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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. threshold π 0 em production
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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
threshold π0 em production • Δ(1232)-excitation and its deformation
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)
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.
Photoproduction • LET (Gauge Inv. + PCAC) gives Threshold electromagnetic production HBChPT (p4) : -1.1 dispersion relation: -1.22 What are the predictions of dynamical models?
Dynamical model for * N → N Both on- & off-shell two ingredients v , t N
DMT Model(Dubna-Mainz-Taipei) Collaborators: S. S. Kamalov (Dubna) D. Drechsel, L. Tiator (Mainz) Guan Yeu Chen (Taipei)
: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
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?
Results for π0photoproductionnear threshold, treeapprox. 10
Photon Beam AsymmetrynearThreshold Data: A. Schmidt et al., PRL 87 (2001) @ MAMI DMT: S. Kamalov et al., PLB 522 (2001) 11
D. Hornidge (CB@MAMI) private communication PRELIMINARY
D. Hornidge (CB@MAMI) private communication PRELIMINARY
D. Hornidge (CB@MAMI) private communication PRELIMINARY
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.
* 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 )
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
bare excitation
photoproduction full almost no bare Δ E2 transition
Experimentally, it is only possible to extract the contribution of the following process, = + dressed vertex bare vertex
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 !!!
For electroproduction : Q2-dependent
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
Pascalutsa and Vanderhaeghen, PR D 73, 034003 (2006)
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.
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.
threshold πphoto- and electro-production ▪threshold charged pion photoproduction is well described by Kroll-Ruderman term
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
K-matrix Pion cloud effects
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 .