measurement of generalized form factors near the pion threshold

• 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









Long term plan with high stat. data



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

• 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.


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


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


N N N


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


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


f W m

0 0 0TTC C 0 0 0TTC C


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


Q2 dependence of the Normalized E0+ Multipole by dipole F. F.

Q2 dependence of the Normalized E0+ Multipole by dipole F. F.



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


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 ) :


* 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 :


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.

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)


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

J. J. Kelly et al., PRC 70:068202 (2004)


J. Lachniet et al., PRL 102:192001 (2009)


1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G



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


• 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.

• 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.


1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G


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


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)


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


W-dependence of L0+ from MAID2007


Lower Q2, Smaller W dependence

Bold –Real part Thin – Imaginary

part


* E=5.754GeV(pol.), LH2 target (unpol.)* IB=3375/6000A, Oct. 2001-Jan. 2002


Cross Section (φ*)

Cross Section (φ*)

Blue shade : systematic uncertainty estimation

Red data : CRS with new analysis


T L T L

TTTT0E 0E insensitive !insensitive !

0E 0E sensitive !sensitive !


0E 0E sensitive !sensitive !LTLT


*0 1 1(cos )T L T L

T L L D D P

0TT

TT D

1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G


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 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




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


1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G


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




2 2 2 2 2 22 22 22 2 2 2 4 2

0 0 1 22 2 2 2 2 2


N N N


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


N N N


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


f W m

2 21 1 1 22 2 2

41Re Re

A i fT L N NM L N E

N


f W m

0 0 2 12 2 2

1Re 4 Re

A i fLT N NN M E

N


f W m

0 0 2 12 2 2

1Re 4 Re

A i fLT N NN M E

N


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


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


f W m

/ /0 0 2 12 2 2

1Im 4 Im

A i fLT N NN M E

N


f W m


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


• 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


• 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.


1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G


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 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




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


1 1N nG G

1 1N nG G

2 2N nG G

2 2N nG G


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




2 2 2 2 2 22 22 22 2 2 2 4 2

0 0 1 22 2 2 2 2 2


N N N


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


N N N


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


f W m

2 21 1 1 22 2 2

41Re Re

A i fT L N NM L N E

N


f W m

0 0 2 12 2 2

1Re 4 Re

A i fLT N NN M E

N


f W m

0 0 2 12 2 2

1Re 4 Re

A i fLT N NN M E

N


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


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


f W m

/ /0 0 2 12 2 2

1Im 4 Im

A i fLT N NN M E

N


f W m


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


Q2 dependence of the scaled cross section for three different W bins

dashsolid


measurement of generalized form factors near the pion threshold

Documents

hadron properties

hadron form factor

f3 f4 h4

f3 f4 h3

f3 f4 h2

m1 m1 f3

f3 f4 h5

h3 h4