Download - Twist 4 Matrix elements
![Page 1: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/1.jpg)
1
Twist 4 Matrix elements
Su Houng Lee 1. S. Choi et al, PLB 312 (1993) 3512. Su Houng Lee, PRD 49 (1994) 2242 3. Su Houng Lee, PRC 57 (1998) 927
![Page 2: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/2.jpg)
2S H Lee
DIS
Relation to Polarization Tensors
Some basics on matrix elements and moments
MQWQWdd
dEdd
M
2/,2
tan,2'
22
221
MWQxF
WQWQxFL2/,
/1,
22
2
222
12
24 de |0|
21 FFpjyjpyedW L
iqy
n
nn2,nL,
4 1/ Md Me |]0T[| xpjyjpyediT iqy
1
0
22-nn ),(M Im QxFdxxTW
1
02
24222-n
2
4n2
n),(),(MM
QQxFQxFdxx
Q
e (E,k)
X
e (E’,k’)
P
q 2
2
22
,/1or
,or
,2/
Qx
Q
QqpQx
x/1
![Page 3: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/3.jpg)
3S H Lee
Diagrammatic rep of Structure function
Diagrammatic rep of OPE
X
P
24 de |0|
21 FFpjxjpxedW L
iqx
n
nn2,nL,
OPE4 Md Me |]00,T[| pQxQxpxediT iqx
P
P
x 0Q Q
P
n
P P
0 0
Q Q
OPE n
1
0
22
2-n1
0
22-n ),( ),( QxFdxxQxFdxx L
![Page 4: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/4.jpg)
4S H Lee
Twist-2 Operators (LO)
|]00,T[|4 pQxQxpxediT iqx
P P
00
Q Q pDQpM |0| 22
2
02 LM
Twist-4 Operators
P P
00
Q Q
P P
00
Q Q
2
5, QFDigg aa
aaA
AAg
iQiQg
2
552
aaaa
V
VVgQg
FDQg
222
22
],[
Politzer (80), Shuryak, Vainshtein (81) , Jaffe, Soldate (81)
![Page 5: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/5.jpg)
5S H Lee
Twist-4 Operators
OPE
gVgVA MM
QxMMM
QxT
83
411e
161
851d 2222
Operators
kP
k Mgmpp
2
41
25
2
2
, QFDig
VVg
AAg
g
aaV
aaA
mass Operators
2QDDmm
mm M
QxM
QxT
4181e
3141d 2222
gVL
gVA
MMdxF
MMMdxF
83
41
21
161
85
21
1
0
4
1
0
42
Politzer (80), Shuryak, Vainshtein (81) , Jaffe, Soldate (81)
Lee (94)
![Page 6: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/6.jpg)
6S H Lee
Parameterizing F2 (=4)
For Cp: BCDMSdata and SLAC data +Virchauz,Milsztajin, PLB274 (92) 221
For Cp-Cn: NMC (combining NMC,SLAC, BCDMSdata)
75.007.0 ,, 222
42 xQxFxCF p
87.18 ,11.33 ,88.16 ,33.3 ,27.0 ,4.0 43210 aaaaab
0 ,1
44
33
2210
b
xxaxaxaxaaxC bp
• We fit to
75.007.0 1 2
2
2
2
2
2
xQ
xCxCFF
FF np
p
n
p
n
• We fit to 96.10 ,44.22 ,32.12 ,14.3 ,27.0 ,4.0 43210 aaaaab
2
23
211)1( :SoldateQxxxF
2
2
23
2111)1( :al.et Gunion Qx
QxxxF
![Page 7: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/7.jpg)
7S H Lee
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
6.02.0 x
![Page 8: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/8.jpg)
8S H Lee
Constraints for matrix elements from experiments
(neutron) GeV 004.0011.0(proton) GeV 004.0005.0
161
85
21
2
21
0
42
gVA MMMdxF
(neutron) GeV 008.0023.0(proton) GeV 012.0035.0
83
41
21
2
21
0
4 gVL MMdxF
Note that the matrix elements A’s for the proton and neutron data are independent.
AM VM
gM gM
proton
neutrondata
proton
neutronMIT Bag
2GeV 1.0 ,12.0 ,6.0,, solution typicalOne gVA MMM
1.0
1.0
![Page 9: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/9.jpg)
9S H Lee
MIT Bag model calculations (Jaffe-Soldate 81)
Definitions
ppm
M
MgMpp
kii
k
N
k
kP
k
|31|2
41
00
2
Calculations
B 0,E ,)(
urgr
rfx • operators
• Normalizations by Jaffe (75)
||21
|0|21
34
4
pyjxjpyexdd
pjxjpxedW
yxiq
iqx
pyypydm
M kii
k
N
k |31|2
003
Vpppp '2'| 33
![Page 10: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/10.jpg)
10S H Lee
Calculations- cont
25
22
552
, QFDig
Qg
QiQig
g
aaV
aaA
• calculations involve spin and spatial parts
pyypydm
M kii
k
N
k |31|2
003
rgrfdrrrgrfdrr 2222222 ,
![Page 11: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/11.jpg)
11S H Lee
MIT Bag model vs experimental constraint
F2: Q2=5 GeV2 s = 0.5
(neutron) GeV 015.0(proton) GeV 027.0
Bag MIT 2
2
s
s
(neutron) GeV 008.0023.0(proton) GeV 012.0035.0
Experiment2
2
gVA MMMdxF
161
85
211
0
42
(neutron) GeV 026.0(proton) GeV 022.0
Bag MIT 2
2
s
s
FL: Q2=5 GeV2 s = 0.5
(neutron) GeV 004.0011.0(proton) GeV 004.0005.0
Experiment2
2
075.0
161064.0
85018.0
21
gV
L MMdxF83
41
211
0
4
075.0
83064.0
41
21
1.0
16112.0
8506.0
21 Typical numbers
1.0
8312.0
41
21
Typical numbers
![Page 12: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/12.jpg)
12S H Lee
a) Bag model calculations only measures correlations between valance quarks
c) Non-trivial test of low energy models of hadrons and QCD
b) Need much more correlation such as
Need more correlations
![Page 13: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/13.jpg)
13S H Lee
A Parameterization based on flavor structure
gudd
gduu
gnp
Vudd
Vduu
Vnp
Auddu
Audd
Aduu
Anp
KQKQM
KQKQM
KQQKQKQM
)(2
)(2
)(
)(2
)(2
)(
2)(
2)(
2)( 2/
pqFDqpMigK
pdduuqiqpM
K
pdiduiupM
K
pdiduiuqiqpM
K
gq
Vq
Aud
Aq
|,|2
||2
|2|2
||2
52
52
552
5552
• Unknowns:: 7 • Constraints: F2 (Proton, Neutron),FL,(proton, neutron) 4
Flavor Structure
Flavor Assumptions
xxuxux
xxdxdx
KK
KK
KK
gu
gd
Vu
Vd
Au
Ad
d)()(
d)()(
• Unknowns:: 7-3 = 4 • Constraints: F2 (Proton, Neutron),FL,(proton) 3
Au
Aud
Ad KKK
![Page 14: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/14.jpg)
14S H Lee
puFDupMigK
pdduuuupM
KpdiduiuuupM
K
gu
Au
Au
|,|2
||2 ,||2
52
2555
2
Typical Result
KuA Ku
V Kug
0.173 GeV2 0.203 -0.2380.112 0.110 -0.3000.083 0.066 -0.329
2552 GeV 083.0||2
pdiduupM
K Aud
2GeV 1.0 ,12.0 ,6.0,, solution typicalOne gVA MMM
![Page 15: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/15.jpg)
15S H Lee
1. Twist-4 matrix elements are interesting itself because, a) First experimental measurements of multiparticle correlation inside
proton b) Old data seems to suggest need much more correlation than
such as
Summary - i
![Page 16: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/16.jpg)
16S H Lee
2. Twist-4 matrix elements are relevant for Vector and Axial vector in medium
Summary - ii
.....0),(
.....0),(
44
44
AVAAVOPEiqxAA
AVVAVOPEiqxVV
KKQcKK
QcpertAxATdxe
KKQcKK
QcpertVxVTdxe
22
1,
2
0,
21,
0,,
)()0,(
)()0,(
0,0,, Re
qs
ss
sds
TLTL
TLTLVVTL
99) (SHLmatter nuclear at ,0)( to ofon contributi Nontrivial 1TL, AVKK
![Page 17: Twist 4 Matrix elements](https://reader036.vdocuments.us/reader036/viewer/2022062222/568163bf550346895dd4deb7/html5/thumbnails/17.jpg)
17S H Lee
2. Analysis suggests Large cancellation in Twist-4 effect in F2
Summary - iii
(neutron) GeV 004.0011.0(proton) GeV 004.0005.0
2
2
(neutron) GeV 008.0023.0(proton) GeV 012.0035.0
,2
21
0
24 dxQxFL
1.0
16112.0
8506.0
21
gVA MMMdxF
161
85
211
0
42
3. OPE suggests Large Twist-4 effect in FL and proportional to Twist-2
,8 222
24 QxFFL