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, June, 2010

2  threshold π 0 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)/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 Threshold electromagnetic production Photoproduction LET (Gauge Inv. + PCAC) gives HBChPT (p 4 ) : -1.1 dispersion relation: What are the predictions of dynamical models?

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

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

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 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 π 0 photoproduction near threshold, tree approx.

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

12 PRELIMINA RY D. Hornidge private communication

13 PRELIMINA RY D. Hornidge private communication

14 PRELIMINA RY D. Hornidge private communication

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

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 Q 2 = 0, recent experiments give, R em = 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 full photoproduction 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 A 1/2 (10 -3 GeV -1/2 ) A 3/2 Q N →  (fm 2 ) N→ΔN→Δ PDG LEGS MAINZ DMT -134 (-80) -256 (-136) (0.009) (1.922) SL -121 (-90) -226 (-155) (0.001) (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 For electroproduction : Q 2 -dependent

25

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 年2月2日 2016年2月2日 2016年2月2日

27 Pascalutsa and Vanderhaeghen, PR D 73, (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 Δ and confirmed by the LQCD calculations.  it predicts  N →  =  N, Q N →  = 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 The end

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

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 Pion cloud effects K-matrix

34

35 different channels predicted by DMT Tree1-loop2-loopFullChPTExp π⁰pπ⁰p (53.1%) (2.2%) ±0.11 π⁺nπ⁺n (3.2%) (0.7%) ± ±0.3

36 DMTHBChPT chiral symmetryyes crossing symmetrynoyes unitarityyesno countingchiral power

37

38

39

40

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

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.