1. HNP 2011, Pohang, Korea12015-11-23 Weak Pion Production and Strangeness Contents on the Hadron Myung-Ki CHEOUN (Soongsil Univ., Korea) and (Soongsil Univ., Korea) and K. S. Kim (Hanguk Aviation Univ.)

2. 2015-11-23HNP 2011, Pohang, Korea2Contents 0. Introduction 1. Motivation - PS and Scalar F.F. in the nucleon 2. Weak Pion Production - Chiral Ward Identity - Sigma and Sigma-like term in the transition amplitude 3. Induced PS FF, Pion F.F. PS F.F., and S F.F. in the transition amplitude for pion production 4. Results ( E_0, L_0,M_0, H_0 amplitudes, C.S.s) 5. Summary

3. 2015-11-23HNP 2011, Pohang, Korea3 Giant Resonance Discrete Excited states Quasi Elastic Region Dip Region Delta Resonance Pion Threshold Cross Section q energy N * Resonance Hadronic Region Typical cross section by incident electron 0. Introduction

4. 2015-11-23HNP 2011, Pohang, Korea4 1.Motivation( scalar FF and sigma term ) Explicit chiral symmetry breaking (ECSB) effects originated from quark masses can be realized as scalar form factor of the nucleon Sigma term is extracted from the pi - N scattering or weak- production from this scalar form factor through a low energy theorem. ( Extrapolation to t =0 point ) ( Extrapolation to t =0 point )

5. 2015-11-23HNP 2011, Pohang, Korea5 Pseudo scalar form factor Pi – N Scatt. (Vector Current) Electro Prod. (Axial Current) Weak Current has both couplings !! => Weak Pion Production

6. 2015-11-23HNP 2011, Pohang, Korea6 With the help of the interpolating pion field defined by and the definition of coupling constant the PS quark density can be parameterized as Contrary to the scalar form factor, therefore, the PS form factor is simply expressed as P.R.C 68,055501 (03) (T.Fuchs & S.Scherer)

7. 2015-11-23HNP 2011, Pohang, Korea7 2. Weak Pion Production We exploit the Green functions C_a,P_a and T_a, the nucleon matrix elements of the time ordered products of the relevant currents i.e., the weak current J, the axial current A, and the PS quark density P

8. 2015-11-23HNP 2011, Pohang, Korea8 By exploiting the LSZ reduction

9. 2015-11-23HNP 2011, Pohang, Korea9 Cheoun, Kim, Phys. Lett. B 645, 422 (07)

10. 2015-11-23HNP 2011, Pohang, Korea10 3. Induced PS FF, Pion FF and PS FF in the pion electro-production The t-channel comprises of the pion poles from the induced PS and PS form factors

11. 2015-11-23HNP 2011, Pohang, Korea11 4. Results (Amplitudes) Cheoun and Kim, JPSJ 79, 074202 (2010) and Phys. Lett. B 645, 422 (2007) Pion form factor is coupled with IPS and PS form factors !!

12. 2015-11-23HNP 2011, Pohang, Korea12 Scalar FF can be realized in L_0 amplitude, but it is too small !!

13. 2015-11-23HNP 2011, Pohang, Korea13 Scalar FF can be realized in the non-zero H_0 amplitude !!

14. 2015-11-23HNP 2011, Pohang, Korea14 5. Results (Cross Sections for electro production)

15. 2015-11-23HNP 2011, Pohang, Korea15 Transverse Cross section No problems in Transverse CS.!!

16. 2015-11-23HNP 2011, Pohang, Korea16 Longitudinal Cross Section Longitudinal CS is so sensitive to FF and low energy limit !!

17. 2015-11-23HNP 2011, Pohang, Korea17 6. Summary 1. In pion electro-production, the t-channel pole in Born terms is explained at the pion threshold as a sum of two pion poles. 2. The former comes from the induced PS form factor in the axial current and the latter results from the time component of the Sigma like term 3. In principle, the t-dependence of both form factors is fully different, so that the unique extraction of the form factors from the experimental data could leave another ambiguity.

18. 2015-11-23HNP 2011, Pohang, Korea18 4. But, under the lowest effective lagrangian which maintains the GT relation, both form factors show the same t-dependence, and as a result the sum was shown to equally account for the t-channel in the tree diagram approach. the tree diagram approach. 5. In weak production, both scalar (sigma) and PS (sigma like) terms appear. In specific, the scalar form factor can be realized in the amplitudes at the pion threshold.

19. 2015-11-23HNP 2011, Pohang, Korea19 Thanks for your attention !!! Thanks for your attention !!!

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23. 2015-11-23HNP 2011, Pohang, Korea23 No expansion in \mu order !! L_0 amplitude Effect of PS F.F. seems not be so large, But it could be important in the extraction of Form Factors, L_0 amplitude High order of \mu could be important in the extraction of relevant form factors !!

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25. 2015-11-23HNP 2011, Pohang, Korea25 Effect of PS F.F. seems not be so large, But it could be important in the extraction of Form Factors, L_0 amplitude