Electroproduction of
soft pions at high Q2
Axial Form Factor Physics at CLAS
May. 29,
2008
Kijun Park
Univ. of South Carolina
Perspective of soft pion in terms of Q2 at threshold
2
Q ~ 0GeV
2
Kroll-Ruderman
1954
Low-Energy Theorem (LET) for Q2=0
Restriction to the charged pion
χral symmetry + current algebra for electroproduction
Q   / m GeV (~ 1GeV )
2
2
Re-derived LETs
Current algebra + PCAC
χral perturbation theory
1960s
Nambu, Laurie, Schrauner
2
1970s
Vainshtein, Zakharov
Q   / m
1990s
Scherer, Koch
2
pQCD factorization methods
Brodsky, Lepage, Efremov, Radyunshkin, Pobylitsa, Polyakov, Strikman, et al
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Perspective of soft pion in terms of Q2 at threshold
Q ~ 1  10GeV
2
2
Light Corn Sum Rule
Reproduce LET for Q2 ~ 1GeV2
Reproduce pQCD for Q2→∞
Extended for near pion threshold regions
Axial Vector & Tensor Form Factor
May. 29, 2008
V. Braun
2007
K. Park
Correlation Function
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
LCSR- based model for the Q2 dependence of the electric,
longitudinal Partial Waves at threshold [GeV-1]
GD (Q 2 )  1/(1  Q 2 / 02 )2
02  0.71GeV 2
Light Cone Sum Rule
V. M. Braun,
arXiv:0709.2319v1
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
LCSR- based model for the Q2 dependence of the electric,
longitudinal Partial Waves at threshold [GeV-1]
GD (Q 2 )  1/(1  Q 2 / 02 )2
02  0.71GeV 2
Light Cone Sum Rule
V. M. Braun,
arXiv:0709.2319v1
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Differential Cross section
 em k f d 
2
d  * 
| |
2
2
8 W W  mN
|  |   T   L   TT cos(2 )  2 (1   ) LT cos( )
2
 2 (1   ) LT ' sin( )
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Partial Wave Series with Legendre Polynomials
from S.F.
Structure Functions vs. Legendre moments
E0 Sensitive !
E0 Insensitive ! l  1
E0 Sensitive !
Legendre moments vs. Multipoles
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Legendre moments vs. Form Factors
N
1
G
G
N
2
GM G E
A0  D0T  L
T L
1
A1  D
1
 2
f
2 2
2
 4k 2Q 2  N 2 c2 g A2 k f 2 2 2 2


4
c
g
k
2
 A f
2
N
4
2
i
Q mN GM   L  ki G2  2
mN GE 
 2 G1  2
2
2


W  mN
W  mN
 mN



1 4c g A ki k f
2
N
2
N
 2
Q
G
Re
G


m
G
Re
G
 1  L N E  2 
M
f W 2  mN2

C0  C0TT  0
D0  D
LT
0

1 c g A ki k f
N
N
 2
Qm
G
Re
G

4
G
Re
G
 2  E  1 
N
M
f W 2  mN2
Axial Vector & Tensor Form Factor

May. 29, 2008
K. Park
Legendre moments vs. Form Factors
N
1
G
G
N
2
GM G E
A0  D0T  L
T L
1
A1  D
1
 2
f
2 2
2
 4k 2Q 2  N 2 c2 g A2 k f 2 2 2 2


4
c
g
k
2
 A f
2
N
4
2
i
Q mN GM   L  ki G2  2
mN GE 
 2 G1  2
2
2


W  mN
W  mN
 mN



1 4c g A ki k f
2
N
2
N
 2
Q
G
Re
G


m
G
Re
G
 1  L N E  2 
M
f W 2  mN2

C0  C0TT  0
D0  D
LT
0

1 c g A ki k f
N
N
 2
Qm
G
Re
G

4
G
Re
G
 2  E  1 
N
M
f W 2  mN2
Axial Vector & Tensor Form Factor

May. 29, 2008
K. Park
Kinematical Coverage
* E=5.754GeV, LH2 target(unpol.)
* Oct. 2001-Jan. 2002
Variable
Unit
Range
# Bin
Width
Q2
GeV2
2.05 ~ 4.16
5
various
W
GeV
1.11 ~ 1.13
3
0.02
-1.0~ 1.0
10
0.2
0. ~ 360.
12
30
cosθ*π
φ *π
Deg.
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Analysis -detail




Cross check Acceptance calculation
- Based on phase space event generator
- GENEV
Re-calculation of Rad. Corr.
- Based on new binning (12φ) from ExcluRad
Study of ExcluRad model dependence
- MAID2003 vs. Sato-Lee 2004
Apply more tight physics cuts
- electron, pion fiducial cuts
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Analysis -detail
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Preliminary
Cross section (φ*)
•
φ* – dependent cross
section in term of W, Q2,
cosθ*
•
Various physics models
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Preliminary
Cross section (φ*)
•
φ* – dependent cross
section in term of W, Q2,
cosθ*
•
Various physics models
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Preliminary
Cross section (φ*)
•
φ* – dependent cross
section in term of W, Q2,
cosθ*
•
Various physics models
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Preliminary
Cross section (φ*)
•
φ* – dependent cross
section in term of W, Q2,
cosθ*
•
Various physics models
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Preliminary
Cross section (φ*)
•
φ* – dependent cross
section in term of W, Q2,
cosθ*
•
Various physics models
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary
results
Preliminary
Structure
Function
 T   L
E0
Sensitive !
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary
results
Preliminary
Structure
Function
 TT
E0
Sensitive !
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary
results
Preliminary
Structure
Function
 LT
E0
Insensitive !
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Legendre Moments (T+L)
Preliminary
Preliminary
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Legendre Moments (TT)
Preliminary
Preliminary
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Preliminary results
Legendre Moments (LT)
Preliminary
Preliminary
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Legendre moments vs. Form Factors for nπ+channel
 n
1
 n
N
1
N
G G
G2  G2
GM  G
GE  G  0
n
M
n
E
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 m  0
Q2  n g A
Q2
1
n
G1 
GM  GA
2
2
2
mN
2
2 Q  2mN

 n
2
G
2
N
2
N
2 2 g Am n
 2
GE  0?
Q  2m
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Legendre moments vs. Form Factors for nπ+channel
 n
1
 n
N
1
N
G G
G2  G2
GM  G
GE  G  0
Assumption in LCSR
V.Braun
arXiv:0710.3265
n
M
n
E
Due to low-energy theorem(LET) relates the S-wave
multipoles or equivalently, the form factor G1, G2 @
threshold m  0
Q2  n g A
Q2
1
n
G1 
GM  GA
2
2
2
mN
2
2 Q  2mN

 n
2
G
2
N
2
N
2 2 g Am n
 2
GE  0?
Q  2m
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Legendre moments vs. Form Factors
 n
1
G
A0  D0T  L
T L
1
A1  D
1
 2
f
 n
2
G
GMn G En
2 2
2
 4k 2Q 2  N 2 c2 g A2 k f 2 2 2 2


4
c
g
k
2
 A f
2
N
4
2
i
Q mN GM   L  ki G2  2
mN GE 
 2 G1  2
2
2


W  mN
W  mN
 mN



1 4c g A ki k f
2
N
2
N
 2
Q
G
Re
G


m
G
Re
G
 1  L N E  2 
M
f W 2  mN2

C0  C0TT  0
D0  D
LT
0

1 c g A ki k f
N
N
 2
Qm
G
Re
G

4
G
Re
G
 2  E  1 
N
M
f W 2  mN2
Axial Vector & Tensor Form Factor

May. 29, 2008
K. Park
Legendre moments vs. Form Factors
 n
1
G
1
 2
f
A0  D0T  L
T L
1
A1  D
C0  C
TT
0
 n
2
G
GMn G En
 4k 2Q 2   n 2 c2 g A2 k f 2 2 2 n 2 
 2
Q m pGM 
 i 2 G1
2
W  mp
 m p


g A  1.267
 
1 4c g A ki k f
2 n
 n
 2
Q GM Re G1
2
2
f W  m p
c   2
f  93MeV
0
D0  D0LT  0
Axial Vector & Tensor Form Factor
 n
 x1  iy1
 n
 x2  iy2
G1
G2
May. 29, 2008
K. Park
Legendre moments vs. Form Factors
 n
1
G

 n
0
E
 n
0
L


 n
2
G
4 em Q
2
8
4 em Q
32
Q  4m
2
2
p
3
p 
m f
2
Q  4m
2
3
p 
m f
2
p
 n
1
G
 n
2
G
GD
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Very
Preliminary
results
Q2 dependence of
the Normalized
E0+ Multipole by
dipole
Lines : MAID07
Bold : Real
Thin : Imaginary
MAID03
SLee04
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
Summary and
Future plans
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 E0+/GD 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
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
MAID2007
Bold –Real part
Thin – Imaginary
part
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park
MAID2007
Bold –Real part
Thin – Imaginary
part
Axial Vector & Tensor Form Factor
May. 29, 2008
K. Park