1. National Taiwan University
Meson-exchange Model vs ChPT in Threshold Neutral Pion Photo- and Electro-production
Shin Nan Yang
National Taiwan University
Collaborators:
Dubna: Kamalov
Mainz: Drechsel, Tiator
Taipei: GY Chen, CT Hung,
CC Lee, SNY
Workshop of Recent Developments in QCD and Quantum Field Theories, November , National Taiwan University, Taiwan

2. Outline Introduction – historical perspective DMT πN model
DMT model for electromagnetic production
of pion
Results for threshold production
Summary

3. Introduction - Historical Perspectives
In 1980’s, two problems in nuclear/hadron physics
received considerable attention
How to unitarize the pion photo- and electro-production
amplitude ?
In 1985, Tanabe and Okaand independently myself proposed to unitarize
the amplitude by including the FSI dynamically
(now dubbed as “dynamical approach”).
FSI very important in (33) channel. This is now called the pion cloud effect.

4. Experiments on threshold photoproduction:
in strong disagreement with “LET” prediction of
We demonstrated first with a separable form (Yang 1989) and later a
meson-exchange model (Lee, Lee, and Yang 1991) ) for interaction,
FSI gives large correction to , and with MEM model, we
could explain the Mainz data.
efforts to construct an realistic and comprehensive model,
Taipei-Argonne model, finished in 2001.
In the meantime, many ChPT calculations (notably Meissner’s group)
and experiments, including electroproduction, were performed.
ChPT can describe the new data of both photo- and electroproduction
reasonably well.

5. Dynamical approach for with Taipei-Argonne interaction Dubna-Mainz-Taipei (DMT) model
A meson-exchange model which provides unified description for both reactions of πN scattering and e.m. production of pion over a wide range of energies, i.e., from threshold to ~ 2 GeV.
Excellent description of the photo- and electroproduction of neutral pion in the threshold region, better than existing ChPT calculations in quite a few cases.
this talk

6. Taipei-Argonne πN model: meson-exchange  N model below 400 MeV

7. Three-dimensional reduction
Cooper-Jennings reduction scheme
It satisfies both
the soft pion theorems and unitarity
Cooper, Jennings, NP A483, 601 (1988).

8. tree approximation of a chiral effective Lagrangian
Approximate by
tree approximation of a chiral effective Lagrangian

9. C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, 034309 (2001)
13 parameters
(4 in ∆ channel)
C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, (2001)

10. Dynamical model for  N →  N
To order e, the t-matrix for
 N →  N is written as
two ingredients
Both on- & off-shell (gauge invariance?)

11. k=| k|, qE : photon and pion on-shell momentum
Multipole decomposition of gives the physical amplitude in channel =( , l , j),
where
(), RπN() :  N scattering phase shift and reaction matrix in channel 
k=| k|, qE : photon and pion on-shell momentum
Fermi-Watson theorem
Both on- & off-shell (gauge invariance?) q k

12. DMT Model obtained from tree diagrams of a chiral effective Lagrangian

13. Chiral perturbation theory
QCD Lagrangian exhibits chiral symmetry with massless quarks.
Spontaneous symmetry breaking leads to massless Goldstone bosons whose interactions with other hadrons vanish at zero momentum.
Nonvanishing quark mass breaks chiral symmetry explicitly.
Weinberg proposed effective field theory to calculate the corrections to chiral limit.
→ chiral perturbation theory (ChPT)
LEC’s at O(q4): 12, 16 for π0 photo- and electro-production.
Hilt et al. PR C88 (2013)055207

14. DMT
ChPT
chiral symmetry
yes
crossing symmetry no
unitarity (Fermi-Watson theorem) ?
counting
loop(g N)
chiral power

15. Results of DMT model near threshold (depends only on )
Photorpoduction:

17. Σ : Eγ = 145 – 190 MeV
S. Schumann et al., A2 and CB-TAPS MAMI Hornidge et al., PRL 111, (2013)
data: Hornidge et al., PRL 111, (2013)
: DMT
: Gasparyan and Lutz [NPA 848, (2010)]
: RChPT (Hilt, Scherer & Tiator)

18. S. Schumann et al., A2 Collab. @ MAMI, PL B750 (2015) 252.
σT : Eγ = 145 – 190 MeV
S. Schumann et al., A2 MAMI, PL B750 (2015) 252.
: DMT, , fits

19. : DMT
: Gasparyan – Lutz
: RChPT
: fit of Hornidge et al.

20. : DMT
: Gasparyan – Lutz
: RChPT
: fit of Hornidge et al.

21. Electroproduction

22. ε: transverse pol. of γ *
data: M. Weis et al., Eur. Phys. J. A 38 (2008) 27
: DMT
: HBChPT [Bernard et al., PLB 383, 116 (1996)]
: RChPT (Hilt, Scherer & Tiator, 2013)

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

24. Chirapatpimol et al., PRL 114, 192503 (2015) , Hall A Collab.
p(e,e’p)π0 with Ee = 1192 MeV

27. Summary DMT model provides excellent description of
the 0 threshold production data (excellent
description of ∆ channel as well).
Two-loop contributions small.
DMT has become a benchmark/guide for
experiments and calculations for 0 threshold
production.
Outlook:
0 threshold production from deuteron
and heavier nuclei?

28. END