Scalar and pseudo-scalar scalar form factors in electro- and weak- pionproduction

Transcription

1 Scalar and pseudo-scalar scalar form factors in electro- and weak- pionproduction Myung-Ki CHEOUN, Kyungsik KIM, Kiseok CHOI (Soongsil Univ., Seoul) Fukuoka, Japan 1

2 Contents 1. Motivation - PS and Scalar FF on the nucleon 2. Electro- and Weak- Pionproduction amplitude near threshold - Chiral Ward Identity - Sigma and Sigma-like terms in the transition amplitudes 3. Induced PS,, Pion, PS,, and Scalar FF in the transition amplitude for the pionproduction 4. Results for multipole amplitudes and X-X sections by charged and neutral currents 5. Summary Fukuoka, Japan 2

3 1.Motivation : Neutrino Reactions Cross Section KSKim, MKC, PRC 83, Giant Resonance Delta Resonance Quasi Elastic Region Hadronic Region N * Resonance energy Dip Region q Discrete Excited states Pion Threshold ε(ε ν ) / ε Typical cross section by incident electron ε ν (MeV) Fukuoka, Japan 3

4 1.Motivation : S and PS f.factors in weak production Pi N Scatt. or Axial Current in Weak Prod. Scalar form factor Electro Prod. or Vector Current in Weak Prod. Pseudo scalar form factor Fukuoka, Japan 4

5 1.Motivation : Pion pole in PS form factor 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 PRC 68, (03) (T.Fuchs & S.Scherer) Fukuoka, Japan 5

6 2. Weak Pionproduction Amplitude We exploit the Green functions C_ab,P_ab and T_ab,, the nucleon matrix elements of the time ordered products of the relevant currents i.e., the weak current W, the axial current A, and the PS quark density P Fukuoka, Japan 6

7 By exploiting the LSZ reduction Cheoun & Kim Phys. Lett. B 645(2007) JPSJ 79, (2010) Fukuoka, Japan 7 MPLA, 24, 945 (2009)

8 3. Induced PS FF, Pion FF and PS FF in the pion electro-production near threshold Under the lowest order t-channel in Born Terms!!! 8

9 4. Results Pion Production via CC for Vector and Axial parts (Amplitudes and X-sections) X 4-1. CC for Vector 4-2. CC for Axial 4-3. NC Fukuoka, Japan 9

10 4-1. Results for Vector part (Amplitudes) Without Expansion in ratio of pion and nucleon masses, mu Here the PS form factor is absorbed in t-channel contribution! Fukuoka, Japan 10

11 Full Calculation Expansion Fukuoka, Japan 11

12 Transverse Cross section Fukuoka, Japan 12

13 4-2. Results for Axial part (Amplitudes) Fukuoka, Japan 13

14 If we take the chiral limit in our results, one can easily obtain the results derived by the chiral perturbation theory. Fukuoka, Japan 14

15 Total Non-Born Born Non-zero cont. due to the sigma term Fukuoka, Japan 15

16 Non-zero cont. due to the sigma term Fukuoka, Japan 16

17 Results (Cross Sections for w-production) w Transverse Pol. Longitudinal Pol. Fukuoka, Japan 17

18 Fukuoka, Japan 18

19 4-3. Pion Production via NC A e + N (elastic scattering) = σ σ R R σ + σ L L γ Ζ p 5 6 ( ) e e p γ 2 F = form factors πα G Q PV pion-nucleon coupling Related to the non-leptonic weak interaction Fukuoka, Japan 19

20 5. Summary 1. In pion electro-production near threshold, the t-channel t pole in Born term is explained as a sum of two pion poles ; from the induced PS form factor and from the time component of the PS form factor. 2. In principle, the t-dependence t of both form factors is fully different, so that the unique extraction of the form factors from the experimental data could leave another ambiguity. 3.. But, under the lowest effective Lagrangian which maintains the GT relation, both form factors show the same t-dependence, t and as a result the sum was shown to equally account for the t-channel t in the tree diagram approach. Fukuoka, Japan 20

21 4. In weak-production by the charged current, the PS and S form factors appeared explicitly. The PS form factor was shown to equally account for the t-channel t in the tree diagram approach. 5. In specific, the S form factor gives the non-zero contributions to L_0^(+) and H_0^(+) amplitudes by the strong cancellations of the Born and Non-Born terms. This is consistent with the chiral perturbation theory. 6. Experimental data near threshold in future, in particular, the asymmetry by neutrino and anti-neutrino, neutrino, will make it clear to understand the role of S form factor in w-production. w 7. Extension to the NC case, which enables us to study the anapole and the PV pion-nn interaction, is in the progress. Fukuoka, Japan 21

22 Thanks for your attention!!! Fukuoka, Japan 22

23 1.Motivation : Scalar form factor 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 this scalar form factor through a low energy theorem on the pi - N scattering or weak- production. ( Extrapolation to t =0 point ) Fukuoka, Japan 23

24 Longitudinal Cross Section Fukuoka, Japan 24

25 Weak currents and Cross sections 1 Charged Current ( + ) J = < N u d + s μ μ 5 C γ (1 γ )[ cosθ sin θ ] + cγ (1 γ )[ d sin θ + s co s θ ] N > 5 = cos { < > < > } ( + ) J θ N γ τ N N γ γ τ N μ C μ ± μ 5 ± 1 < N γ τ N >= u ( p ')[ Fγ + F iσ q ] τ ] u( p) μ ± 1 μ 2 μν ν ± 2 m < N γ γ τ N >= u ( p ')[ F γ γ + F γ q ] τ ] u( p) F A μ μ 5 ± A μ 5 P 5 ν ± (0) = 1.26 F = P C V (vector) AV (axial-vector) 2 mfa 2 q + m r r V V 1 r r V 1 r r J = F σ ( F + F ) iσ q + F ( p + p ') A m 2m V 1 r r r J = F + F σ ( pfew + Body p ') Systems 2012, 0 1 A m Fukuoka, Japan 2 π C C CVC 05 25

26 Weak currents and Cross sections 1 Neutral Current = < N [( uγ u dγ d) ( uγ γ u dγ γ d) sγ s+ sγ γ s N > μ μ μ 5 μ 5 μ μ 5 2 (0) 2 γ J = < N [ uγ (1 γ ) u dγ (1 γ ) d sγ (1 γ ) s N > 2 sin θ J μ μ 5 μ 5 μ 5 W μ isovector-v isovector-av strange-v strange-av 2sin 3 3 S S 2 γ V A V A θ J μ μ μ μ W μ = V 1 V V = < N ( uγ u dγ d) N >= u( p')[ F γ + F iσ q] τ u( p) μ μ μ 1 μ 2 μν m A = < N ( uγγu dγγd) N >= u( p')[ F γγ + if γq ] τu( p) μ μ 5 μ 5 A μ 5 P 5 ν S 1 1 S 1 S V = < N sγ s N >= u( p')[ F γ + F iσ q] u( p) μ μ 1 μ 2 μν 2 2 2m S 1 1 S A = < N sγγs N >= G u( p') γγu( p) μ μ 5 1 μ S S 2 Few Body S Systems S 2012, F (0) = 0 F ( q 0), Fukuoka,, G Japan not well det er min ed 26 Fukuoka, Japan μ 2 1

27 Difference of conventional and our approaches Effect of PS F.F. seems not be so large, But it could be important in the extraction of Form Factors, L_0 amplitude Fukuoka, Japan 27

28 E_0 amplitude E0PHAmaldiLscale E0PHChLE0PHCh's full cal.l High order of mu could be important in the extraction of axial mass!! Fukuoka, Japan 28

29 L_0 amplitude L0P k_0hamaldi L0PHKoch L0PHCh-a :I L0PHCh-b L0PHCh-c :I L0PHFullL No expansion in mu order!! 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!! Fukuoka, Japan 29

30 Expansion Under GT relation Fukuoka, Japan 30

31 LSND DIF DAR Fukuoka, Japan 31