Nucleon Transition Formfactors with MAID from Low to High Q²

1. Lothar Tiator Johannes Gutenberg Universität Mainz Nucleon Transition Formfactors with MAIDfrom Low to High Q² CRC 1044 Nucleon Resonance Structure in Exclusive Electroproduction at High Photon Virtualities EmNN*2012, University of South Carolina, Columbia, SC, 2012

2. 2 very recent review articles on this subject: Electromagnetic excitation of nucleon resonances LT, Dieter Drechsel, Sabit Kamalov and Marc Vanderhaeghen European Journal Special Topics 198, 141-170 (2011) Electroexcitation of nucleon resonances Inna Aznauryan and Volker Burkert Progress in Particle and Nuclear Physics 67, 1-54 (2012)

3. theoretical poles and experimental bumps poles in the complex plane W bumps on the physical axis W

4. N and D resonances with overall3and 4 stars below 2 GeV (new, PDG2012) <- new in PDG2012<- upgraded from **

5. 9 2 4 1 8 7 3 5 6 9 7 4 1 5 weak very strong weak 8 2 weak weak strong 3 6 no pole weak strong

6. nucleon response to real and virtual photons

7. Inclusive Cross Section for Real and Virtual Photo Absorption

8. Inelastic Electron Scattering in the Resonance Region

10. in general: • transition form factors can only be obtained by • partial wave analysis, e.g. MAID, JLabseparate S11, P11, P33, D13, F15, etc from angular distributions • and background / resonance separationseparate bg and res parts in each partial wave

11. Form Factors in the Electroproduction Process

12. Form Factors in MAID2007

13. MAID

14. s-channel resonance contributions e.g. for S11(1535) unitarity is build in through coupling to other open channels:

15. background - I

16. background - II

17. background - III background from unitarization (in K-matrix approximation): (Born + Vec)(1 + itpN) = Born+Vec + i BV tpN other background contributions, not included in MAID: • loop contributions from pion rescattering • loop contributions from channel coupling with hN, KL, KS, rN, ... • u-channel resonance contributions • t-channel Regge contributions (more important for high W than high Q²)

18. data base for pion electroproduction (from Mainz, Bonn, Bates and JLab, mostly from CLAS)

19. definition of the NN* transition form factors helicity amplitudes: Sachs form factors: covariant form factors: for spin ½ resonances as Roper P11 or S11 we get only 2 ff

20. helicity amplitudes and form factors

21. N to Delta (1232) transition form factors MAID analysis JLab analysis one of few cases with disagreement between Mainz and JLab analysis MAID Sato-Lee

22. N to Delta (1232) transition form factors MAID analysis JLab analysis MAID analysis revisited for narrow energy range ~ 1232 MeV one of few cases with disagreement between Mainz and JLab analysis MAID Sato-Lee

23. perturbative QCD

24. helicity asymmetry and pQCD limit P33 (hard) spin-flavor excitation, pQCD may show up at much larger Q²D13, F15 (soft) orbital excitation in the quark modelD15, P13 behave differently (A3/2dominates at Q²~ 3 GeV²)

25. empirical parametrizations the magnetic ND form factors has a very simple form Q²max 10 GeV² 5 GeV² 5 5 5 5 5 5 ? 4 ? 4 4 4 for all other resonances we use the general form: numerical examples for a few resonances: (complete results are found in our Review EPJ ST 198 (2011) 141)

26. empirical parametrizations for large Q² the Maid parametrization with Gaussian forms for large Q² is convenient and leads to fewer terms However, it violates pQCD, which predicts: A1/2(Q²) ~ 1/Q3 A3/2(Q²) ~ 1/Q5 S1/2(Q²) ~ 1/Q3 new ansatz:

27. transition FFs for N -> N*(1440)and N -> N*(1535) excitation from MAID and JLab analysis

28. transition FFs for N -> N*(1520)and N -> N*(1680) excitation data : practically all underlying cross sections that went into the fits are from CLAS analysis : MAID MAID JLab new JLabppMokeev et al.

29. spatial distribution of charge and magnetization spherical charge densities in a 3-dim sphere: r traditional way for nuclei A>>1 with ff in the Breit frame F(Q2) = GE(Q2), GM(Q2) : Sachs ff by transverse charge densities on a 2-dim disc: bx more correct way for light systems with ff in the infinite momentum frame F(Q2) = F1(Q2), F2(Q2) : Dirac/Pauli ff

30. transverse transition densitiesfor the Nucleon and N -> Roper excitation

31. transition form factors on the lattice N -> Delta N -> Roper Huey-Wen Lin et al., 2008 Constantia Alexandrou et al., 2008 N-Roper quenched with mp=720 MeV N-Delta unquenched with mp=360 MeV F1 GM F2 pion cloud problem at small Q²

32. lattice update 2011/12 preliminary result 2012 with large error N -> Roper N -> Delta Huey-Wen Lin et al., 2011 Constantia Alexandrou et al., 2011

33. Summary with the unitary isobar model we have analyzed p0 and p+electroproduction data in the range 0 < Q² < 5 GeV²(in the D(1232) range up to 8 GeV²) for most 4* resonances we have obtained single-Q² amplitudes A1/2, A3/2, S1/2and Q²-dependent transition form factors this kind of analysis should also work up to Q² = 10 GeV²at least for helicity l=1/2 : A1/2(Q²) and S1/2(Q²)A3/2ND(Q²) is perhaps the only l=3/2 transition form factorsurviving at Q² = 10 GeV²

35. transition FFs for N -> N*(1675)and N -> N*(1720) excitation