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

Transcription

1 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 and the Structure of the Nucleon June 1, 21 Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 1 / 22

2 1 Motivation 2 Covariant spectator quark model Quark current Baryon wave functions Electromagnetic transition current 3 Results: γn P 11 (144) transition form factors Form factors physical point Form factors lattice γn Roper form factors Meson cloud γn Roper Helicity amplitudes 4 Conclusions Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 2 / 22

3 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

4 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

5 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Theory- Quark model: angular momentum (1/2) parity (+) first radial excitation of the nucleon large mass (bare mass) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

6 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Theory- Quark model: angular momentum (1/2) parity (+) first radial excitation of the nucleon large mass (bare mass) Experimentally- large width ( 3 MeV) Decay: πn, ππn molecular like state (ππn = π, σn...) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

7 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Theory- Quark model: angular momentum (1/2) parity (+) first radial excitation of the nucleon large mass (bare mass) Experimentally- large width ( 3 MeV) Decay: πn, ππn molecular like state (ππn = π, σn...) Goal: study of the valence quark content in the Roper system (Valence quarks dominates at large Q 2 ) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

8 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Theory- Quark model: angular momentum (1/2) parity (+) first radial excitation of the nucleon large mass (bare mass) Experimentally- large width ( 3 MeV) Decay: πn, ππn molecular like state (ππn = π, σn...) Goal: study of the valence quark content in the Roper system (Valence quarks dominates at large Q 2 ) Framework: covariant quark model (Spectator c ) -Franz Gross Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

9 Motivation and goals Understand of the electromagnetic structure of the resonance P 11 (144) Roper N Interpret the available information from γn N transition Why? Mysterious resonance Theory- Quark model: angular momentum (1/2) parity (+) first radial excitation of the nucleon large mass (bare mass) Experimentally- large width ( 3 MeV) Decay: πn, ππn molecular like state (ππn = π, σn...) Goal: study of the valence quark content in the Roper system (Valence quarks dominates at large Q 2 ) Framework: covariant quark model (Spectator c ) -Franz Gross compare with CLAS data & MAID analysis estimate meson cloud contribution Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 3 / 22

10 Spectator quark model quark current Constituent quarks (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 quark-antiquark gluon dressing Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 4 / 22

11 Spectator quark model quark current Constituent quarks (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 Vector meson dominance parameterization: quark-antiquark gluon dressing m 2 v M 2 h Q2 f 1± = λ q + (1 λ q ) m 2 v + Q 2 + c ± (Mh 2 + Q2 ) 2 { m 2 v f 2± = κ ± d ± m 2 v + Q 2 + (1 d M 2 } h ±) Mh 2 + Q2 2 poles: m v = m ρ and M h = 2M N ; κ ± nucleon mag. mom. 5 parameters to be determined: λ q, mixture coefficients c ± and d ± with d + = d [4 parameters] Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 4 / 22

12 Results: Nucleon form factors (I) 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) Val. Q contributions for γn Roper MENU 21; June 4, 21 5 / 22

13 Results: Nucleon form factors (II) F Gross, GR and MT Peña, PRC 77, 1522 (28) model II G Ep /G Mp /µ p 1.5 G En Quark current fixed [4 parameters] No pion cloud (explicit)... but VMD Adjust 2 parameters in the nucleon wave function Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 6 / 22

14 Spectator quark model Wave functions Wave functions: B = quark diquark p 1 Ψ B = (flavor) (spin) (orbital) (radial) ε P Nucleon wave function: [PRC 77,1522 (28)] Simplest structure S-state in quark-diquark Ψ N (P, k) = 1 [ Φ I Φ S + Φ 1 IΦ 1 S] ψn (P, k) 2 k Ψ P Roper wave function: Ψ R (P, k) = 1 2 [ Φ I Φ S + Φ 1 IΦ 1 S] ψr (P, k) ψ R first radial excitation of ψ N Φ,1 I isospin; Φ,1 S spin combination of quark states written in terms of baryon properties Covariant Ψ B : ( P M N )Ψ N =, ( P M R )Ψ R = Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 7 / 22

15 Spectator quark model Nucleon and Roper wf Scalar wave functions deppendent of P (baryon) and k (diquark) χ B = (M B m D ) 2 (P k) 2 M B m D, M B = baryon mass; m D = diquark mass Momentum range parameters β 1 (long) and β 2 (short) 1 ψ N (P, k) = N m D (β 1 + χ N )(β 2 + χ N ) β 3 χ R 1 ψ R (P, k) = N R (β 1 + χ R ) m D (β 1 + χ R )(β 2 + χ R ) Harmonic oscilator potential- 1st order in χ R Nucleon orthogonal to Roper: ψ R (P +, k)ψ N (P, k) fix β = 3 k Q [no parameters] 2 = Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 8 / 22

16 Spectator quark model Electromagnetic transition current Quark current j µ I Baryon wave function Ψ B J µ Spectator formalism: relativistic inpulse approximation J µ = 3 Ψ f (P +, k)j µ I Ψ i(p, k) λ k P + Franz Gross: PR186, 1448 (1969); F Gross er al PRC 45, 294 (1992) N Ψ f k Ψ i diquark on-shell P N J µ = ū R (P + ) ) } {(γ µ qqµ q 2 F1 (Q 2 ) + iσµν q ν M R + M F 2 (Q 2 ) u(p ) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 9 / 22

17 γn Roper form factors [PRD 81, 742 (21)] F1 (Q 2 ) = 3 2 j 1I + 1 3(M R + M) 2 Q 2 2 (M R + M) 2 + Q 2 j 3I M R + M Q 2 M (M R + M) 2 + Q 2j 4I, F2 (Q 2 ) = 3 M R + M 4 M j 2I (M R + M) 2 (M R + M) 2 + Q 2j 3I + M R + M 2M (M R + M) 2 3Q 2 (M R + M) 2 + Q 2 j 4I, Isospin coefficients GR, MTP, and FG, PRC 77, 1522 (28) j 1 = 1 6 f f 1 τ 3, j 3 = 1 6 f f 1 τ 3 j 2 = 1 6 f f 2 τ 3, j 4 = 1 6 f f 2 τ 3 Overlap integral: I(Q 2 ) = k ψ R (P +, k)ψ N (P, k), Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 1 / 22

18 γn Roper form factors- results.2.15 CLAS data.2 F 1.1 F CLAS data CLAS data - Aznauryan et al PRC 8, 5523 (29) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

19 γn Roper form factors- results.2.15 CLAS data.2 F 1.1 F CLAS data CLAS data - Aznauryan et al PRC 8, 5523 (29) Discrepance for Q 2 < 1.5 GeV 2 Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

20 γn Roper form factors- results.2.15 CLAS data.2 F 1.1 F CLAS data CLAS data - Aznauryan et al PRC 8, 5523 (29) Discrepance for Q 2 < 1.5 GeV 2 Good description for Q 2 > 1.5 GeV 2 Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

21 γn Roper form factors- results.2.15 CLAS data.2 F 1.1 F CLAS data CLAS data - Aznauryan et al PRC 8, 5523 (29) Discrepance for Q 2 < 1.5 GeV 2 Good description for Q 2 > 1.5 GeV 2 M R = 144 MeV, Effect of the Roper mass? Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

22 γn Roper form factors- bare mass Model with meson cloud dressing (EBAC) Suzuki et al; PRL 14, 4232 (21) Bare mass: M R 175 MeV πn,ππ N π ηn -1 A(1357,-76) ρn Im (E) (MeV) -2 B(1364,-15) C(182,-248) -3 σn Re (E) (MeV) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

23 γn Roper form factors- bare mass.2.15 CLAS data Spectator (M=1.75 GeV).2 CLAS data Spectator (M=1.75 GeV) F F Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

24 Form factors in lattice, [HW Lin et al PRD, (28)] Lattice Spectator (lattice regime) F 1.2 Lattice Spectator (lattice regime) F Extension for lattice Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

25 Form factors in lattice, [HW Lin et al PRD, (28)] Lattice Spectator (lattice regime) F 1.2 Lattice Spectator (lattice regime) F Extension for lattice Description of lattice data (Q 2 < 1 GeV 2 ) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

26 Form factors in lattice, [HW Lin et al PRD, (28)] Lattice Spectator (lattice regime) F 1.2 Lattice Spectator (lattice regime) F Extension for lattice Description of lattice data (Q 2 < 1 GeV 2 ) Good description of physical high Q 2 data Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

27 Form factors in lattice, [HW Lin et al PRD, (28)] Lattice Spectator (lattice regime) F 1.2 Lattice Spectator (lattice regime) F Extension for lattice Description of lattice data (Q 2 < 1 GeV 2 ) Good description of physical high Q 2 data valence quark contributions under control Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

28 Form factors in lattice, [HW Lin et al PRD, (28)] Lattice Spectator (lattice regime) F 1.2 Lattice Spectator (lattice regime) F Extension for lattice Description of lattice data (Q 2 < 1 GeV 2 ) Good description of physical high Q 2 data valence quark contributions under control estimate meson cloud at low Q 2 Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

29 γn Roper form factors- results MAID.2.15 CLAS data MAID.2 F F CLAS data MAID Spectator QM: valence contributions F val i Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

30 γn Roper form factors- results MAID.2.15 CLAS data MAID.2 F F CLAS data MAID Spectator QM: valence contributions F val i Compare with MAID fit F i - Tiator et al PLB 672, 344 (29) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

31 γn Roper form factors- results MAID.2.15 CLAS data MAID.2 F F CLAS data MAID Spectator QM: valence contributions Fi val Compare with MAID fit Fi - Tiator et al PLB 672, 344 (29) Meson cloud: F mc i = Fi Fi val Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

32 γn Roper Meson cloud contributions- MAID fit F Spectator QM (valence) MAID Meson cloud (MAID) F Spectator QM (valence) MAID Meson cloud (MAID) Fi mc (Q 2 ) = Fi (Q 2 ) Fi val (Q 2 ) F1 F1 MAID Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

33 γn Roper Meson cloud contributions- CLAS F Spectator QM (valence) MAID Meson cloud (MAID) Meson cloud (CLAS data) F Spectator QM (valence) MAID Meson cloud (MAID) Meson cloud (CLAS data) Fi mc (Q 2 ) = Fi (Q 2 ) Fi val (Q 2 ) F1 F1 CLAS Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

34 γn Roper Helicity amplitudes A 1/2 (Q 2 ) CLAS data MAID S 1/2 (Q 2 ) CLAS data MAID Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

35 γn Roper Helicity amplitudes -meson cloud 6 A 1/2 (Q 2 ) 5 S 1/2 (Q 2 ) 4 2 MAID CLAS meson cloud -5 MAID CLAS meson cloud A mc i (Q 2 ) = A i (Q 2 ) A val i (Q 2 ) Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

36 γn Roper: Conclusions γn Roper Good description of high Q 2 data and lattice data [ parameters] Valence quark degrees of freedom under control estimate meson cloud contributions Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 2 / 22

37 γn Roper: Conclusions γn Roper Good description of high Q 2 data and lattice data [ parameters] Valence quark degrees of freedom under control estimate meson cloud contributions Method can be applied to higher resonances Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 2 / 22

38 γn Roper: Conclusions γn Roper Good description of high Q 2 data and lattice data [ parameters] Valence quark degrees of freedom under control estimate meson cloud contributions Method can be applied to higher resonances Other applications: Nucleon form factors PRC 77, 1522 (28) γn transition: PRD 78, (28); PRD 8, 138 (29) Ω form factors PRD8, 334 (29) form factors arxiv: [hep-ph], PLB 678, 355 (29) Octet magnetic moments (w/ pion cloud) arxiv: [hep-ph] Form factors in lattice JPG36, (29) Thank you Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, 21 2 / 22

39 Bibliography (part 1) A pure S-wave covariant model for the nucleon, F. Gross, G. Ramalho and M. T. Peña, Phys. Rev. C 77, 1522 (28). Fixed-axis polarization states: covariance and comparisons, F. Gross, G. Ramalho and M. T. Peña, Phys. Rev. C 77, 3523 (28). A Covariant model for the nucleon and the, G. Ramalho, M. T. Peña and F. Gross, Eur. Phys. J. A 36, 329 (28). D-state effects in the electromagnetic N transition, G. Ramalho, M. T. Peña and F. Gross, Phys. Rev. D 78, (28). Nucleon and γn lattice form factors in a constituent quark model, G. Ramalho and M. T. Peña, J. Phys. G 36, (29). Valence quark contribution for the γn quadrupole transition extracted from lattice QCD, G. Ramalho and M. T. Peña, Phys. Rev. D 8, 138 (29). Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22

40 Bibliography (part 2) Electromagnetic form factors of the Delta in a S-wave approach, G. Ramalho and M. T. Peña, J. Phys. G 36, 854 (29). A relativistic quark model for the Ω electromagnetic form factors, G. Ramalho, K. Tsushima and F. Gross, Phys. Rev. D 8, 334 (29). Using baryon octet magnetic moments and masses to fix the pion cloud contribution, to appear in PLB, F. Gross, G. Ramalho and K. Tsushima, arxiv: [hep-ph]. Electric quadrupole and magnetic octupole moments of the, G. Ramalho, M. T. Peña and F. Gross, Phys. Lett. B 678, 355 (29). Electromagnetic form factors of the in a D-wave approach, G. Ramalho, M. T. Peña and Franz Gross, arxiv: [hep-ph] Valence quark contributions for the γn P 11 (144) form factors, G. Ramalho and K. Tsushima, Phys. Rev. D 81, 742 (21). Gilberto Ramalho (IST, Lisbon) Val. Q contributions for γn Roper MENU 21; June 4, / 22