Marc Vanderhaeghen Johannes Gutenberg Universität, Mainz College of William & Mary

1. Overview of nucleon structure studies Marc Vanderhaeghen Johannes Gutenberg Universität, Mainz College of William & Mary Lattice 2008 Williamsburg, July 14-19, 2008

2. nucleon form factors (generalized) parton distributions spin, tomography nucleon resonances Δ(1232),…

3. Pun05 Gay02 proton e.m. form factor : status green : Rosenbluth data (SLAC, JLab) JLab/HallA recoil pol. data new JLab/HallC recoil pol. exp. (spring 2008) : extension up to Q2 ≈ 8.5 GeV2 new MAMI/A1 data up to Q2 ≈ 0.7 GeV2

4. neutron e.m. form factor : status MAMI JLab/HallC JLab/CLAS JLab/HallA new MIT-Bates (BLAST) data for both p and n at low Q2 new JLab/HallA double pol. exp. (spring 07) : extension up to Q2 ≈ 3.5 GeV2 completed

5. Two-photon exchange effects Rosenbluth vs polarization transfer measurements of GE/GM of proton SLAC, Jlab Rosenbluth data Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002) Two methods, two different results ! 2γ exchangeproposed as explanation Guichon, Vdh (2003)

6. Observables including two-photon exchange Real parts of two-photon amplitudes

7. Normal spin asymmetries in elastic eN scattering directly proportional to the imaginary part of 2-photon exchange amplitudes spin of beam OR target NORMAL to scattering plane OR on-shell intermediate state order of magnitude estimates : target : beam :

8. Beam normal spin asymmetry New MAMI A4 data at backward angles Ee = 0.300 GeV Θe = 145 deg Ee = 0.570 GeV Θe = 35 deg Ee = 0.855 GeV Θe = 35 deg data : MAMI A4 theory : Pasquini & Vdh (2004) also : SAMPLE, Happex, G0, E-158

9. Two-photon exchange calculations partonic calculation elastic contribution N GPDs Chen, Afanasev, Brodsky, Carlson, Vdh (2003) Blunden, Melnitchouk, Tjon (2003, 2005)

10. Real part of Y2γ ε-independence of GEp/GMp in recoil polarization cross section difference in e+ and e- proton scattering non-linearity of Rosenbluth plot Also imaginary part from induced out-of-plane polarization single-spin target asymmetry Hall C 04-019, completed Hall B 07-005; Olympus/Doris with refurbished BLAST detector Hall C 05-017; being analyzed by-product of 04-019/04-108? Hall A 05-015 (3He ) whether two-photon exchange is entirely responsible for the discrepancy in the FF extraction is to be determined experimentally

11. test ofε-dependence of Pt / Pl new JLab/Hall C data (2008) PRELIMINARY, not to be quoted 1γ result for Pt / Pl The preliminary data for Q2=2.5 GeV2 show no ε-dependence of GEp/GMp at the 0.01 level

12. nucleon FF : lattice prospects F1V state of art : connected diagrams -> OK for isovector quantities LHPColl. full QCD lattice calculations Pion masses down to less than 300 MeV √(r2)1V chiral extrapolation to physical mass Leinweber, Thomas, Young (2001) next step : inclusion of disconnected diagrams

13. LHPC results see talk : Meifeng Lin valence DWF on Asqtad staggered sea GEV new mπ = 293 MeV factor 4 reduction in error modest mπ dependence <r12>V

14. RBC results see talk : T. Yamazaki arXiv:0802.0863 [hep-lat] 2 degenerate dynamical flavors of DWF F1V mπ= 0.493 GeV mπ= 0.607 GeV mπ= 0.695 GeV Puzzle: no strong chiral behavior expected at Q2 ≈ 1 GeV2 , however more than factor 2 deviation with data ! see also talks : J. Zanotti, Ph. Haegler, T. Korzec, H.-W. Lin, … F2V

15. quark transverse charge densities in nucleon (I) q+ = q0 + q3 = 0 photon only couples to forward moving quarks quark charge density operator unpolarized nucleon

16. quark transverse charge densities in nucleon (II) transversely polarized nucleon transverse spin e.g. along x-axis : dipole field pattern

17. empirical quark transverse densities in proton ρ0 ρT induced EDM : dy= - F2p (0) . e / (2 MN) data : Arrington, Melnitchouk, Tjon (2007) densities : Miller (2007); Carlson, Vdh (2007)

18. empirical quark transverse densities in neutron ρT ρ0 induced EDM : dy= - F2n (0) . e / (2 MN) data : Bradford, Bodek, Budd, Arrington (2006) densities : Miller (2007); Carlson, Vdh (2007)

19. empirical transverse transition densities for N -> Δexcitation combination ofM1,E2,C2FFs data : MAID 2007 , Drechsel, Kamalov, Tiator (2007) densities : Carlson, Vdh (2007)

20. monopole dipole quadrupole

21. Generalized Parton Distributions : yield 3-dim quark structure of nucleon Burkardt (2000,2003) Belitsky,Ji,Yuan (2004) Elastic Scattering transverse quark distribution in coordinate space DIS longitudinal quark distribution in momentum space DES (GPDs) fully-correlated quark distribution in both coordinate and momentum space

22. * Q2 >> t = Δ2 x + ξ x - ξ P - Δ/2 P + Δ/2 GPD (x, ξ ,t) GPDs : ξ = 0 Fourier transform of GPDs : simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse positionb

23. y3 Handbag (bilocal) operator : new way to probe the nucleon Y- y0 y 0 generalized probe ( Y ≈ 0 ) ( W±, Z0 ) probe spin 2 (graviton) probe electroweak form factors energy-momentum form factors

24. Why GPDs are interesting Unique tool to explore the internal landscape of the nucleon : 3D quark/gluon imaging of nucleon Access to static properties : constrained (sum rules) by precision measurements of charge/magnetization orbital angular momentum carried by quarks

25. GPDs : transverse image of the nucleon (tomography) Hu(x, b? ) x Guidal, Polyakov, Radyushkin, Vdh (2005) b?(fm)

26. quark contribution to proton spin X. Ji (1997) with parametrizations for E q : GPD : based on MRST2002 μ2 = 2 GeV2 lattice : full QCD, no disconnected diagrams so far see talks on Fri : hadron structure

27. Bethe-Heitler DVCS on protonJLab/Hall A @ 6 GeV DVCS GPDs Difference of polarized cross sections Q2 ≈ 2 GeV2 xB = 0.36 Unpolarized cross sections also JLab/CLAS, HERMES, H1 / ZEUS

28. DVCS on neutron 0 because F1(t) is small 0 because of cancelation of u and d quarks n-DVCSgives access to the least known and constrained GPD,E JLab /Hall A (E03-106) : preliminary data

29. Sphere: Prolate: Q20=0 Q20/R2 > 0 Oblate: Q20/R2 < 0 electromagnetic N -> Δ(1232) transition J P=3/2+ (P33), M' 1232 MeV,  ' 115 MeV N ! transition:  N !  (99%),  N !  (<1%) non-zero values for E2 and C2 : measure of non-spherical distribution of charges spin 3/2 Role of quark core (quark spin flip) versus pion cloud

30. Q2 dependence of E2/M1 and C2/M1 ratios data points : M1 MIT-Bates (Sparveris et al., 2005) MAMI : Q2 = 0 (Beck et al., 2000) Q2 = 0.06 (Stave et al., 2006) Q2 = 0.2 (Elsner et al., 2005, Sparveris et al., 2006) E2/M1 EFT calculation predicts the Q2 dependence C2/M1 no pion loops pion loops included Pascalutsa, Vdh (2005) also Gail, Hemmert

31. mπ dependence of E2/M1 and C2/M1 ratios Q2 = 0.1 GeV2 quenched lattice QCD results : at mπ= 0.37, 0.45, 0.51 GeV linear extrapolation in mq ~ mπ2 Nicosia – MIT group :Alexandrou et al. (2005) EFT calculation discrepancy with lattice explained by chiral loops(pion cloud)! Pascalutsa, Vdh (2005) full QCD results available Alexandrou et al. data points : MAMI, MIT-Bates

32. Magnetic Dipole Moment of (1232)- resonance octet baryonMDMs : precession in external magnetic fied • J P = 3/2+, M = 1232 MeV,  = 115 MeV • N ->  transition:  N ->  (99%),  N ->  (<1%) decuplet baryonMDMs : only Ω-lives long enough (weak decay) to be measurable by precession method how about other – strongly decaying -decuplet baryons ?  p! (+!’ + )!0 p

33. Status of μΔ p! (+!’+ )!0 p forΔ+ : high precision exp. underway using Crystal Ball @ MAMI

34. Chiral behavior of the -resonance magnetic moment quenched lattice points : Leinweber (1992) Cloet,Leinweber,Thomas (2003) Lee et.al. (2004) – revised (2006) chiral calculations Real parts Pascalutsa, Vdh (2004) Imag. parts

35. full lattice QCD calculations : Ω- anisotropic clover dynamical lattices (JLab) background field method Periodic b.c. : magnetic flux continuous over boundary B = n . 2 π / L2 : Damgaard, Heller (1988) μΩ in physical nuclear magnetons NERSC mΩ= 1.65 GeV Kyklades @ WM EXP. -2.02 ± 0.05 C. Aubin JLab

36. full lattice QCD calculations : Δ anisotropic clover dynamical lattices : 243 x 128,aS = 0.1, at = 0.036 fm background field method (patched) mπ= 366 MeV μΔ in physical nuclear magnetons C. Aubin

37. Summary Nucleon form factors : -> high precision data at low Q2 : map out transverse quark densities in nucleon -> difference Rosenbluth vs polarization data GEp /GMp : mainly understood as due to two-photon exchange effects (new expt. planned) -> PV e-scattering : strangeness contributions to E and M distributions very small -> lattice QCD : state-of-art full QCD calculations go down to mπ~ 300 MeV, some puzzles GPDs : -> unifying theme in hadron physics (form factors, parton distributions) -> provide a tomographic image of nucleon -> access to angular momentum of quarks/gluons in nucleon -> encouraging experimental results coming out of HERMES, H1/ZEUS, JLab@6 GeV indicating twist-2 dominance -> future programs : COMPASS, dedictated JLab@12 GeV, EIC… Nucleon excitation spectrum : -> precision data on NΔform factors : shape of hadrons -> chiral EFT is used in dual role : describe both observables and use in lattice extrapolations strong non-analytic behavior in quark mass due to opening of πN decay channel (interplay of scales)