Chiral symmetry and Δ(1232) deformation in pion electromagnetic production

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. threshold π0 em production • Δ(1232)-excitation and its deformation

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. 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)/Fπ], where ψ represents the Nambu-Goldstone fields. 2. The predictions of ChPT are given by expansions in the Nambu-Goldstone masses and momentum.

5. Photoproduction • LET (Gauge Inv. + PCAC) gives Threshold electromagnetic production HBChPT (p4) : -1.1 dispersion relation: -1.22 What are the predictions of dynamical models?

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

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

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

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. Results for π0photoproductionnear threshold, treeapprox. 10

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

12. D. Hornidge (CB@MAMI) private communication PRELIMINARY

13. D. Hornidge (CB@MAMI) private communication PRELIMINARY

14. D. Hornidge (CB@MAMI) private communication PRELIMINARY

15. How about electroproduction? HBChPT calculations have only been performed up to O(p3) by V. Bernard, N. Kaiser, and u.-G. Meissner, Nucl. Phys. A 607, 379 (1996), 695 (1998) E.

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

17. Δ(1232) deformation

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 Q2 = 0, recent experiments give, Rem = E2/M1  -2.5 %, (MAMI & LEGS) ( indication of a deformed  )

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. bare excitation

21. photoproduction full almost no bare Δ E2 transition

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

23. Comparison of our predictions for the helicity amplitudes, QN → 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. For electroproduction : Q2-dependent

26. NΔ Transition form factors Magnetic Dipole Form Factor Quadrupole Ratios CLAS Hall A Hall C MAMI CLAS Hall A Hall C MAMI Pion cloud REM QM RSM 0.2 Pascalutsa, Vanderhaeghen • No sign for onset of asymptotic behavior, REM→+100%, RSM→ const. • REM remains negative and small, RSM increases in magnitude with Q2. • Large meson-baryon contributions needed to describe multipole amplitudes Sato, Lee 2014年9月18日 26

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

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. Summary • Existing data give clear indication of a deformed Δand confirmed by the LQCD calculations. it predicts N → = 3.516 N , QN → = -0.081 fm2, and REM = -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. The end

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

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. K-matrix Pion cloud effects

35. different channels predicted by DMT

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

42. Existing data between Q2 = 0-6 (GeV/c)2 indicate • hadronic helicity conservation and scaling are still not yet observed in this region of Q2 . • REM still remains negative. • | RSM | strongly increases with Q2. • Impressive progress have been made in the lattice QCD calculation for N → Δ e.m. transition form factors • More data at higher Q2will be available from Jlab upgrade • Other developments: N →Δ generalized parton distributions (GPDs),two-photon exchange effects,chiraleffective field theory approach. • extension of dynamical model to higher energies .