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 9 - 11, 2017 National Taiwan University, Taiwan

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

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.

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.

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

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

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

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

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, 034309 (2001)

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?)

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

DMT Model obtained from tree diagrams of a chiral effective Lagrangian

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

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

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

Σ : Eγ = 145 – 190 MeV S. Schumann et al., A2 and CB-TAPS Collab. @ MAMI Hornidge et al., PRL 111, (2013) 062004 data: Hornidge et al., PRL 111, (2013) 062004 : DMT : Gasparyan and Lutz [NPA 848, (2010)] : RChPT (Hilt, Scherer & Tiator)

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

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

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

Electroproduction

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)

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

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

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?

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