measurement of generalized form factors near the pion threshold
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/1.jpg)
![Page 2: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/2.jpg)
• First time extracting preliminary E0+/GD multipole 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 Gm
n 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
• First time extracting preliminary E0+/GD multipole 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 Gm
n 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
![Page 3: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/3.jpg)
• First time extracting preliminary E0+/GD multipole 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 Gm
n 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
• First time extracting preliminary E0+/GD multipole 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 Gm
n 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
![Page 4: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/4.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 5: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/5.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Low-Energy Theorem (LET) for Q2=0Restriction to the charged pionChiral symmetry + current algebra for electroproduction
1954
1960s
Kroll-Ruderman
Nambu, Laurie, Schrauner
Re-derived LETsCurrent algebra + PCACChiral perturbation theory
1970sVainshtein, Zakharov
1990sScherer, Koch
pQCD factorization methodsBrodsky, Lepage, Efremov, Radyunshkin, Pobylitsa, Polyakov, Strikman, et al
![Page 6: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/6.jpg)
• 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
![Page 7: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/7.jpg)
2* 2 2
| |8
fem
N
k dd
W W m
2
* 2 2| |
8fem
N
k dd
W W m
2
'
| | cos(2 ) 2 (1 ) cos( )
2 (1 ) sin( )
T L TT LT
LT
2
'
| | cos(2 ) 2 (1 ) cos( )
2 (1 ) sin( )
T L TT LT
LT
2
1 ,NT MGG 2
1 ,NT MGG
22 ,N
L EGG 22 ,N
L EGG
1 2Re ,Re , ,LN N
T E MG G G G 1 2Re ,Re , ,LN N
T E MG G G G
1 2/ Im , Im , ,L
N NT E MG G G G 1 2
/ Im , Im , ,LN N
T E MG G G G
0TT 0TT
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 8: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/8.jpg)
1NG
1NG
2NG
2NG
MGMG EGEG
2 2 2 2 2 22 22 22 2 2 2 4 2
0 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 2 2 2 2 22 2
2 22 2 2 2 4 20 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 0TTC C 0 0 0TTC C
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 9: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/9.jpg)
2 2 2 20( ) 1/(1 / )DG Q Q
2 20 0.71GeV
2 2[ ]Q GeV2 2[ ]Q GeV
2 2[ ]Q GeV 2 2[ ]Q GeV
V. M. Braun et al., Phys. Rev. D 77:034016, 2008.
Dashed Lines : pure LCSR
symbol index
Solid Lines : LCSR using experimental EM form factor as input
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 10: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/10.jpg)
Q2 dependence of the Normalized E0+ Multipole by dipole F. F.
Q2 dependence of the Normalized E0+ Multipole by dipole F. F.
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 11: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/11.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 12: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/12.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
F1 = E0+ + 3*cos(θ)*(E1+ + M1+)
F2 = 2*M1+ + M1-
F3 = 3*(E1+ - M1+)
F4 = 0
F5 = S0+ + 6*cos(θ)*S1+
F6 = S1- - 2*S1+
H1 = (-1/sqrt(2))*cos(θ/2)*sin(θ)*(F3 + F4)
H2 = -1*sqrt(2)*cos(θ/2)*(F1 - F2 - sin(θ)*(F3 - F4))
H3 = (1/sqrt(2))*sin(θ/2)*sin(θ)*(F3 - F4)
H4 = sqrt(2)*sin(θ/2)*(F1 + F2 +(cos(θ/2))**2*(F3 + F4))
H5 = -1*(sqrt(Q2)/abs(k_cm))*cos(θ/2)*(F5 + F6)
H6 = (sqrt(Q2)/abs(k_cm))*sin(θ/2)*(F5 - F6)
Helicity amplitudes ( Hi ) :
Using six amplitudes ( Fi ) : ** if lπ = 1
![Page 13: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/13.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
σT+L = (1/2)*(H1² + (H2²)*(H3²) + H4²) + ε*(H5² + H6²)
σTT = H3*H2 - H4*H1
σLT = (-1/sqrt(2))*( H5*(H1 - H4) + H6*(H2 + H3) )
Structure functios vs. Helicity amplitudes ( Hi ) :
![Page 14: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/14.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
* E0+, S0+ are dominated in this regime.
** M1-, S1- were used from MAID2007 model prediction.
*** for I=3/2I=3/2 case, following correlation functions are acceptable.
→ GD′ =(1+Q2/mu_02)²
→ GM = 3.*exp(-0.21*Q2)/(1. +0.0273*Q2 -0.0086*Q2²)/GD′
→ M1+ = (Y_O/52.437)* GM * sqrt(((2.3933+Q2)/2.46)**2-0.88)* 6.786
→ E1+ = -0.02 * M1+
→ R_sm =-6.066 -8.5639*Q2 +2.3706*Q2² +5.807* sqrt(Q2) -0.75445* Q2²* sqrt(Q2)
→ S1+ = R_sm*M1+/100.
where, mu_02=0.71, Y_O is the interpolation value from SAID model.
Constraints :
![Page 15: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/15.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
![Page 16: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/16.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
![Page 17: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/17.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
Q2 dependence of the Normalized E0+ , L0+ and E1+ Multipole by dipole F. F.
![Page 18: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/18.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 19: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/19.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
P.E. Bosted Phys. Rev. C 51 (1995)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
0 /nDE G
0 /nDE G
0nE EG G 0nE EG G
J.J. KellyPhys. Rev. C 70 (2004)
S. PlatchekovNucl.Phys. A 70 (1990)0n
E EG G 0nE EG G
![Page 20: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/20.jpg)
J. J. Kelly et al., PRC 70:068202 (2004)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 21: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/21.jpg)
J. Lachniet et al., PRL 102:192001 (2009)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 22: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/22.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
0 /nDE G
0 /nDE G
0nE EG G 0nE EG G J.J. Kelly
Phys. Rev. C 70 (2004)
J. Lachniet (2009)Phys. Rev. Lett. 102CLAS DATA
![Page 23: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/23.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
• 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.
• 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.
![Page 24: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/24.jpg)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 25: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/25.jpg)
• 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 N and *N scattering under QCD S-, P- and D partial waves.
• 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 N and *N scattering under QCD S-, P- and D partial waves.
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 26: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/26.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
0nE EG G 0nE EG G
Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold 0m 0m
P.E. Bosted Phys. Rev. C 51 (1995)
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
Scherer, Koch, NPA534(1991)Vainshtein, Zakharov NPB36(1972)
Assumption in LCSRV.Braun PRD77(2008)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 27: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/27.jpg)
1nG
1nG
2nG
2nG
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
1/ DG1/ DG
1/ DG1/ DG
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 28: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/28.jpg)
W-dependence of L0+ from MAID2007
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
Lower Q2, Smaller W dependence
![Page 29: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/29.jpg)
Bold –Real part Thin – Imaginary
part
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 30: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/30.jpg)
* E=5.754GeV(pol.), LH2 target (unpol.)* IB=3375/6000A, Oct. 2001-Jan. 2002
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 31: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/31.jpg)
Cross Section (φ*)
Cross Section (φ*)
Blue shade : systematic uncertainty estimation
Red data : CRS with new analysis
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 32: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/32.jpg)
T L T L
TTTT0E 0E insensitive !insensitive !
0E 0E sensitive !sensitive !
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 33: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/33.jpg)
0E 0E sensitive !sensitive !LTLT
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 34: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/34.jpg)
*0 1 1(cos )T L T L
T L L D D P
0TT
TT D
![Page 35: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/35.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
0nE EG G 0nE EG G
Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold 0m 0m
P.E. Bosted Phys. Rev. C 51 (1995)
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
Scherer, Koch, NPA534(1991)Vainshtein, Zakharov NPB36(1972)
Assumption in LCSRV.Braun PRD77(2008)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 36: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/36.jpg)
2 2 22 2 22 2 2
0 0 12 2 2 2
41 A fT L n nip M
p p
c g kk QA D G Q m G
f m W m
2 2 22 2 22 2 2
0 0 12 2 2 2
41 A fT L n nip M
p p
c g kk QA D G Q m G
f m W m
21 1 12 2 2
41Re
A i fT L n nM
p
c g k kA D Q G G
f W m
2
1 1 12 2 2
41Re
A i fT L n nM
p
c g k kA D Q G G
f W m
0 0 0LTD D 0 0 0LTD D
1.267Ag 1.267Ag
2c 2c
93f MeV 93f MeV 0 0 0TTC C 0 0 0TTC C
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
1nG
1nG
2nG
2nG
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 37: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/37.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
0nE EG G 0nE EG G
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2
2 2 2
2 2
2n nA N
EN
g mG G
Q m
2
2 2 2
2 2
2n nA N
EN
g mG G
Q m
Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold 0m 0m
P.E. Bosted Phys. Rev. C 51 (1995)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 38: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/38.jpg)
2 2 2 2 2 22 22 22 2 2 2 4 2
0 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 2 2 2 2 22 2
2 22 2 2 2 4 20 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 0TTC C 0 0 0TTC C
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
1nG
1nG
2nG
2nG
1.267Ag 1.267Ag
2c 2c
93f MeV 93f MeV
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 39: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/39.jpg)
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
* 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
/ /0 0 2 12 2 2
1Im 4 Im
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
/ /0 0 2 12 2 2
1Im 4 Im
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 40: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/40.jpg)
1nG
1nG
2nG
2nG
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
1/ DG1/ DG
1/ DG1/ DG
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 41: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/41.jpg)
• 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
![Page 42: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/42.jpg)
• 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
![Page 43: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/43.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
0nE EG G 0nE EG G
Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold 0m 0m
P.E. Bosted Phys. Rev. C 51 (1995)
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
2
2 2 2
2 20
2n nA N
EN
g mG G
Q m
Scherer, Koch, NPA534(1991)Vainshtein, Zakharov NPB36(1972)
Assumption in LCSRV.Braun PRD77(2008)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 44: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/44.jpg)
2 2 22 2 22 2 2
0 0 12 2 2 2
41 A fT L n nip M
p p
c g kk QA D G Q m G
f m W m
2 2 22 2 22 2 2
0 0 12 2 2 2
41 A fT L n nip M
p p
c g kk QA D G Q m G
f m W m
21 1 12 2 2
41Re
A i fT L n nM
p
c g k kA D Q G G
f W m
2
1 1 12 2 2
41Re
A i fT L n nM
p
c g k kA D Q G G
f W m
0 0 0LTD D 0 0 0LTD D
1.267Ag 1.267Ag
2c 2c
93f MeV 93f MeV 0 0 0TTC C 0 0 0TTC C
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
1nG
1nG
2nG
2nG
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 45: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/45.jpg)
1 1N nG G
1 1N nG G
2 2N nG G
2 2N nG G
2( )nM M n DG G G Q 2( )nM M n DG G G Q
0nE EG G 0nE EG G
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2 2
12 2 2
1
2 22n nA
M AN N
gQ QG G G
m Q m
2
2 2 2
2 2
2n nA N
EN
g mG G
Q m
2
2 2 2
2 2
2n nA N
EN
g mG G
Q m
Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold Due to low-energy theorem(LET) relates the S-wave multipoles or equivalently, the form factor G1, G2 @ threshold 0m 0m
P.E. Bosted Phys. Rev. C 51 (1995)
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 46: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/46.jpg)
2 2 2 2 2 22 22 22 2 2 2 4 2
0 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 2 2 2 2 22 2
2 22 2 2 2 4 20 0 1 22 2 2 2 2 2
441 A f A fT L N NiN M L i N E
N N N
c g k c g kk QA D G Q m G k G m G
f m W m W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
2 21 1 1 22 2 2
41Re Re
A i fT L N NM L N E
N
c g k kA D Q G G m G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 2 12 2 2
1Re 4 Re
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
0 0 0TTC C 0 0 0TTC C
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
1nG
1nG
2nG
2nG
1.267Ag 1.267Ag
2c 2c
93f MeV 93f MeV
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 47: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/47.jpg)
1 1 1nG x iy
1 1 1nG x iy
2 2 2nG x iy
2 2 2nG x iy
* 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
/ /0 0 2 12 2 2
1Im 4 Im
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
/ /0 0 2 12 2 2
1Im 4 Im
A i fLT N NN M E
N
c g k kD D Qm G G G G
f W m
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 48: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/48.jpg)
1nG
1nG
2nG
2nG
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 13
44
8pemn n
p
Q Q mE G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
2 2 2
0 23
44
32pemn n
p
Q Q mL G
m f
1/ DG1/ DG
1/ DG1/ DG
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park
![Page 49: Measurement of Generalized Form Factors near the Pion Threshold](https://reader035.vdocuments.us/reader035/viewer/2022062518/5681469a550346895db3b180/html5/thumbnails/49.jpg)
Q2 dependence of the scaled cross section for three different W bins
dashsolid
CLAS Hadron Spectroscopy meeting Sep. 26, 2009 K. Park