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Measurement of Generalized Form Factors near the Pion Threshold In high momentum transfer square. Sep. 26, 2009 CLAS Hadron Spectroscopy Meeting. K. Park. Previous Summary and plans. * Last collaboration meeting @ Jun. 2009.
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Measurement of Generalized Form Factors near the Pion Threshold In high momentum transfer square Sep. 26, 2009 CLAS Hadron Spectroscopy Meeting K. Park
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
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
Quick Review... CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
Differential Cross Section No D-wave contribution CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Legendre moments vs. Form Factors V. Braun PRD 77(2008) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
Question ??? Alternative way to extract multipoles near pion threshold region ? CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
I. G. Aznauryan, PRD 57, 2727 (1998) Multipoles Analysis Structure functios vs. Helicity amplitudes ( Hi ) : CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
I. G. Aznauryan, PRD 57, 2727 (1998) Multipoles Analysis Constraints : CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
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
Question ??? CLAS Gmn measurement as input instead of using parametrization ? CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
J. J. Kelly et al., PRC 70:068202 (2004) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Neutron magnetic form factor from CLAS J. Lachniet et al., PRL 102:192001 (2009) CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
BACKUP SLIDES CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Prediction MAID2007 W-dependence of L0+ from MAID2007 Lower Q2, Smaller W dependence CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Prediction MAID2007 Bold –Real part Thin – Imaginary part CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
Structure Function Preliminary sensitive ! insensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Structure Function Preliminary sensitive ! CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Preliminary Preliminary Preliminary Legendre –moments
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
Legendre moments vs. Form Factors CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
Legendre-moments vs. F. F. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
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
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
Legendre moments vs. Form Factors CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
Legendre-moments vs. F. F. CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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
Multipolesvs. F. F. for nπ+channel CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
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