1. Chiral symmetry and Δ(1232) deformation in pion electromagnetic production Shin Nan Yang Department of Physics National Taiwan University “11th International Workshop on Meson Production, Properties and Interaction”, KRAKÓW, POLAND, 10 - 15 June, 2010

2. 2  threshold π 0 em production  Δ(1232)-excitation and its deformation

3. 3 Consequence of exact chiral symmtry: parity doubling of all hadronic states (Wigner-Weyl mode) ? spontaneously broken (Nambu-Goldstone mode) → massless pseudoscalar (0 - ) boson (Goldstone theorem)

4. 4 Chiral perturbation theory (ChPT) An effetctive field theory which utilizes the concepts of spontaneously broken chiral symmetry to replace 1. quark and gluon fields by a set of fields U(x) describing the d.o.f. of the observed hadrons. For the Nambu-Goldstone boson sector, U(x)=exp[iψ(x)/F π ], where ψ represents the Nambu-Goldstone fields. 2. The predictions of ChPT are given by expansions in the Nambu-Goldstone masses and momentum.

5. 5 Threshold electromagnetic production Photoproduction LET (Gauge Inv. + PCAC) gives HBChPT (p 4 ) : -1.1 dispersion relation: -1.22 What are the predictions of dynamical models?

6. 6 Both on- & off-shell v , t  N two ingredients Dynamical model for  * N →  N

7. 7 DMT Model (Dubna-Mainz-Taipei) Collaborators: S. S. Kamalov (Dubna) D. Drechsel, L. Tiator (Mainz) Guan Yeu Chen (Taipei)

8. 8  Three-dimensional Bethe-Salpeter formulation obtained with Cooper-Jennings reduction scheme, and with the following driving terms, in pseudovector  NN coupling, given by chiral couplin g :Taipei-Argonne meson-exchange πN model

9. 9 HBChPT ： a low energy effective field theory respecting the symmetries of QCD, in particular, chiral symmetry perturbative calculation － crossing symmetric DMT ： Lippman-Schwinger type formulation with potential constructed from chiral effective lagrangian unitarity － loops to all orders What are the predictions of DMT?

10. 10 Results for π 0 photoproduction near threshold, tree approx.

11. 11 Photon Beam Asymmetry near Threshold Data: A. Schmidt et al., PRL 87 (2001) @ MAMI DMT: S. Kamalov et al., PLB 522 (2001)

12. 12 PRELIMINA RY D. Hornidge (CB@MAMI) private communication

13. 13 PRELIMINA RY D. Hornidge (CB@MAMI) private communication

14. 14 PRELIMINA RY D. Hornidge (CB@MAMI) private communication

15. 15 How about electroproduction? HBChPT calculations have only been performed up to O(p 3 ) by V. Bernard, N. Kaiser, and u.-G. Meissner, Nucl. Phys. A 607, 379 (1996), 695 (1998) E.

16. 16 M. Weis et al., Eur. Phys. J. A 38 (2008) 27

17. 17 Δ(1232) deformation

18. 18  * N →  transition In a symmetric SU(6) quark model the electromagnetic excitation of the  could proceed only via M1 transition. If the  is deformed, then the photon can excite a nucleon into a  through electric E2 and Coulomb C2 quadrupole transitions. At Q 2 = 0, recent experiments give, R em = E2/M1  -2.5 %, (MAMI & LEGS) ( indication of a deformed  )

19. 19 In DMT, in a resonant channel like (3,3), resonance  excitation plays an important role. If a bare  is assumed such that the transition potential v  consists of two terms where = background transition potential

20. 20 bare excitation

21. 21 full photoproduction almost no bare Δ E2 transition

22. 22 Experimentally, it is only possible to extract the contribution of the following process, =+ dressed vertex bare vertex

23. 23 A 1/2 (10 -3 GeV -1/2 ) A 3/2 Q N →  (fm 2 ) N→ΔN→Δ PDG-135-255-0.0723.512 LEGS-135-267-0.1083.642 MAINZ-131-251-0.08463.46 DMT -134 (-80) -256 (-136) -0.081 (0.009) 3.516 (1.922) SL -121 (-90) -226 (-155) -0.051 (0.001) 3.132 (2.188) Comparison of our predictions for the helicity amplitudes, Q N →  and  N →  with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values. Q N→  =  Q   > 0,  is oblate !!!

24. 24 For electroproduction : Q 2 -dependent

25. 25

26. 26 NΔ Transition form factors Quadrupole RatiosMagnetic Dipole Form Factor  No sign for onset of asymptotic behavior, R EM →+100%, R SM → const.  R EM remains negative and small, R SM increases in magnitude with Q 2.  Large meson-baryon contributions needed to describe multipole amplitudes R EM R SM CLAS Hall A Hall C MAMI CLAS Hall A Hall C MAMI QM Pion cloud 0.2 Pascalutsa, Vanderhaeghen Sato, Lee 26 2016年2月2日 2016年2月2日 2016年2月2日

27. 27 Pascalutsa and Vanderhaeghen, PR D 73, 034003 (2006)

28. 28 Summary  DMT dynamical model, which starts from a chiral invariant Lagrangian, describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy.  Predictions of DMT near threshold are in excellent agreement with the most recent data from MAMI while existing HBChPT have problems.

29. 29 Summary  Existing data give clear indication of a deformed Δ and confirmed by the LQCD calculations.  it predicts  N →  = 3.516  N, Q N →  = -0.081 fm 2, and R EM = -2.4%, all in close agreement with experiments.   is oblate  bare  is almost spherical. The oblate deformation of the  arises almost exclusively from the pion cloud.

30. 30 The end

31. 31 ▪ threshold charged pion photoproduction is well described by Kroll-Ruderman term threshold π photo- and electro-production

32. 32 Weinberg: (1966) interaction between Goldstone boson and other hadrons ~ q at low energies, where q is the relative momentum between boson and target, e.g., ♠ s-wave π-hadron scattering length ♠ πN interaction Results of lowest chiral perturbation theory

33. 33 Pion cloud effects K-matrix

34. 34

35. 35 different channels predicted by DMT Tree1-loop2-loopFullChPTExp π⁰pπ⁰p -2.26 -1.06 (53.1%) -1.01 (2.2%) -1.1-1.33±0.11 π⁺nπ⁺n 27.72 28.62 (3.2%) 28.82 (0.7%) 28.8528.2±0.628.3±0.3

36. 36 DMTHBChPT chiral symmetryyes crossing symmetrynoyes unitarityyesno countingchiral power

37. 37

38. 38

39. 39

40. 40

41. 41 Alexandrou et al., PR D 94, 021601 (2005)

42. 42  E xisting data between Q 2 = 0-6 (GeV/c) 2 indicate hadronic helicity conservation and scaling are still not yet observed in this region of Q 2. R EM still remains negative. | R SM | strongly increases with Q 2.  Impressive progress have been made in the lattice QCD calculation for N → Δ e.m. transition form factors  More data at higher Q 2 will be available from Jlab upgrade  Other developments: N →Δ generalized parton distributions (GPDs), two-photon exchange effects, chiral effective field theory approach.  extension of dynamical model to higher energies.