twist 4 matrix elements
DESCRIPTION
Twist 4 Matrix elements. Su Houng Lee 1. S. Choi et al, PLB 312 (1993) 351 2. Su Houng Lee, PRD 49 (1994) 2242. Some basics on matrix elements and moments. DIS. e (E’,k’). e (E,k). X. P. Polarization Tensors. Where w =2pq/q 2. OPE. P. P. Diagrammatic rep of Structure function. - PowerPoint PPT PresentationTRANSCRIPT
1
Twist 4 Matrix elements
Su Houng Lee
1. S. Choi et al, PLB 312 (1993) 351
2. Su Houng Lee, PRD 49 (1994) 2242
S H Lee 2
DIS
Polarization Tensors
Some basics on matrix elements and moments
e (E,k)
X
e (E’,k’)
P
MQWQWd
d
dEd
d
M
2/,2
tan,2'
22
221
MWQxFWQWQxFL 2/, ,/1, 22
2222
12
24 de |0|
2
1FFpjxjpxedW L
iqx
n
nn2,nL,
4 Ad Ae |]0T[| pjxjpxediT iqx
1
0
22-nn ),(A Im QxFdxxTW
Where =2pq/q2
1
02
24222-n
2
4n2
n
),(),(
AA
Q
QxFQxFdxx
Q
S H Lee 3
Diagrammatic rep of Structure function
Diagrammatic rep of OPE
X
P
24 de |0|
2
1FFpjxjpxedW L
iqx
n
nn2,nL,
4 Ad Ae |]00,T[| pQxQxpxediT iqx
P
P
x 0Q Q
P P P
0 0
Q Q
OPE
S H Lee 4
Twist-2 Operators
|]00,T[|4 pQxQxpxediT iqx
P P
00
Q Q pDQpA |0| 22
2
02 LA
Twist-4 Operators
P P
00
Q Q
P P
00
Q Q
pFDQpAG |0],[| 524
pQQpA aa || 554
1
pQp
pFDQpA
aa ||
|0],[|
2
242
S H Lee 5
Twist-4 Operators
OPE
gg AA
QxAAA
QxT
8
3
4
11e
16
1
8
51d 2
2221
22
Operators
kP
k AgMppO
2
4
1
25
52
522
5521
, QFDigO
QgO
QQgO
g
aa
aa
mass Operators
2QDDmOm
mm A
QxA
QxT
4
181e
3
141d
2222
g
g
AAdxF
AAAdxF
8
3
4
1
2
1
16
1
8
5
2
1
21
0
42
211
0
42
S H Lee 6
Parameterizing F2 (=4)
For Cp: BCDMSdata and SLAC data +Virchauz,Milsztajin, PLB274 (92) 221
For Cp-Cn: NMC (combining NMC,SLAC, BCDMSdata)
222
42 ,QxFxCF p
87.18 ,11.33 ,88.16 ,33.3 ,27.0 ,4.0 43210 aaaaab
0 ,1
44
33
2210
b
x
xaxaxaxaaxC bp
• We fit to
2
2
2
2
2
2 1Q
xCxC
F
F
F
F np
p
n
p
n
• We fit to
96.10 ,44.22 ,32.12 ,14.3 ,27.0 ,4.0 43210 aaaaab
2
23
2
11)1( :Soldate
Q
xxxF
2
2
2
32
111)1( :al.et Gunion
Q
x
Q
xxxF
S H Lee 7
Parameterizing FL (=4)
Parameterization using transverse basis (Ellis, Furmanski, Petronzio 82)
2224 ,4 TTTL kxfkkdF
P P
00
Q Q
SLAC data analyzed by Sanchex Guillen etal. (91)
22222
24 GeV 01.003.0 ,8 QxFFL
34 1 1 Soldate xxFL
S H Lee 8
Constraints for matrix elements from experiments
(neutron) GeV 004.0011.0
(proton) GeV 004.0005.0
16
1
8
5
2
12
221
1
0
42
gAAAdxF
(neutron) GeV 008.0023.0
(proton) GeV 012.0035.0
8
3
4
1
2
12
22
1
0
4 gL AAdxF
Note that the matrix elements A’s for the proton and neutron data are independent.
1A 2A
gA gA
proton
neutrondata
proton
neutronMIT Bag
2221 MeV 300 GeV 1.0 solution typicalOne gAAA
S H Lee 9
MIT Bag model calculations (Jaffe-Soldate 81)
Definitions
pOOpM
A
AgMppO
kii
k
N
k
kP
k
|3
1|
2
4
1
00
2
Calculations
B 0,E ,)(
urgr
rfx • operators
• Normalizations by Jaffe (75)
||2
1
|0|2
1
34
4
pyjxjpyexdd
pjxjpxedW
yxiq
iqx
pyOyOpydM
A kii
k
N
k |3
1|
200
3
Vpppp '2'| 33
S H Lee 10
Calculations- cont
25
52
522
5521
, QFDigO
QgO
QQgO
g
aa
aa
• calculations involve spin and spatial parts
pyOyOpydM
A kii
k
N
k |3
1|
200
3
rgrfdrrrgrfdrr 2222222 ,
S H Lee 11
MIT Bag model vs experimental constraint
F2: Q2=5 GeV2 s = 0.5
(neutron) GeV 015.0
(proton) GeV 027.0
16
1
8
5
2
1 Bag MIT
2
221
1
0
42
s
sgAAAdxF
(neutron) GeV 008.0023.0
(proton) GeV 012.0035.0
8
3
4
1
2
1 Experiment
2
22
1
0
4 gL AAdxF
(neutron) GeV 004.0011.0
(proton) GeV 004.0005.0
16
1
8
5
2
1 Experiment
2
221
1
0
42
gAAAdxF
(neutron) GeV 026.0
(proton) GeV 022.0
8
3
4
1
2
1 Bag MIT
2
22
1
0
4
s
sgL AAdxF
FL: Q2=5 GeV2 s = 0.5
S H Lee 12
A Parameterization based on flavor structure
Flavor structure
gudd
gduu
gnp
uddduunp
udduuddduunp
KQKQA
KQKQA
KQQKQKQA
)(2
)(2
)(
2)(
22)(
22)(
121)(
21)(
21)( 2/
pdduupM
K
puFDupM
igK
pdduuuupM
K
iu
gu
iu
|2|2
|,|2
||2
2
52
2
• 7 Unknowns: F2,FL, proton, neutron target 4 constraints
S H Lee 13
1. Twist-4 matrix elements are interesting itself because,
a) First experimental measurements of multiparticle correlation inside proton
b) Need much more correlation than
such as
Summary - i
c) Non-trivial test of low energy models of QCD d) QCD sum rules for hadrons in nuclear matter
S H Lee 14
2. To answer the questions, need experimental update on
Summary - ii
(neutron) GeV 004.0011.0
(proton) GeV 004.0005.0,
2
21
0
242 dxQxF
(neutron) GeV 008.0023.0
(proton) GeV 012.0035.0,
2
21
0
24 dxQxFL