1. Kijun Park Univ. of South Carolina Kijun Park Univ. of South Carolina Axial Form Factor Physics at CLAS May. 30, 2008 HSWG meeting Electroproduction of soft pions at high Q 2

2. In historically, Threshold pion photo- and electroproduction is the very old subject that has been receiving continuous attention from both EXP. and THEO. sides for many years. Pion mass vanishing approximation in Chiral Symmetry allows us to make exact prediction for threshold cross section known as LET The LET established the connection between charged pion electroproduction and axial form factor in nucleon. Therefore, It is quiet interesting to extracting Axial Form Factor which is dominated by S- wave transverse multipole E0+ in LCSR In historically, Threshold pion photo- and electroproduction is the very old subject that has been receiving continuous attention from both EXP. and THEO. sides for many years. Pion mass vanishing approximation in Chiral Symmetry allows us to make exact prediction for threshold cross section known as LET The LET established the connection between charged pion electroproduction and axial form factor in nucleon. Therefore, It is quiet interesting to extracting Axial Form Factor which is dominated by S- wave transverse multipole E0+ in LCSR Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

3. Perspective of soft pion in terms of Q2 at threshold Low-Energy Theorem (LET) for Q 2 =0 Restriction to the charged pion χ ral symmetry + current algebra for electroproduction Re-derived LETs Current algebra + PCAC χ ral perturbation theory pQCD factorization methods 1954 1960s 1970s Kroll-Ruderman Nambu, Laurie, Schrauner Vainshtein, Zakharov 1990s Scherer, Koch Brodsky, Lepage, Efremov, Radyunshkin, Pobylitsa, Polyakov, Strikman, et al Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

4. LCSR [Light Cone Sum Rule]: An advantage of study because soft contribution to hadron form factor can be calculated in terms of DA ’ s that enter pQCD calculation without other nonperturbative parameters. Constructed relating the amplitude for the radiative decay of Σ +(p γ ) to properties of the QCD vacuum in alternating magnetic field. New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. LCSR [Light Cone Sum Rule]: An advantage of study because soft contribution to hadron form factor can be calculated in terms of DA ’ s that enter pQCD calculation without other nonperturbative parameters. Constructed relating the amplitude for the radiative decay of Σ +(p γ ) to properties of the QCD vacuum in alternating magnetic field. New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

5. Correlation Function Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park Light Cone Sum Rule V. M. Braun, arXiv:0709.2319v1 Light Corn Sum Rule Reproduce LET for Q 2 ~ 1GeV 2 Reproduce pQCD for Q 2 →∞ 2007 V. Braun Extended for near pion threshold regions

6. LCSR- based model for the Q 2 dependence of the electric, longitudinal Partial Waves at threshold [GeV -1 ] Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park MAID07 Arnt et al.

7. Differential Cross section Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park No D-wave contribution

8. Legendre moments vs. Multipoles Structure Functions vs. Legendre moments Partial Wave Series with Legendre Polynomials from S.F. Sensitive ! Insensitive ! Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

9. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park V.Braun arXiv:0710.3265

10. VariableUnitRange# BinWidth Q2Q2 GeV 2 2.05 ~ 4.165various WGeV 1.11 ~ 1.1330.02 cosθ * π -1.0~ 1.0100.2 φ *πφ *π Deg. 0. ~ 360.1230 Kinematical Coverage * E=5.754GeV, LH2 target (unpol.) * Oct. 2001-Jan. 2002 Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

11. Cross check Acceptance calculation - Based on phase space event generator - compare between GeNEV and AAO Re-calculation of Rad. Corr. - Based on new binning (12 φ ) from ExcluRad Study of ExcluRad model dependence - MAID2003 vs. Sato-Lee 2004 Apply more tight physics cuts - electron, pion fiducial cuts Cross check Acceptance calculation - Based on phase space event generator - compare between GeNEV and AAO Re-calculation of Rad. Corr. - Based on new binning (12 φ ) from ExcluRad Study of ExcluRad model dependence - MAID2003 vs. Sato-Lee 2004 Apply more tight physics cuts - electron, pion fiducial cuts Analysis -detail Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

12. Analysis -detail Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park RC difference is less than few % in nπ + channel !!

13. Cross section ( φ* ) Preliminary results φ* – dependent cross section in term of W, Q 2, cosθ* Various physics models Preliminary Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

14. Cross section ( φ* ) φ* – dependent cross section in term of W, Q 2, cosθ* Various physics models Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

15. Cross section ( φ* ) φ* – dependent cross section in term of W, Q 2, cosθ* Various physics models Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

16. Structure Function Sensitive ! Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

17. Sensitive ! Preliminary Structure Function Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

18. Insensitive ! Preliminary Structure Function Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

19. Legendre Moments (T+L) Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

20. Legendre Moments (TT) Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

21. Legendre Moments (LT) Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

22. Legendre moments vs. Form Factors for n π + channel Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G 1, G 2 @ threshold P.E. Bosted Phys. Rev. C 51 (1995) P.E. Bosted Phys. Rev. C 51 (1995) Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) Assumption in LCSR V.Braun arXiv:0710.3265 Assumption in LCSR V.Braun arXiv:0710.3265

23. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

24. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

25. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

26. Very Preliminary results MAID03 SLee04 Lines : MAID07 Bold : Real Thin : Imaginary Q 2 dependence of the Normalized E 0+ Multipole by dipole Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park Preliminary RC corr. base on MAID03 RC corr. base on S-Lee04 Color index

27. Legendre moments vs. Form Factors for n π + channel Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G 1, G 2 @ threshold P.E. Bosted Phys. Rev. C 51 (1995) P.E. Bosted Phys. Rev. C 51 (1995) Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park P.E. Bosted Phys. Rev. C 51 (1995) P.E. Bosted Phys. Rev. C 51 (1995)

28. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

29. Legendre moments vs. Form Factors Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park * Real parts x1, x2 can be determined by A1, D0 legendre coeff. * 3 Eqs. 4 parameter should be determined * Imaginary parts y1, y2 can be determined in 2cases * Asymmetry helps to determine complete form factor

30. Very Preliminary results Assumption of G E n =0 Assumption of Im(G 2 )=y 2 =0 Lines : MAID07 Bold : Real Thin : Imaginary Q 2 dependence of the Normalized E 0+ Multipole by dipole Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park Preliminary Color index

31. Complete Cross check Acceptance calculation - based on different simulation Re-calculation of Rad. Corr. - based on new binning Extract new cross sections based on above Extract very preliminary E 0+ /G D for channel Still ….. Double check out the cross section more careful work to get form factor after more frequent communication with theory group Calculate the systematic errors Complete Cross check Acceptance calculation - based on different simulation Re-calculation of Rad. Corr. - based on new binning Extract new cross sections based on above Extract very preliminary E 0+ /G D for channel Still ….. Double check out the cross section more careful work to get form factor after more frequent communication with theory group Calculate the systematic errors Summary and Future plans Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

32. BACKUP

33. Cross section ( φ* ) φ* – dependent cross section in term of W, Q 2, cosθ* Various physics models Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

34. Cross section ( φ* ) φ* – dependent cross section in term of W, Q 2, cosθ* Various physics models Preliminary Preliminary results Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

35. MAID2007MAID2007 Bold –Real part Thin – Imaginary part Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

36. MAID2007MAID2007 Bold –Real part Thin – Imaginary part Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park

37. Threshold Pion Production @ Workshop, Jlab Feb. 19, 2008 V. M. Braun

38. Axial Form Factor @ Spectroscopy Meeting May. 30, 2008 K. Park Neutron Magnetic Structure