The Role of Higher Twists in Determining

Polarized Parton Densities

E. Leader (London), A. Sidorov (Dubna), D. Stamenov (Sofia)

12th International Workshop on Deep Inelastic ScatteringStrbske Pleso, Slovakia, April 14-18, 2004

?! 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

pQCD

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

If only A|| is measured 1

12 )1(~ | |

F

g

D

A

2222 /4 QxM N - kinematic factor

NB. cannot be neglected in the SLAC, HERMES and JLab kinematic regions

1

1 F

g

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

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 - ,A , n1

1

1p

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

(preliminary)

JLab Hall A n

n

F

g

1

1

d

d

F

g

1

1

206 exp. p.

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/0309048]

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/Hall A: PRL 92 (2004) 012004

JLab/Hall A

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

Recent results from the fit to the world data including the JLab and HERMES/d data

a very good description of the HERMES/d data

2=11.8 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

858.0 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

negligible NOT is g toscorrection HT of size The 1

scorrection HTon of Dependence 2

If JLab/Hall A and HERMES/d data are included in the analysis, the HT corrections to g1 are better determined, especially for the neutron target

? resultsst higher twi theinfluence )(gfor

schemeion factorizat theof choice theHow

LT1

LT1)(gin effects NNLO

theof estimationan

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 ~

in relativistic CQM

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/Hall A: PRL 92 (2004) 012004

JLab/Hall A

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

Recent results from the fit to the world data including the JLab and HERMES/d data

a very good description of the HERMES/d data

2=11.8 for 18 points

PD( g1NLO+ HT) practically do NOT change !!

Ch. Weiskopf 02-043 Thesis (2002)

2n-p1

2p1

2n1

0.012]GeV [-0.042

]GeV 0.010 [0.007

GeV ] 0.007 [0.049

dxxh pp 75.0

005.0

1 )( dxxh pn 60.0

015.0

1 )(

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

In some Bag models0

small

negative

In agreement withInstanton approach

The first moments of HT

A.S., Chr. Weiss in preparation

dxxQg pp 1

0

211 ),(

585.038 DFa

0.07 0.15-

SU(3) SU(3)

CLAS Coll/, Phys.Rev.Lett.91:222002,2003

at Q2=0.99 and 1.20 GeV2

World data on g1 2 points

CONCLUSIONS

The fit to the present data on g1 is essentially improved, especially in the LO case, when the higher twist terms of g1

are included in the analysis

The size of HT corrections have been extracted from thedata in model independent way and found to be NOT negligible

To extract correctly the polarized PD from the g1 data,

the HT corrections to g1 have to be taken into account in the analysis.

The HT corrections to g1 and F1 compensate each other in g1/F1

)( 1 HTgPD LT well consistent with )/( 11LTLT FgPD

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.