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Analysis of Generalized Form Factors near Pion Threshold - CLAS Hadron Spectroscopy Meeting

This meeting discussed extracting the preliminary E0+/GD multipole near the pion threshold through the nπ+ channel, focusing on the dominant real part contribution. Important topics include asymmetry data for determining L0+, correction of pion mass, and improved radiative corrections. Plans for long-term high-stat data studies were also addressed, along with the use of Light Cone Sum Rule for hadron form factor calculations. The presentation covered differential cross sections, Legendre moments, and form factor predictions using different techniques and assumptions.

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Analysis of Generalized Form Factors near Pion Threshold - CLAS Hadron Spectroscopy Meeting

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  1. Measurement of Generalized Form Factors near the Pion Threshold In high momentum transfer square Sep. 26, 2009 CLAS Hadron Spectroscopy Meeting K. Park

  2. Previous Summary and plans * Last collaboration meeting @ Jun. 2009 • First time extracting preliminary E0+/GDmultipole near the pion threshold through nπ+channel • Real part contribution is dominated • In experiment side : - Asymmetry data is important to determine L0+ - Cross check is needed by multipoles analysis - Direct use the F.F. of Gmn from CLAS instead parameterization • In theory side : - Second order correction of pion mass - More serious study for error estimation (one-loop correction) - Improved radiative correction in sum rule - DA’s parameters from LQCD become available CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  3. Previous Summary and Plans * Today’s meeting @ Sep. 2009 • First time extracting preliminary E0+/GDmultipole near the pion threshold through nπ+channel • Real part contribution is dominated • In experiment side : - Asymmetry data is important to determine L0+ - Cross check is needed by multipoles analysis - Direct use the F.F. of Gmn from CLAS instead parameterization • In theory side : - Second order correction of pion mass - More serious study for error estimation (one-loop correction) - Improved radiative correction in sum rule - DA’s parameters from LQCD become available Long term plan with high stat. data CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  4. Quick Review... CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  5. Perspective of soft pion in terms of Q2 at threshold Q2=0 GeV2 Low-Energy Theorem (LET) for Q2=0 1954 Kroll-Ruderman Restriction to the charged pion Chiral symmetry + current algebra for electroproduction 1960s Nambu, Laurie, Schrauner Q2 << Λ/mπ~ 1GeV2 1970s Re-derived LETs Vainshtein, Zakharov Current algebra + PCAC 1990s Chiral perturbation theory Scherer, Koch Q2~ 1 - 10 GeV2 ??? Q2 >> Λ/mπ pQCD factorization methods Brodsky, Lepage, Efremov, Radyunshkin, Pobylitsa, Polyakov, Strikman, et al CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  6. LCSR (Light Cone Sum Rule) • Constructed relating the amplitude for the radiative decay of Σ+(pγ) to properties of the QCD vacuum in alternating magnetic field. • 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. • New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  7. Differential Cross Section No D-wave contribution CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  8. Legendre moments vs. Form Factors V. Braun PRD 77(2008) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  9. Prediction LCSR symbol index Dashed Lines : pure LCSR Solid Lines : LCSR using experimental EM form factor as input V. M. Braun et al., Phys. Rev. D 77:034016, 2008. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  10. LCSR Preliminary Q2 dependence of the Normalized E0+Multipole by dipole F. F. • Using…. • Measurement of differential cross sections • Extract structure functions (s T+L, s TT, s LT) • Extract Legendre moments • Plug into LCSR… Assumption of Im(G2)=y2=0 Assumption of GEn =0 Preliminary Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ Black MAId07 L0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  11. Question ??? Alternative way to extract multipoles near pion threshold region ? CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  12. I. G. Aznauryan, PRD 57, 2727 (1998) Multipoles Analysis Using six amplitudes ( Fi ) : ** if lπ = 1 Helicity amplitudes ( Hi ) : CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  13. I. G. Aznauryan, PRD 57, 2727 (1998) Multipoles Analysis Structure functios vs. Helicity amplitudes ( Hi ) : CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  14. I. G. Aznauryan, PRD 57, 2727 (1998) Multipoles Analysis Constraints : CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  15. Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  16. Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  17. Multipoles extraction Q2 dependence of the Normalized E0+ , L0+ and E1+Multipole by dipole F. F. Blue : E0+ using LCSR w/ zero pion mass Red : E0+ using LCSR w/ real pion mass Black : E0+ from multipole analysis Blue : E1+ from multipole analysis Red lines : LCSR solid line : pure calc. dash line : exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  18. Question ??? CLAS Gmn measurement as input instead of using parametrization ? CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  19. Form factors and Multipole for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) S. Platchekov Nucl.Phys. A 70 (1990) J.J. Kelly Phys. Rev. C 70 (2004) Preliminary Preliminary Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  20. J. J. Kelly et al., PRC 70:068202 (2004) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  21. Neutron magnetic form factor from CLAS J. Lachniet et al., PRL 102:192001 (2009) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  22. Form factors and Multipole for nπ+channel J. Lachniet (2009) Phys. Rev. Lett. 102 CLAS DATA J.J. Kelly Phys. Rev. C 70 (2004) Preliminary Red lines : LCSR solid line : pure calc. dash line :exp. F. F. input Blue line : MAID07, E0+ CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  23. Summary • As first time, E0+ multipole comparison near pion threshold between two methods (LCSR, multipole fit) was performed. • Multipole analysis gives us same answer for extracting E0+ multipole with LCSR method. • however, the fitting chi2 should be improved ...(future plan) • Direct use of neutron magnetic form factor from CLAS publication gives consistent result with F.F. parametrization. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  24. BACKUP SLIDES CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  25. Theoretical imrovement plans • Enrgy dependent generalized form factors generated by FSI • Adding D-wave contributio model • Tune calculation with low Q2 and high W experimental data • Systematic approach in the global PWA analysis framework in Np and g*N scattering under QCD S-, P- and D partial waves. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  26. Legendre–moment vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Assumption in LCSR V.Braun PRD77(2008) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  27. Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  28. Prediction MAID2007 W-dependence of L0+ from MAID2007 Lower Q2, Smaller W dependence CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  29. Prediction MAID2007 Bold –Real part Thin – Imaginary part CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  30. Kinematical Coverage * E=5.754GeV(pol.), LH2 target (unpol.) * IB=3375/6000A, Oct. 2001-Jan. 2002 CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  31. Preliminary Results Preliminary Cross Section (φ*) φ* – dependent cross section in term of W, Q2, cosθ* Various physics models Blue shade : systematic uncertainty estimation Red data : CRS with new analysis CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  32. Structure Function Preliminary sensitive ! insensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  33. Structure Function Preliminary sensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  34. Preliminary Preliminary Preliminary Legendre –moments

  35. Legendre–moment vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Assumption in LCSR V.Braun PRD77(2008) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  36. Legendre moments vs. Form Factors CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  37. l-moments vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  38. Legendre-moments vs. F. F. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  39. Legendre moments vs. Form Factors * 3 Eqs. 4 parameter should be determined * Real parts x1, x2 can be determined by A1, D0 legendre coeff. * Imaginary parts y1, y2 can be determined in 2cases * Asymmetry helps to determine complete form factor CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  40. Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  41. Historically, threshold pion in the photo- and electroproduction is the very old subject that has been receiving continuous attention from both experiment and theory sides for many years. • Pion mass vanishing approximation in Chiral Symmetry allows us to make an 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 very interesting to extracting Axial Form Factor which is dominated by S- wave transverse multipole E0+ in LCSR CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  42. LCSR (Light Cone Sum Rule) • Constructed relating the amplitude for the radiative decay of Σ+(pγ) to properties of the QCD vacuum in alternating magnetic field. • 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. • New technique : the expansion of the standard QCD sum rule approach to hadron properties in alternating external fields. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  43. Legendre–moment vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Assumption in LCSR V.Braun PRD77(2008) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Scherer, Koch, NPA534(1991) Vainshtein, Zakharov NPB36(1972) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  44. Legendre moments vs. Form Factors CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  45. l-moments vs. F. F. for nπ+channel P.E. Bosted Phys. Rev. C 51 (1995) Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  46. Legendre-moments vs. F. F. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  47. Legendre moments vs. Form Factors * 3 Eqs. 4 parameter should be determined * Real parts x1, x2 can be determined by A1, D0 legendre coeff. * Imaginary parts y1, y2 can be determined in 2cases * Asymmetry helps to determine complete form factor CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  48. Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

  49. Scaled cross section X Q6 Q2 dependence of the scaled cross section for three different W bins Preliminary Color index Rad.Corr. with MAID03 Rad. Corr. With SLee04 dash solid CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park

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