Chiral symmetry and 1232 deformation in pion electromagnetic

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

Ø threshold π0 em production Ø Δ(1232)-excitation and its deformation 2

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

Chiral perturbation theory (Ch. PT) • 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 Ch. PT are given by expansions in the Nambu-Goldstone masses and momentum. 4

Threshold electromagnetic production Photoproduction • LET (Gauge Inv. + PCAC) gives HBCh. PT (p 4) : -1. 1 dispersion relation: -1. 22 What are the predictions of dynamical models? 5

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

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

: 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 8

HBCh. PT：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? 9

Results for π0 photoproduction near threshold, tree approx. 10

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

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

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

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

How about electroproduction? HBCh. PT 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. 15

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

Δ(1232) deformation 17

* N → transition l In a symmetric SU(6) quark model the electromagnetic excitation of the could proceed only via M 1 transition. l If the is deformed, then the photon can excite a nucleon into a through electric E 2 and Coulomb C 2 quadrupole transitions. l At Q 2 = 0, recent experiments give, Rem = E 2/M 1 -2. 5 %, (MAMI & LEGS) ( indication of a deformed ) 18

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 19

bare excitation 20

photoproduction full almost no bare Δ E 2 transition 21

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

A 1/2 (10 -3 Ge. V-1/2) A 3/2 QN → (fm 2) N→Δ PDG -135 -255 -0. 072 3. 512 LEGS -135 -267 -0. 108 3. 642 MAINZ -131 -251 -0. 0846 3. 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, 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 !!! 23

For electroproduction : Q 2 -dependent 24

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NΔ Transition form factors Magnetic Dipole Form Factor Pion cloud Quadrupole Ratios CLAS Hall A Hall C MAMI REM QM Pascalutsa, Vanderhaeghen Sato, Lee CLAS Hall A Hall C MAMI RSM 0. 2 No sign for onset of asymptotic behavior, REM→+100%, RSM→ const. REM remains negative and small, RSM increases in magnitude with Q 2. Large meson-baryon contributions needed to describe multipole amplitudes 26 Saturday, October 3, 2020 26

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

Summary Ø 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 Ge. V photon lab. energy. Ø Predictions of DMT near threshold are in excellent agreement with the most recent data from MAMI while existing HBCh. PT have problems. 28

Summary Ø Existing data give clear indication of a deformed Δ and confirmed by the LQCD calculations. it predicts N → = 3. 516 N , QN → = -0. 081 fm 2, 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. 29

The end 30

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

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 32

K-matrix Pion cloud effects 33

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different channels predicted by DMT Tree 1 -loop 2 -loop Full Ch. PT Exp π⁰p -2. 26 -1. 06 (53. 1%) -1. 01 (2. 2%) -1. 00 -1. 1 -1. 33± 0. 11 π⁺n 27. 72 28. 62 (3. 2%) 28. 82 (0. 7%) 28. 85 28. 2± 0. 6 28. 3± 0. 3 35

DMT HBCh. PT chiral symmetry yes crossing symmetry no yes unitarity yes no counting chiral power 36

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

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