29), MAID fit Good agreement for Q 2 > 1.5 GeV 2 Difference for Q 2 < 1.5 GeV 2 manifestation of meson cloud Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

49 γn N(144) helicity amplitudes R = A 1/2 (Q 2 ) = R [ F 1 (Q 2 ) + F 2 (Q 2 ) ] S 1/2 (Q 2 ) = R 2 M R + M Q 2 q [ F 1 (Q 2 ) τf 2 (Q 2 ) ] πα [(M R M) 2 + Q 2 ], K = M2 R M2, τ = M R MK 2M R q = photon momentum in Roper rest frame Q 2 (M R + M) 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

50 γn N(144) helicity amplitudes [PRD 81, 742 (21)] A 1/2 (Q 2 ) CLAS data Spectator (valence) MAID S 1/2 (Q 2 ) CLAS data Spectator (valence) MAID GR and K Tsushima PRD 81, 742 (21) Good description of the data (Q 2 > 1.5 GeV 2 ) N(1535) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

51 N(1535) wave function [N(1535) = S11 S] Approximations: See NSTAR211 Pointlike diquark k ρ = 1 2 (k 1 k 2 ) [no internal diquark P-states] Pure spin 1/2 core: N(1535) = cos θ S S = 1/2 sin θ S S = 3/2 S = 1/2 [Karl-Isgur model: cos θ S.85] Spin states (diquark-quark system with L = 1, P = 1): X X ρ `+1 2 1m; 1, , 1 Y1m(ˆk 2 2 λ ) m 1 2 ρ [MA] ψ S11 (P,k) = m X X λ `+1 2 1m; 1, , 1 Y1m(ˆk 2 2 λ ) m 1 2 λ m N S [MS] m D (β P k m DM S ) ( β P k m DM S ) ψ N (P,k) No adjustable parameters predictions Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

52 γn N(1535) form factors [arxiv: [hep-ph]] Form factors: F 1, F 2 I (Q 2 ) Overlap integral (S11 rest frame): q = M2 S M2 2M S : photon moment I (Q 2 k z ) = k ψ S11 (P S11, k)ψ N (P N, k) k = const q (Q 2 ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

53 γn N(1535) form factors [arxiv: [hep-ph]] Form factors: F 1, F 2 I (Q 2 ) Overlap integral (S11 rest frame): q = M2 S M2 2M S : photon moment I (Q 2 k z ) = k ψ S11 (P S11, k)ψ N (P N, k) k = const q (Q 2 ) If M S = M I () = N, S11 orthogonal states Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

54 γn N(1535) form factors [arxiv: [hep-ph]] Form factors: F 1, F 2 I (Q 2 ) Overlap integral (S11 rest frame): q = M2 S M2 2M S : photon moment I (Q 2 k z ) = k ψ S11 (P S11, k)ψ N (P N, k) k = const q (Q 2 ) If M S = M I () = N, S11 orthogonal states If M S M I () No orthogonality [Consequence of relativistic generalization (boost of a state)] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

55 γn N(1535) form factors [arxiv: [hep-ph]] Form factors: F 1, F 2 I (Q 2 ) Overlap integral (S11 rest frame): q = M2 S M2 2M S : photon moment I (Q 2 k z ) = k ψ S11 (P S11, k)ψ N (P N, k) k = const q (Q 2 ) If M S = M I () = N, S11 orthogonal states If M S M I () No orthogonality [Consequence of relativistic generalization (boost of a state)] Range of application of the model? (I () ) q defines the momentum scale Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

56 γn N(1535) form factors [arxiv: [hep-ph]] Form factors: F 1, F 2 I (Q 2 ) Overlap integral (S11 rest frame): q = M2 S M2 2M S : photon moment I (Q 2 k z ) = k ψ S11 (P S11, k)ψ N (P N, k) k = const q (Q 2 ) If M S = M I () = N, S11 orthogonal states If M S M I () No orthogonality [Consequence of relativistic generalization (boost of a state)] Range of application of the model? (I () ) q defines the momentum scale If Q 2 q 2 =.23 GeV2 I () Model valid for Q 2 > 2.3 GeV 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

57 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al PDG Model compared with CLAS and MAID data Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

58 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al PDG Model compared with CLAS and MAID data F 1 OK; F 2 wrong sign Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

59 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al PDG Model compared with CLAS and MAID data F1 OK; F 2 wrong sign... Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

60 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al PDG Model compared with CLAS and MAID data F1 OK; F 2 wrong sign... There is also estimates of valence contributions (EBAC) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

61 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) PDG Model compared with EBAC: J. Diaz et al PRC 6, 2527 (29) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

62 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) PDG Model compared with EBAC: J. Diaz et al PRC 6, 2527 (29) F 1 close to EBAC (valence quark core) (Q2 < 2 GeV 2 ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

63 γn N(1535) form factors [arxiv: [hep-ph]] F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) PDG Model compared with EBAC: J. Diaz et al PRC 6, 2527 (29) F 1 close to EBAC (valence quark core) (Q2 < 2 GeV 2 ) F 2 close to valence estimate (Q2 1 GeV 2 ) (F 2 )Sp (F 2 )QM Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

64 γn N(1535) helicity amplitudes 15 A 1/2 (1-3 GeV -1/2 ) 1 5 CLAS data MAID analysis Dalton et al EBAC (bare) PDG S 1/2 (1-3 GeV -1/2 ) CLAS data MAID analysis EBAC (bare) [ A 1/2 = 2b F1 + M ] S M M S + M F 2, S 1/2 = 2b(M S + M) q [ ] MS M Q 2 M S + M F 1 τf2 p v [(MS M) 2 + Q 2 ][(M S + M) 2 + Q 2 ] u q =, b = et (M S M) 2 + Q 2 2 2M S 8M(M S 2 M2 ), τ = Q (M S + M) 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

65 γn N(1535) form factors F 2 * (Q 2 ) CLAS data MAID analysis Dalton et al EBAC (bare) PDG What if we use F 2? (Q2 > 1.5 GeV 2 ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

66 γn N(1535) helicity amplitudes [arxiv: [hep-ph]] 15 A 1/2 (1-3 GeV -1/2 ) 1 5 CLAS data MAID analysis Dalton et al EBAC (bare) PDG S 1/2 (1-3 GeV -1/2 ) CLAS data MAID analysis EBAC (bare) F 2 = (data), F 1 from Spectator model Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

67 γn N(1535) helicity amplitudes [arxiv: [hep-ph]] 15 A 1/2 (1-3 GeV -1/2 ) 1 5 CLAS data MAID analysis Dalton et al EBAC (bare) PDG S 1/2 (1-3 GeV -1/2 ) CLAS data MAID analysis EBAC (bare) F2 = (data), F 1 from Spectator model Very good description of A 1/2 and S 1/2 for Q 2 > 2.3 GeV 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

68 γn N(1535) helicity amplitudes [arxiv: [hep-ph]] Implication of F 2 = : Model with valence quark meson cloud: Cancelation of valence quark contributions and meson cloud contributions F B 2 (Q 2 ) + F mc 2 F2 B = valence quarks; F mc 2 = meson cloud Consequence: for Q 2 > 1.8 GeV 2 [ q Q 1 + τ ]: 1 + τ M S 1/2 S 2 M2 2 2M S Q A 1/2 S 1/2 scales with A 1/2 GR and K Tsushima arxiv: [hep-ph] Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

69 Relation between A 1/2 and S 1/2 (MAID) 15 A 1/2 (1-3 GeV -1/2 ) 1 5 CLAS data MAID analysis Dalton et al PDG MAID fit S 1/2 (1-3 GeV -1/2 ) -1-2 CLAS data MAID analysis MAID fit Scaling (MAID) MAID parametrization A 1/2 : 1 + τ M S 1/2 S 2 M2 2 2M S Q A 1/2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

70 γn N (1535) asymptotic behavior [arxiv: [hep-ph]] 15 F 1 * (Q 2 ) CLAS data MAID analysis Dalton et al pqcd A 1/2 (1-3 GeV -1/2 ) 1 5 CLAS data MAID analysis Dalton et al PDG pqcd Comparing with pqcd, Carlson et al. PRL 81, 2646 (1998) Model and Data overestimates pqcd result Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

71 Spin 3/2 resonances: transition currents γn (1232) or (16): [ J µ = ū β (P + ) G 1 q β γ µ + G 2 q β P µ + G 3 q β q µ G 4 g βµ] γ 5 u(p ) u β Rarita-Schwinger spinor q µ J µ = G 4 = (M + M N )G (M2 M 2 N)G 2 Q 2 G 3 G M = G E = G C = M N nˆ(3m 3(M N +M + M ) N)(M + M) + Q 2 G o 1 +(M 2 MN)G 2 2 2Q 2 G 3 M n M N 3(M N +M ) M N 3(M N +M ) A 1/2 = N o (M 2 MN 2 Q 2 ) G1 (M 2 MN)G 2 2 2Q 2 G 3 M o n4m G 1 + (3M 2 + MN 2 + Q 2 )G 2 + 2(M 2 MN 2 Q 2 )G [G M 3G E], A 3/2 = N 2 [G M + G E], S 1/2 G C Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

72 Spin 3/2 resonances: wave functions wave function: EPJA 36, 329 (28); PRD 78, (28); PRD 8, 138 (29) Ψ = N [Ψ S + aψ D3 + bψ D1 ] S = 3 2, D3 = 2 3 2, D1 = Wave functions fited to form factor data [G M, G E, G C ] S-state model: good description of G M data EPJA, 36, 329 (28) With D-states: S-state G M Fit physical data EBAC (core) G E, G C Fit lattice QCD data (bare contribution) Extracting valence quark contributions from lattice QCD: G latt X (m latt π Model {}}{ ) G B X(m latt π ) mlatt π m phys π G B X(physical) GR and MT Peña PRD 8, 138 (29) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

73 Lattice: Alexandrou et al, PRD 77, 8512 (28) EBAC: J. Diaz et al, PRC 75, 1525 (27) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5 γn : G M (Q2 ) on lattice [PRD 8, 138 (29)] Lattice m π = 563 MeV Physical Point Lattice m π = 411 MeV Physical Point G M * 1 G M * G M * Lattice m π = 49 MeV Physical point B G M 1 Core contributions (EBAC model) m π =.138 GeV

74 γn : G M (Q2 ) (valence) GR and MT Peña PRD 8, 138 (29) G M */(3G D ) Data Core Bare Bare EBAC model Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

75 γn : G M (Q2 ) (valence + pion cloud [phenomenological]) GR and MT Peña PRD 8, 138 (29) G M */(3G D ) Data Core Bare Bare + Pion cloud Bare EBAC model G π M = λ π Λ 2 π Λ 2 π +Q2 2 (3GD) G B M () 3G D.7 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

76 γn : G E (Q2 ), G C (Q2 ) on lattice [PRD 8, 138 (29)] Fit to lattice QCD data (bare contribution) Alexandrou et al, PRD, 77, 8512 (28) G E * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Physical point G C * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Physical Point Q 2 ( GeV 2 ) D3 state:.72% D1 state:.72% Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

77 γn : G E (Q2 ), G C (Q2 ) (bare) [PRD 8, 138 (29)] G E * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Experimental data G C * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Experimental data Compare with Physical data Small valence quark contributions GR, MT Peña PRD 8, 138 (29) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

78 γn : G E (Q2 ), G C (Q2 ) (bare + pion cloud) G E * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Experimental data G C * (Q 2 ) Lattice m π = 563 MeV Lattice m π = 49 MeV Lattice m π = 411 MeV Experimental data Pion cloud [Large N c ; no additional parameters] Pion cloud dominant; Good global description (Q 2 < 1.5 GeV 2 ) callibration valence quark contribution (all Q 2 ) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

79 γn (16) [PRD 82, 737 (21)].5 (16) as the 1st radial excitation of (1232) EPJA, 36, 329 (28) [S-state] G E, G C G M * -.5 Bare Bare : G B M() = Effects of π cloud? Decay BR (16) πn.153±.19 (16) π.59±.1 (16) πn(144).13±.4 G M * Bare Bare + pion cloud Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

80 γn (16): pion cloud GR and K.Tsushima, PRD 82, 737 (21) B 1 B 2 B B B B B (a) (b) Dominance of diagram (a): leading order in χpt Pion cloud generalization of γn (1232) Including channels: πn, π, πn, π Assuming equal masses in the loops: G π M = (λ N π + λ N π λ B π f πb B + λ π + λ π ) ( ) Λ 2 2 π Λ 2 π + Q 2 (3G D ) determined by the Data (Γ and BR) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

81 γn (16) form factors [PRD 82, 737 (21)] G M * Bare Bare + π N Bare + π N + π N* Bare + π N + π N*+ π Bare + π N + π N*+ π + π * G M * Bare Bare + pion cloud Valence quark dominance for high Q 2 GR and K.Tsushima, PRD 82, 737 (21) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

82 γn (16) helicity amplitudes [PRD 82, 737 (21)] 1 2 A 1/2 (1-3 GeV -1/2 ) 5-5 Bare Bare + pion cloud A 3/2 (1-3 GeV -1/2 ) Bare Bare + pion cloud Valence quark dominance for high Q 2 GR and K.Tsushima, PRD 82, 737 (21) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

83 Conclusions Conclusions: Quark model (calibrated by Nucleon and γn data) Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

84 Conclusions Conclusions: Quark model (calibrated by Nucleon and γn data) Good description of N(939),N(144),N(1535) data [No extra parameters] Large Q 2 lattice data Valence quark degrees of freedom under control Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

85 Conclusions Conclusions: Quark model (calibrated by Nucleon and γn data) Good description of N(939),N(144),N(1535) data [No extra parameters] Large Q 2 lattice data Valence quark degrees of freedom under control Good description of (1232), (16) data Including pion cloud effects (important) Lattice data [ (1232)] Dominance of valence quark for Q 2 > 2 GeV 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

86 Conclusions Conclusions: Quark model (calibrated by Nucleon and γn data) Good description of N(939),N(144),N(1535) data [No extra parameters] Large Q 2 lattice data Valence quark degrees of freedom under control Good description of (1232), (16) data Including pion cloud effects (important) Lattice data [ (1232)] Dominance of valence quark for Q 2 > 2 GeV 2 Prespective of extension to other resonances P 11 (171), D 13 (152), S 11 (165),... Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

87 Nucleon Resonance Structure σ T (1232) P 33 γ p -> n π + N(144) P 11 N(152) D W (MeV) N(1535) S 11 (16) P 33 N(165) S 11 N(168) F 15 N(171) P 11 Q 2 = 1 GeV 2 Gilberto Ramalho (IST, Lisbon) Covariant quark-diquark model May 16, / 5

Valence quark contributions for the γn P 11 (1440) transition

Valence quark contributions for the γn P 11 (144) transition Gilberto Ramalho (Instituto Superior Técnico, Lisbon) In collaboration with Kazuo Tsushima 12th International Conference on Meson-Nucleon Physics