the role of higher twists in determining polarized parton densities e. leader (london), a. sidorov...
TRANSCRIPT
The Role of Higher Twists in Determining
Polarized Parton Densities
E. Leader (London), A. Sidorov (Dubna), D. Stamenov (Sofia)
10th International Workshop on HIGH ENERGY SPIN PHYSICS Dubna, September 16-20, 2003
?! effects HT of role e th2Q lowat are datapresent theoflot A
OUTLINE
data DIS fromG and )(
data DIS (neutrino)current charged NO are There
inclusive qq
Peculiarity of the polarized DIS
+ HTpQCD1g analysis of Method
densitiesparton polarized NLO effects, HT - Results
fit data the toapproachesdifferent
experiment andeory between th Connection
To separate q and q SIDIS, W production
Axial (gluon) anomaly
_
Conclusions
HT effects
one of the best tools to study
the structure of nucleon
Inclusive DIS
Q2 = -q2 = 4EE`sin2 l`
l k`
k
N
x = Q2/(2M)
P
q = E – E`
Fi(x, Q2) gi(x, Q2)
unpolarized SF polarized SF
DIS regime ==> Q2 >> M2, >> M
DIS Cross Section Asymmetries
Measured quantities ,||
dd
ddA
dd
ddA |
)()()(2121 | ||
, , , ggAAAA where A1, A2 are the virtual photon-nucleon asymmetries.
At present, A|| is much better measured than A
If A|| and A are measured Fg 11/
If only A|| is measured 1
121 )1( | |
Fg
AD
AN
2222 /4 QxM N - kinematic factor
NB. cannot be neglected in the SLAC, HERMES and JLab kinematic regions
As in the unpolarized case the main goal is:
to test QCD
to extract from the DIS data the polarized PD
)Qx,(G)Qx,(G )QG(x,
)Qx,(q)Qx,(q )Q(x,q
)Qx,(q)Qx,(q )Qq(x,
222
222
222
where "+" and "-" denote the helicity of the parton, along or opposite to the helicity of the parent nucleon, respectively.
The knowledge of the polarized PD will help us:
to make predictions for other processes like polarizedhadron-hadron reactions, etc.
more generally, to answer the question how the helicityof the nucleon is divided up among its constituents:
Sz = 1/2 = 1/2 (Q2) + G (Q2) + Lz (Q2)
= ssdduu
the parton polarizations q a and G are the first moments
1
0
22a ),()(QΔq Qxqdx a
1
0
22 ),()ΔG(Q QxGdx
of the helicity densities: ),( ,),(),,( 222 QxGQxuQxu
_
DIFFICULTIES, specific for the polarized case
futurenear in data DIS ) (current charged
be NOT willand NO are There
neutrino
]determined principle,in be,cannot , and ,[
data DIS fromG and )( inclusive dudu
VV
In order to extract q (qV) and q
Semi-inclusive DIS data (SMC, HERMES)
)],(),([2
1),( 2222
1 QxqQxqeQxgfN
qqLO
f
fh QzxA
),,( 2
1
ef2 qf(x,Q2) Df
h (z,Q2)
ef2 qf(x,Q2) Df
h (z,Q2)
Semi-inclusive Asymmetries
Fragmentation functions
In LO QCD
Extra uncertainty in SIDIS Dhq(z,Q2)
Progress in determining Dhq (Kretzer, Leader, Christova)
du DD , well constrained now (in LO QCD)
sD is undetermined within a factor 2 !
N.B. In the unpolarized case we have never used SIDIS in order to determined PD !
In order to extract correctly the polarized PD from SIDIS data,well determined FF are needed. Although this research is in progress,this is still NOT done at present for all FF.
22 Wand lowat are datapresent theoflot A Q
2222 4 , 51 GeVWGeVQ
HT corrections should be important !
An important difference between the kinematic regions of the unpolarized and polarized data sets
While in the determination of the PD in the unpolarized case we can cut the low Q2 and W2 data in order to eliminate the less known non-perturbative HT effects, it is impossible to perform such a procedure for the present data on the spin-dependent structure functions without loosing too much information.
)/1( 2QO
DATA CERN EMC - p1A SMC - dp
11 A ,A
DESY HERMES -n1
1
1 A ,p
p
F
g
SLAC E142, E154 -n1A E143, E155 - d
d
p
p
F
g
F
g
1
1
1
1 ,
185 exp. p.
The data on are really the experimental values of the quantity1A
N
N
F
g
1
12 )1(
NN
NN
NN
AA
AF
g
D
A
21
21
12
)()1(
very well approximated witheven when can not been neglected
small and 2A
Theory In QCD HTLT QxQxQx ),(g),(g),(g 21
21
21
22TMC /),(h QQxtarget mass corrections which are calculable J. Blumlein, A.Tkabladze
2221 /),(h),(g QQxQx HT
]2
)()
2)(
1()[(21
),(22
221
f
Gsq
sN
qqpQCD N
CG
QC
QqqeQxg
f
functionst coefficien , WilsonCC Gq
In NLO pQCD
dynamical HT power corrections => non-perturbative effects (model dependent)
polarized PD evolve in Q2
according to NLO DGLAP eqs.
pQCDLT QxQx ),(g),(g 21
21
Factorization scheme dependence
Beyond the LO approximation the PD are scheme depended !
In the unpolarized case )()()( 21 sschemenschemen OPDMPDM
In the polarized case because of the gluon anomaly 1
0 222
)(
1~),()(
QQxGdxQG
s
n=1
qΔfor least at
ion,approximat bad a is LO 0.01 0.1 1
-0.03
-0.02
-0.01
0.00
__
x
Q2 = 1 GeV2
xs
JET MS
80.0 , Gss
)1()(
)(2
)()(
)1()()(
2)(
)()()(
2
22
2
2
22
OQ
QGQ
NQ
OQss
GQ
Qssss
MS
sfMSJET
MS
sMSJET
the bigger the differenceThe larger G
On theoretical grounds we prefer to use the JET scheme(all hard effects are absorbed in the Wilson coefficient functions).
Carlitz, Collins, Mueller (1988)Efremov, Teryaev (1989); Muller, Teryaev (1997)Anselmino, Efremov, Leader (1995)
In the JET scheme (as well as in AB scheme)
22 Q oft inpedenden are ),ss( as wellas ,)( Q
it is meaningful to directly interpret as the contribution of the quark spins to the nucleon spin and to compare its value obtained from DIS region with the predictions of the different (constituent, chiral, etc.) quark models at low .2Q
0.2 0.4 0.6 0.8-1.5
-1.0
-0.5
0.0
0.5
World data + JLab + HERMES/d (prel.)
x
deuteron-1.5
-1.0
-0.5
0.0
0.5 neutron-1.5
-1.0
-0.5
0.0
0.5
hA1 (
x)
[GeV
2 ]
NLO JET
proton
Connection between Theory and Experiment
GRSV, LSS
LT
LT
QxFQxg
QxFQxg
),(),(
),(),(
21
21
exp
21
21
LT
LT
QxFQxg
QxA),(),(
)1(),( 21
212
exp2
1
221
212
exp2
1
)(),(),(
)1(),(1
Qxh
QxFQxg
QxAA
LT
LT
effects. HT tosensitive less
are way by this extracted PPD theand Fg
ratio in the
other each compensate F and toscorrection HT The
1
1
11g
0)(1 xhA
E.Leader, A.Sidorov, D.Stamenov [hep-ph/0212085] Eur. Phys. J. C23, 479 (2002)
0.4 0.6 0.8 1.0-0.1
0.0
0.1
0.2 Q2 [GeV2] 4.83
3.52
2.71
g1
n/F1
n
X
JLAB'03 (preliminary) LSS 2001(NLO/JET)
Eur. Phys. J. C23, 479 (2002)
significant improvement of the precision of the data
-LSS 2001 (Q2 = 5 GeV2)
[21] Leader,Sidorov,Stamenov, Euro Phys. J. C23, 479 (2002)
PD polarized NLO(JET) LSS'2001 theusing /Fg
of valuesalexperiment JLAB for the spredictionOur n
1n1
JLab: nucl-ex/0308011
0.01 0.1 1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
g 1d /F1d
X
E143 (SLAC) HERMES (preliminary)
(g1
LT+h/Q2)/F1
exp
Very recent (unpublished) results from the fit to theworld data including the JLab and HERMES/d data
a very good description of the HERMES/d data
2=11.0 for 18 points
PD( g1NLO+ HT) practically do NOT change !!
Ch. Weiskopf 02-043 Thesis (2002)
SMC; Blumlein, Bottcher
)1(
]),(1[2
),(),(
),(),(
2exp
2
exp2
2
21
exp
21
21
QxRx
QxFQxg
QxFQxg LT
]),(1[2),(),(
),( exp2
exp2
2
21
exp2
1 QxRxQxFQxg
QxA LT
)GRSV(fit in the important and sizeable be tofound is
(x)hon contributi 'ist'higher tw e``effectiv thecase In this 1A
fits data into included be tohave ,(x)/Qh ,g to
scorrection HT thedata, g from PPD correctly extract To21g
1
1
case in this negligible NOT also is (x)h that found have We
.)F( Fin which procedure a used have
Sassot Florian, de AAC;
1A
LT2exp 2
(GRSV)
METHOD of ANALYSIS
)1(
]),(1[2
),(/)(),(
),(),(
2exp
2
exp2
2
221
exp
21
21
QxRx
QxFQxhQxg
QxFQxg N
LT
]),(1[2),(
/)(),(),( exp
2
exp2
2
221
exp2
1 QxRxQxF
QxhQxgQxA
NLT
data thefit to a from determined be to)5,2,1( 10)(),( iparametersxhxh in
ip
Input parton densities
4)1,2,(i . , , 1 220 parfreeAGeVQ ii
),(),( 20
20 QxfxAQxf MRST
iiii
8-2(SR) = 6 par. associated with PD
moments its from )Q(x,g calculate to
usedbeen has methodtion transforma-Mellin inverse The
LT2N
1
R1998 (SLAC)NMC
HT to g1 included in model independent way
The sum rule (1) reflects the isospin SU(2) symmetry, whereas the relation (2) is a consequence of the SU(3) flavour symmetry treatment of the hyperon -decays.
While isospin symmetry is not in doubt, there is some questionabout the accuracy of assuming SU(3)f symmetry in analyzing
hyperon -decays. The results of the recent KTeV experiment
at Fermilab on the -decay of , however, are all consistent with exact SU(3)f symmetry. Taking into account the experimental uncertainties one finds that SU(3)f breaking is at most of order 20%.
SR for n=1 moments of PD
DFQss
QddQuua
3))((2
))(())((2
228
))(())(( 22 QddQuug A .00351.2670
025.0585.0
(1)
(2)
e 0
0.051.32 fg .210
0.17-1
1
KTeV experiment Fermilab
e 0
-decay
SU(3)f prediction for the form factor ratio g1/f1
Experimental result
.00351.2670g fg
A1
1
A good agreement with the exact SU(3)f symmetry !
From exp. uncertainties SU(3) breaking is at most of order 20%
RESULTS OF ANALYSIS
Kinematic region - 185 exp. p.
Quality of the fits
0.01 0.1 10.0
0.2
0.4
0.6
0.8
0.1 1
-0.4
-0.2
0.0
0.2
0.4
0.01 0.1 10.0
0.2
0.4
0.6
0.8
0.1 1
-0.4
-0.2
0.0
0.2
0.4
0.01 0.1 10.0
0.2
0.4
0.6
0.8
0.1 1-0.6
-0.4
-0.2
0.0
0.2
0.4
SMCAp
1E142An
1
E143
gp
1 / Fp
1E154An
1
neutronproton
HERMES
gp
1 / Fp
1
X X
HERMES
An
1
22 GeV 58 Q <1 0.75 x 0.005
achieved. is data g and A
world theofn descriptio goodA very
11
885.0 NLO(JET)
892.0 LO 2
,
2,
NLODF
LODF
LSS, Phys. Rev. D67 (2003) 074017
NLO JET
Higher twist effects
Fit LO
HT=0
NLO
HT=0
LO+HT NLO+HT
244.5 218.8 150.7 145.0
DF 185-6 185-6 185-16 185-16
1.36 1.22 0.892 0.858DF/2
2
targeton the depends HT of shape The 221
21 /)(),(),( QxhQxgQxg N
LT
0.5
-0.2
-0.1
0.0
0.1
0.2
0.3Proton
LO NLO JET
hg 1 (x)
[G
eV2 ]
0.0 0.5 1.0
-0.2
-0.1
0.0
0.1
0.2
0.3
Neutron
0.0 0.5 1.0
-0.2
-0.1
0.0
0.1
0.2
0.3
0.5 1.0
-0. 2
-0. 1
0.0
0.1
0.2
0.3
X
negligible NOT is g toscorrection HT of size The 1
scorrection HTon of Dependence 2
0.0 0.2 0.4 0.6 0.8
-0.1
0.0
0.1
0.2
0.3
NLO JET
x
Neutron
0 .0 0 .2 0 .4 0 .6 0 .8
-0.1
0.0
0.1
0.2
0.3World dataWorld data + JLab (prel)
+ HERMES/d (prel)
hg 1 (x)
[GeV
2 ]
Proton
HT corrections to g1 are better determined now, especially for the neutron target
LSS, hep-ph/0309048
? resultsst higher twi theinfluence )(gfor
schemeion factorizat theof choice theHow
LT1
LT1)(gin effects NNLO
theof estimationan
0.0 0.2 0.4 0.6 0.8 1.0
-0.1
0.0
0.1
0.2
0.3Neutron
X
0.0 0.2 0.4 0.6 0.8 1.0
-0.1
0.0
0.1
0.2___ NLO JET
NLO MS
hg 1 (x)
[G
eV2 ]
Proton
221
21 /)(),(),( QxhQxgQxg N
LT
0.01 0.1 1
0.0
0.1
0.2
0.3
0.4
PD(g1
NLO/F1
NLO)
x
xG(x)
0.01 0.1 1
-0.4
-0.3
-0.2
-0.1
0.0
x
-x(d+d)
0.01 0.1 1
-0.2
-0.1
0.0
x
-x(s+s)
0.01 0.1 10.0
0.1
0.2
0.3
0.4
x
PD (g1
NLO + HT)
-x(u+u)
NLO polarized PD
determined well)d+ d(),u+u (
0.58=D-3F=a
valuesymmetric SU(3) its afor accept if
determined wellreasonably )s+s(
8
8
large be toseemsit but
d,constraine not wellG
)/()( 111NLONLONLO FgPDHTgPD
859.0858.0 2,
2, NLODFNLODF
!account into taken be tohave
g toscorrection HT then the
R and )(F viaexpressed is F If
1
expexp21
G and )( data DIS From inclusive qq
NLO(JET) 22 1GeVQ
0.07 0.14 )()(Qa
0.05 0.15 - )()ss( 22
0
2
MS
MS
Q
Q
0.06 0.32
0.48 0.80 )G(Q
0.03 0.09 - )ss(
0.04 0.43- ))(Qdd(
0.03 0.84 ))(Quu(
2
2
2
JET
N.B. In JET scheme as well as , do NOT depend on Q2.
n=1 moments of PD, JET scheme, Q2=1 GeV2
the correlations between the parameters are taken into account
1/2 = ½ + + Lz = 0.96 + Lz
Lz is negative
Spin sum rule:
)( ss
~ 0.6 at Q2 ~ 0 in relativistic CQM
Non-negative s would imply a total breaking of SUf(3) flavor symmetry
in hyperon -decays, which contradicts to the present data.
New HERMES data on (hep-ex/0307064)
Extra uncertainty in SIDIS Dhq(z,Q2)
Progress in determining Dhq (Kretzer, Leader, Christova)
du DD , well constrained now (in LO QCD)
sD is undetermined within a factor 2 !
)(,1
)(,1 , KK
dd AA
01.003.003.0 sLO QCD: <Q2 > = 2.5 GeV2
In all analyses of inclusive DIS data, it is found that s is negative.
01.006.0 sLO QCD: at Q2 = 4 GeV2 (Blumlein, Bottcher)
Also, if 0s 2.08 a
)025.0585.0( 8 a
2.0328 DFsdua
CONCLUSIONS
The fit to the present data on g1 is essentially improved, especially in the LO case, when the higher twist termsare included in the analysis.
The size of HT corrections have been extracted from thedata in model independent way
)( 1 HTgPD LT )/( 11LTLT FgPDwell consistent with
To extract correctly the polarized PD from the g1 data,
the HT corrections to g1 have to be taken into account in the analysis.
Inclusive DIS measurements are sensitive only to
thus a new probe is needed to separate quark
and anti-quark polarized PD from SIDIS, W production
(HERMES, COMPASS, RHIC)
Given the limited range and precision of present g1(x,Q2) measurements, one would like
a direct measurement of G (COMPASS, RHIC)
MORE GENERALLY
)qq(
Data at larger Q2 and smaller x would be very important
for our understanding of the spin properties of the nucleon.