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

HNP 2011, Pohang, KoreaHNP 2011, Pohang, Korea 1123年 4月 21日23年 4月 21日

Weak Pion Production and Weak Pion Production and Strangeness Contents on theStrangeness Contents on the

HadronHadron

Myung-Ki CHEOUNMyung-Ki CHEOUN (Soongsil Univ., Korea) and (Soongsil Univ., Korea) and

K. S. KimK. S. Kim(Hanguk Aviation Univ.)(Hanguk Aviation Univ.)

23年 4月 21日23年 4月 21日 HNP 2011, Pohang, KoreaHNP 2011, Pohang, Korea 22

ContentsContents0. Introduction0. Introduction1. Motivation1. Motivation- PS and Scalar F.F. in the nucleon- PS and Scalar F.F. in the nucleon2. Weak Pion Production2. Weak Pion Production- Chiral Ward Identity- Chiral Ward Identity- - Sigma Sigma and and Sigma-like termSigma-like term in the transition in the transition

amplitudeamplitude3. 3. Induced PS FFInduced PS FF, Pion F.F. , Pion F.F. PS F.F.PS F.F. , and , and S F.F.S F.F.

in the transition amplitude for pion productionin the transition amplitude for pion production4. Results ( E_0, L_0,M_0, H_0 amplitudes, C.S.s) 4. Results ( E_0, L_0,M_0, H_0 amplitudes, C.S.s) 5. Summary5. Summary


Giant Resonance

Discrete Excited states

Quasi Elastic Region

Dip Region

Delta Resonance

Pion Threshold

Cross Section

q

energyN* Resonance

Hadronic Region

Typical cross section by incident electron0

0.05

0.1

0.15

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0 10 20 30 40 50 60

(

) /

(MeV)

0. 0. IntroductionIntroduction


1.Motivation(1.Motivation(scalar FF and sigma scalar FF and sigma

termterm) ) Explicit chiral symmetry breaking (ECSB) effects Explicit chiral symmetry breaking (ECSB) effects

originatedoriginatedfrom quark masses can be realized as from quark masses can be realized as scalar form scalar form

factorfactor of of the nucleonthe nucleon

Sigma term Sigma term is extracted from the pi - N scattering or is extracted from the pi - N scattering or weak-production from this weak-production from this scalar form factorscalar form factor through a low energy theorem. through a low energy theorem.

( Extrapolation to t =0 point ( Extrapolation to t =0 point ))


Pseudo scalar form factor

Pi – N Scatt. (Vector Current)

Electro Prod. (Axial Current)

Weak Current has both couplings !! => Weak Pion Production


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 factoris simply expressed as

P.R.C 68,055501 (03) (T.Fuchs & S.Scherer)


2. Weak Pion 2. Weak Pion Production Production

We exploit the Green functions C_a,P_a and We exploit the Green functions C_a,P_a and T_a, the nucleon matrix elements of the T_a, the nucleon matrix elements of the time ordered products of the relevant time ordered products of the relevant currents i.e., currents i.e., the weak current Jthe weak current J, the , the axial axial current Acurrent A, and the , and the PS quark density PPS quark density P


By exploiting the LSZ reduction


Cheoun, Kim, Phys. Lett. B 645, 422 (07)


3. Induced PS FF, Pion FF and PS 3. Induced PS FF, Pion FF and PS FF in the pion electro-productionFF in the pion electro-production

The t-channel comprises of the pion poles from the induced PS and PS form factors


4. Results 4. Results (Amplitudes) (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 !!


Scalar FF can be realized in L_0 amplitude, but it is too small !!


Scalar FF can be realized in the non-zero H_0 amplitude !!


5. Results (Cross 5. Results (Cross Sections for electro Sections for electro production)production)


0 0.1 0.2 0.3 0.4

2

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dsigmatFulandsigmatKKochdsigmatFFullTransverse Cross section

No problems in Transverse CS.!!


0 0.1 0.2 0.3 0.4

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4

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dsigmatFulandsigmalKKochdsigmalFFulldsigmalFcKochcCdsigmaloursLongitudinal Cross Section

Longitudinal CS is so sensitive to FF and low energy limit !!


6. Summary6. Summary1.1.In pion electro-production, the t-channel pole in In pion electro-production, the t-channel pole in

Born terms is explained at the pion threshold as Born terms is explained at the pion threshold as a sum of two pion poles. a sum of two pion poles.

2. The former comes from the induced PS form 2. The former comes from the induced PS form factor in the axial current and the latter results factor in the axial current and the latter results from the time component of the Sigma like term from the time component of the Sigma like term

3. In principle, the t-dependence of both form 3. In principle, the t-dependence of both form factors is fully different, so that the unique factors is fully different, so that the unique extraction of the form factors from the extraction of the form factors from the experimental data could leave another experimental data could leave another ambiguity. ambiguity.


4. But, under the lowest effective lagrangian 4. But, under the lowest effective lagrangian which maintains the GT relation, both form which maintains the GT relation, both form factors show the same t-dependence, and as a factors show the same t-dependence, and as a result the sum was shown to equally account result the sum was shown to equally account for the t-channel infor the t-channel in

the tree diagram approach. the tree diagram approach.

5. In weak production, both scalar (sigma) and PS 5. In weak production, both scalar (sigma) and PS (sigma like) terms appear. In specific, the (sigma like) terms appear. In specific, the scalar form factor can be realized in the scalar form factor can be realized in the amplitudes at the pion threshold. amplitudes at the pion threshold.


•Thanks for your Thanks for your attention !!!attention !!!


0.1 0.2 0.3 0.4

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0

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L0Pk_0AmaldiL0PKochL0PCha : IL0PChbL0PChc : IL0PFullNo 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 !!


Difference of conventional and our approaches

0 0.1 0.2 0.3 0.4 0.5

0

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Effect of PS F.F. seems not be so large,But it could be important in the extraction of Form Factors, L_0 amplitude

Documents

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