Chiral symmetry and ?(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 p0 em production
- ?(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)expi?(x)/Fp, - where ? represents the Nambu-Goldstone

fields. - 2.

The predictions of ChPT are given by expansions

in the Nambu-Goldstone masses and momentum.

- Threshold electromagnetic production

Photoproduction

- LET (Gauge Inv. PCAC) gives

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 pN 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

HBChPTa low energy effective field theory

respecting the symmetries of QCD, in

particular, chiral symmetry

perturbative calculation - crossing symmetric

DMTLippman-Schwinger type formulation with

potential constructed from chiral effective

lagrangian unitarity - loops to all

orders

What are the predictions of DMT?

Results for p0 photoproductionnear threshold,

tree approx.

10

Photon Beam Asymmetry near Threshold

Data A. Schmidt et al., PRL 87 (2001) _at_

MAMI DMT S. Kamalov et al., PLB 522 (2001)

11

D. Hornidge (CB_at_MAMI) private communication

PRELIMINARY

D. Hornidge (CB_at_MAMI) private communication

PRELIMINARY

D. Hornidge (CB_at_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.

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

16

?(1232) deformation

? 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 ? E2 transition

Experimentally, it is only possible to extract

the contribution of the following process,

dressed vertex

bare vertex

A1/2 (10-3GeV-1/2) A3/2 QN ? ? (fm2) ?N??

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-Lees prediction. The numbers within the

parenthesis in red correspond to the bare values.

Q N? ? ? Q? ? gt 0, ? is oblate !!!

For electroproduction

Q2-dependent

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N? Transition form factors

Quadrupole Ratios

Magnetic Dipole Form Factor

Pion cloud

REM

QM

RSM

0.2

- 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

26

2015?8?6?

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 ? and 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.

The end

- threshold p photo- 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 p-hadron scattering length
- ? pN interaction

Results of lowest chiral perturbation theory

K-matrix

Pion cloud effects

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different channels predicted by DMT

Tree 1-loop 2-loop Full ChPT Exp

pp -2.26 -1.06 (53.1) -1.01 (2.2) -1.00 -1.1 -1.330.11

p?n 27.72 28.62 (3.2) 28.82 (0.7) 28.85 28.20.6 28.30.3

DMT HBChPT

chiral symmetry yes yes

crossing symmetry no yes

unitarity yes no

counting chiral power

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

- 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 ? ? e.m. transition form

factors - More data at higher Q2 will be available from

Jlab upgrade - Other developments N ?? generalized parton

distributions - (GPDs), two-photon exchange effects, chiral

effective field theory - approach.
- extension of dynamical model to higher energies