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

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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
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• threshold p0 em production
• ?(1232)-excitation and its
• deformation

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• 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)

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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.
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• Threshold electromagnetic production

Photoproduction

• LET (Gauge Inv. PCAC) gives

HBChPT (p4) -1.1 dispersion relation -1.22
What are the predictions of dynamical models?
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Dynamical model for ? N ? ? N
Both on- off-shell
two ingredients
v?? , t? N
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DMT Model (Dubna-Mainz-Taipei)
Collaborators S. S. Kamalov (Dubna)
D. Drechsel, L. Tiator (Mainz)
Guan Yeu Chen (Taipei)
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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
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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?
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Results for p0 photoproductionnear threshold,
tree approx.
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Photon Beam Asymmetry near Threshold
Data A. Schmidt et al., PRL 87 (2001) _at_
MAMI DMT S. Kamalov et al., PLB 522 (2001)
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D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
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D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
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D. Hornidge (CB_at_MAMI) private communication
PRELIMINARY
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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.
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M. Weis et al., Eur. Phys. J. A 38 (2008) 27
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?(1232) deformation
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? 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 ? )

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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

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bare excitation
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photoproduction
full
almost no bare ? E2 transition
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Experimentally, it is only possible to extract
the contribution of the following process,


dressed vertex
bare vertex
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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 !!!
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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

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2021?6?11?
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Pascalutsa and Vanderhaeghen, PR D 73, 034003
(2006)
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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.

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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.

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The end
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• threshold p photo- and
• electro-production

• ? threshold charged pion photoproduction is well
  
• described by Kroll-Ruderman term

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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
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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
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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)
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• 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