Unpolarized Semi-Inclusive Hadron Electroproduction with CLAS M. Osipenko HEP2010 workshop, January 5, 2010, Valparaíso, Chile.

Unpolarized Semi-Inclusive Hadron Electroproduction

with CLAS

M. OsipenkoHEP2010 workshop,

January 5, 2010,Valparaíso, Chile

2

Jefferson Lab

presently 0.6 GeVPresently0.6 GeV

E~0.8-6 GeVE/E~10-4

P~40-85%P/P~3%

I~1nA-200A

Continuous 3-beam 1.5 GHz

3

CLAS detector•4 detector operating at luminosity L~1034 cm-2s-1

•Charged particles detectionp/p~0.5-1%, /~1 mrad, e~15-

50•Neutral particles detection (E/E~10%),n (0.5<pn<2 GeV)•Particle identificatione/ separation, TOF (~200 ns)New inner calorimeter

4

Semi-inclusive Kinematics

( ) ( ) ( )V hq p P h p X

2( )ht q p

2 2Q q

~h h hp Pp Ez

q Pq

2

h

T T h

p qp p p q

q

????????????????????????????????????????????????????????

'h e

5 independent variables

Detect the scattered electron in coincidence with hadron h: e+pe'+h+X

Final state:

,h h hp E p

2 2

2 2

q Qx

qP M

,q k k q

In OPE approximation:

Four-momenta in Lab:

Initial state:

,0P M

1h hP

P p qpx

P qP

2( )ht P p or

or

5

Observables

5

1 2 3 42 22 cos cos 2

T

hEdN y

dxdQ dzdp d p

H H H H

2( , , , )i i x Q z tH H

3

1 2

(2 )cos

2

y

H

H H

Cross section is described by 4 functions of 4 variables:

Azimuthal asymmetries (moments):

4

1 2

cos 22

HH H

2

4

2N

xQ

beam

yE

2

2Mx

Q 2 21

14

y y 2xy

2

1

1

where

coscos

n dn

d

J.Levelt & P.Mulders, PRD49

2 max 222

2 2 2 20

TpT

h T

h h T

pH E dp

E m p

HpT-integrated cross section:

6

Semi-Inclusive Kinematical Domains

elastic peakepe’p’

resonances

•Exclusive production

•Inclusive production:

•MX<1÷2 GeV - Resonance region

•MX>1÷2 GeV - Deep Inelastic

Scattering (DIS)

•Q2<1 GeV2 † - Non-perturbative

•Q2>1 GeV2 † - Perturbative

•Current fragmentation

•Target fragmentation

inelastic

,

n

0

epe’p’X

epe’+X

J.P.Albanese et al.,PLB144

Y CMS rapidity

7

SIDIS: constant in

22 ( ) ( )h

q q qq

H e f x D z2

2 ( , )hq q

q

H e M x z

( )qf x

Current fragmentation Target fragmentation

( )hqD z

( , )hqM x z

1 22H xH

L.Trentadue & G.Veneziano, PLB323

X.Ji et al., PRD71 J.C.Collins, PRD57Factorization

proved

( )qf x( )h

h dD z

dz

( )d

f xdx

8

SIDIS: -dependence

2 21 1( , ) ( , )

cos 2( ) ( )

BM T Th x p H z p

f x D z

p xP k

2 2

22 22

2 1

1cos ~ 1 4

1 (1 )

n

nn T

T

k z pyn

y Qp

HH H

1.Cahn effect:

2.Berger effect (Collins fragmentation):

3.Boer-Mulders function h1┴ (TMD) contribution:

D.Boer&P.Mulders, PRD57

2

( )cos ~

( , , )

h

n T

n dg z p

2 2 2 2Tp p k z

0, cos , sin ,0k k k

H1┴ from e+e- collisions

R.N.Cahn, PRD40

E.Berger, ZPC4

4.Higher Order pQCD corrections:2

2

(2 ) 1( )cos 1

2 1 (1 )S y yQ

zy

H.Georgi&H.Politzer, PRL40

( )h hadron wave

function

9

Structure Function Separation 1 2 1 2 cos cos 2 cos 2 cos 2

h

H HE

Np

coscos

d

d

cos 2

cos 2d

d

Two methods of separation:1. fit of -dependence2. event-by-event moments

10

pT and t dependences

2 22 2

0

DIST TH H p dp

2

22

2 2 0

T

T

p

p

TH p H e

pT dependence cannot be calculated by ordinary pQCD, only TMD-based approach will permit for a complete description of the measurement. One has to integrate the data in pT

2:

22 2 min

t

tTH p H t e

11

<pT2>

2 2 2 2Tp p k z

22 2maxT Tp p z

z=0.5

Parton model predicts simple dependence of the mean transverse momentum:

p

2 2 2T p

p p k

preliminary

preliminary

12

Data vs. pQCD 22 ( ) ( )q

q

H e q x D z CTEQ 5, Kretzer

Q2=2.4 GeV2

+ -

Code from: F. Ceccopieri preliminary

13

Q2-dependence at z=0.5

+

preliminary

14

Q2-dependence at x=0.34

+

preliminary

15

<cos>Cahn - M.Anselmino et al., PRD71, Berger – A.Brandenburg et al.,

PLB347

<Q2>=2.2 GeV2

16

<cos2> <Q2>=2.2 GeV2

Cahn - M.Anselmino et al., PRD71, Berger – A.Brandenburg et al., PLB347

17

Q2-dependence for +

22 max

2

2 min

22 max

2

2 min

2

2

( , )

TT

T

T

TT

T

T

pppn

T T

pn pp

p

T

p

p e dp

f z

e dp

We compared our data on φ-dependent terms with EMC measurement (J.Aubert et al., PLB130) performed at significantly higher Q2:curves show Cahn effect prediction corrected for threshold effect:

<cos>

<cos2>

EMC(83)CLAS

x=0.24z>0.2

pT>0.2 GeV 22maxTp z

and n=1,2

Larger threshold effect predicted in: A.Konig and P.Kroll, ZPC16

18

Target FragmentationEMC, E=280 GeV

2 CM

F

px

W

CLAS, Ee=6 GeV Q2=2 GeV2, x=0.27

+ -

p Both pions are produced in CM, while protons are

from target fragmentation

region.

19

Data & pQCD

22 ( , )q P

q

H e M x x

1. Lack of scaling;2. Huge gluon

contribution is necessary to describe this data;

3. Hadron mass corrections are expected to give significant contribution.

fit to our data

x=0.33

Calculations contain target fragmentation only:

22 ( )q

q

F e q x

F. Ceccopieri,PLB655

preliminary

20

<cosnφ> vs. pT for proton• Proton <cos> and <cos2f> have the same sign of pion asymmetries;• Larger at low xP.

Q2=2 GeV2

x=0.27

preliminary

21

Summary1. We measured 5-fold differential semi-inclusive electro-production

cross sections for +, - and p in a wide kinematical range in all 5 independent variables;

2. Data for pions are in reasonable agreement with naïve current fragmentation pQCD calculations (difference is of the order of systematic errors ~20%);

3. Data for proton, in HERA representation, lack the scaling property;4. For pions, the measured <cos> moment is incompatible with

Cahn and Berger effects and in striking disagreement with high Q2 data, while <cos2> is compatible with zero in agreement with theory except for low-z region.

5. <cosn> asymmetries for protons have the same sign as for pions and increase in magnitude at low xP.

22

BACKUP SLIDES

23

Graudenz variable

Lab hH

Ez

(1 cos )CM CMCM h

H

Ez

M

h hH

p p Pz z

k qP

Struck quark light cone momentum fraction carried by the detected hadron, used in pQCD calculation, is commonly approximated:

(1 )

CMh

G CMp

Ez

E x

D.Graudenz,Fortsch.Phys.45

LO pQCDD(zG)

In e+e- function D(z) is measured as a function of:

2 2CMh hE p q

zss

24

Machine Upgrade•Beam energy increase up to 12 GeV (11 for Halls

A,B,C):

•5 new cryomodules to each LINAC

•gain increase up to 1.1 GeV/LINAC

•one new recirculation arc for Hall-D

•85 A maximum beam current

•maximal beam power 1 MWatt

25

CLAS Upgrade•Luminosity up to 1035 cm-2s-1

•Preshower calorimeter

•New drift chamber

•Improved TOF ~50-60 ps

•High threshold Cherenkov

•Central detector 40-130

Electromagnetic calorimeter

TOF

Tracking detector

•Vertex detector

•No photon tagger

p/p~0.3%+0.1%p~1mrad, ~5-40e/ > 103 (p<4.8 GeV)

p/p~2%~8 mrad, ~40-135

26

Central detectorSuperconducting solenoid

B~5 Tesla

Scintillator counterTOF, t~50 ps

Tracking detectorgas filled

cathode chamberp/p~2.2 % at p=1 GeV

Neutron Detectorplastic scintillators

t~100 ps

Silicon strip/MicroMegavertex detector

~100 m

Flux returniron

27

CLAS12 - Expected Performance Forward Detector Central Detector

Angular coverage: Tracks (inbending) 8o - 37o 40o - 135o

Tracks (outbending) 5o - 37o 40o - 135o Photons 3o - 37o 40o - 135o

Track resolution:p (GeV/c) 0.003p + 0.001p2 pT=0.02pT

(mr) 1 5 (mr) 2 - 5 2 Photon detection:Energy range > 150 MeV > 60 MeV E/E 0.09 (1 GeV) 0.06 (1 GeV)(mr) 3 (1 GeV) 15 (1 GeV)Neutron detection:eff 0.5 (p > 1.5 GeV/c) Particle id:e/ >>1000 ( < 5 GeV/c)

>100 ( > 5 GeV/c) /K (4) < 3 GeV/c 0.6 GeV/c/p (4) < 5 GeV/c 1.3 GeV/c

28

• High luminosity gives access to large x

• Valence quarks only• No explicit hard gluons

(if observable couples to valence quarks)

• Hadronic fluctuations of the virtual photon are suppressed

• x1 limit, sensitive test for spin-flavor symmetry breaking

• x>1 region for nuclear targets to probe high density quark matter

• Polarization: beam, target, recoil

• Distribution of the spin in the nucleon

H1, ZEUS

12 GeV upgrade kinematical reach

29

kT- Dependent Parton Distributionsf1, g1 studied for decades: h1 essentially unknown

)kx,(fkd)x(f T1T2

1

In standard notations

Study pQCD evolution in kT:

Q2=5 GeV2

Q2=10 GeV2

Q2=20 GeV2Hadronization

model is necessary to obtain information on distributions in quark transverse momentum kT.

30

z-dependence at fixed pT

2

22

2 2 2

1T

T

p

p

T

T

H p H ep

2 2 22Tp a b z

At large pT the suppression of z-distribution is clearly seen, but its contribution to the integral is small (low pT dominates) and modeled by phenomenological transverse momentum distribution:

TH

pz

W

different pT

31

Normalization

0Fx

2 CMhE

zs

1

( )tot

dD z

dz

T H Hp z W z

1

0

( ) ( ) ( )e e h h

h q qq

n s D z D z dz

1

0,

1( ) ( ) ( ) ( ) ( )

( )ep h h

h q q q qqq

q q

n s f x D z f x D z dzf x

In e+e- collisions

In SIDIS, neglecting target fragmentation contribution

Hadron multiplicity:

TH

pz

W=>

Cut on xF removes part of the pT region breaking normalization of transverse momentum distribution.

=>

32

<cosφ> vs zThe same situation.

Data are integrated over x and Q2 in DIS region.

33

<cos2φ> vs z

The same situation.

<Q2>=2.3 GeV2

Data are integrated over x and Q2 in DIS region.

34

Azimuthal angle definition

,cos

h

h

k q p q

k q p q

?????????????????????????? ??

?????????????????????????? ??

k – initial electron 3-momentum,ph – hadron 3-momentum,q – virtual photon 3-momentum

Trentoconvention

35

pT-dependence

cos Tp

Prelim

inary

Prelim

inary

Q2=2.4 GeV2, x=0.26, z=0.23

CLAS The same pT behavior for all structure functions => trivial kinematical factors for azimuthal asymmetries <cos> and <cos2>H3 contribution is negativeH4 is mostly positiveSuggest only internal transverse motion of quarks (Cahn)?

Structure functions were separated by fitting dependences in each separate kinematical bin.Only bins with complete -coverage were considered.

2cos 2 Tp

up to pT~1 GeV

36

e- measurement1. Cherenkov Counter (CC) uniquely identify electrons up to P~3 GeV2. Electromagnetic Calorimeter (EC) separates high energy electrons

e-

-

e-

-+CC noise

37

e- inclusive1. Inclusive cross sections obtained with the same data are in good

agreement with world data.2. Little effort needed to complete the inclusive data analysis at 6 GeV

CLAS E1-6 CLAS E1-6Bodek fit Bodek fit

World World

38

Ep-elastic

39

+ measurement1. Pions are well identified by Time Of Flight (TOF) measurement in

all accessible kinematical range2. Loss of events in data and Monte Carlo (MC) simulations due to PID

cuts was checked in +n peak

all positive hadrons

selected events

+n peak

background

40

+ semi-inclusive1. New CLAS data are in agreement with previously published

measurements within given uncertainties2. Comparison also shows non-trivial pT-behavior

pT=0.07 GeV/c

pT=0 or 0.1

41

+ semi-inclusive

Kinematics does not match perfectly, some extrapolations have been performed in CLAS data.

42

EMC data

EMC, PLB95

Much larger <pT2> values measured by EMC, but seen to increase

rapidly with W.

43

Mass Corrections

2 2

2

2

41 1

q xx

P M xQ

2 2

2

1

41 1

hh

pz

Epz

q M xQ

At low energies masses are not negligible, one has to use correct variables (Mulders, PRD49):

44

xF cutCut on xF simply remove low-z part of the spectrum. Its application always destroy the good agreement with pQCD calculations in these region.

BEBC (CERN), PLB87

45

EM

C d

ata

vs.

pQ

CD

46

EMC data vs. pQCD

F. Ceccopieri F. Ceccopieri

47

Parameterization dependence

CTEQ 5 LOGRV 98 LO

MRST cg LO

CTEQ 5 NLOGRV 98 NLO

MRST cg NLO

1. Very small uncertainty due to parton distribution function2. Larger uncertainty due to fragmentation function

48

ZEUS data

ZEUS, PLB481

ZEUS, PLB481

1. The same limitations as for EMC and E665

2. More detailed data sample in hep-ex/0608053 represented in different variables (pseudorapidity and minimum hadronic energy in HCM) and integrated also over neutral hadrons appears hard to compare

0.01<x<0.1180<Q2<7220 GeV2

0.2<z<1

49

EMC and E665 data

E665, PRD48

EMC, Z.Phys.C34

cos ( ) cosCT

CT T

p

n p dp n

1. The same limitations also in E665 data2. Minimum transverse momentum of hadrons is commonly used pT

C which can mask possible sign change at low pT

3. Strong xF variation is seen by EMC

Q2>4 GeV2

40<W2< 450 GeV2

Q2>3 GeV2

100<W2< 900 GeV2

50

EMC data in pT

l

yE

1 2

1( ) (2 )

1 (1 )

yf y y

y

EMC, PLB130EMC, Z.Phys.C34

1. Summed over all charged hadrons positive and negative, no PID2. Integrated over all other variables: x, Q2, z3. Radiative corrections with Monte Carlo

2 2

1( )

1 (1 )

yf y

y

Q2>4 GeV2

40<W2< 450 GeV2

51

Interference term

52

Kinematical Separation (for )

Separation is possible by means of a cut on the energy flow from the virtual photon to the measured hadron.

Currentfragmentation

Targetfragmentatio

n

log( )1

2 log( )

h h

h h

E p

E p

Hadron rapidity

Current

Target

x=0.3, Q2=3 GeV2

Pionelectroproduction

53

Mulders Rapidity Gap

(1 )h h

t

p Ez

x P

2

2h h h

h h h

p p p

p p M

2 2k hM M p

( ) 2ln ln

CM

c Muldersc

h

qz

M

2 21ln ln ln

2h h h

CMh h h

p p p

p M M

h h hp E p

h hc

p Ez

q

( ) 2(1 )ln ln

CM

t Mulderst

h

x Pz

M

(1 ) (1 )W x ys x Mq qy

k E

ln lnCM

Mulders

h

Wz

M

54

Longitudinal Momentum

+ p

CEBAF beam energy in combination with CLAS acceptance allow to explore current fragmentation for light mesons and target fragmentation for baryons. ( )2 h CM

F

px

W In DIS Feynman permits to disentangle two regions,

however, at small invariant masses W separation is ambiguous.

target

target

target

currentcurrent

current

6 GeV beam energy

55

Rapidity gap at CLAS

2

2

1ln ln

1CM

Mulders hm xz

z Q x

Separation of the current and target fragments:Berger criterion 2CM

+

p1

log2

h h

h h

E p

E p

Usefulkinematics

ExclusiveBoundaryMX~Mn

DIS only!

Q2=2 GeV2

W>

2 G

eV

current

current

56

CLAS Acceptance 0

( )

( )

DATA

GEN

GSIM

N d

N d

cos cos cos cosDATA GSIM GEN

n n n n

Zero-order approximation:

φ-constant term

Acceptance mixes Fourier coefficients

with different n.

57

Fourier analysis of acceptance100 harmonic expansion: CLAS acceptance is cosine-like. Even number of sectors generate mostly even functions in azimuthal distributions.

even (cos nφ) odd (sin nφ)

DATAFourier series

DATAFourier series

58

CLAS Acceptance

/ 01 1 2 2cos sin cos 2 sin 2 ...

2eff acc A

A A B A B 2

, ,

0

1( )cosDATA GSIM DATA GSIM

nI LN n d

( ) ( )LN

n nA A

, , ,0 1 2( ) cos cos 2DATA GEN DATA GEN DATA GENV V V

2

, , , ,0 1 2

0

01 2

1cos cos 2

cos cos 2 ... cos2

DATA GSIM DATA GSIM DATA GSIM DATA GSIMnI V V V

AA A n d

, , , ,1 1 2 20 1 22 2

DATA GSIM DATA GSIM DATA GSIM DATA GSIMn n n nn n

A A A AI A V V V

0,1,2,...n

/1( ) ( ) ( )acc effN A

L

59

CLAS Acceptance

0 2 1~DATAV H H1 3~DATAV H

nA

2 4~DATAV H

1 1

GSIM GEN

N N N NI A V

1 1

DATA DATA

N N N NI A V

Only first 10 harmonics are significant, but 20 harmonics are kept in the analysis.

60

Three methods Comparison of the three

methods for structure function separation:

1. Fit of φ-distribution2. Moments method in zero-

order approximation3. Moments method

accounting for N=20 harmonics of CLAS acceptance

Higher harmonics are important in the extraction of φ–even observables from CLAS data

61

Pseudo-data Cross CheckPseudo-data generated in a limited kinematical area from a known model (different from that used in the reconstruction) were used to check that the two extraction procedures are able to extract correct φ-moments.

modelmodel

62

Results of Integration

22 2 0DIS

T TH p H p

Different assumptions yield slightly different results in low-z region.

Exponential pT

Exponential tNumerical pT integ.Numerical t integ.

exact formulano Eh/p|| correction

unphysical high pT tail

Correct expression for low energy: 2 max 2

222 2 2 2

0

TpTDIS

h T

h h T

H pH E dp

E m p

LO pQCD

63

Leading Protons at HERA

P

x

x

21

CM

L F P

pP kx x x

Pk W

2 22 2( , , , ) ( , ) ( , )D P

P P PF x t Q f x t F Q

2 2( )HERA i CLASt P P M s t

DIS on a Pomeron

target

parton momentum fraction in Pomeron

Chekanov, NPB658

64

Leading Particle Effect

Systematic study of different reactions with hadron and lepton beams showed:

1. only particles present in the initial state can be leading particles in the final state,

2. more valence quarks from initial state particles are present in the particle measured in the final state then more likely particle to be leading.

Basile, Nuovo Cim.A66

Leading particle is defined as the particle carrying most of the specific jet (current or target) momentum in CM reference frame.

65

Data vs. Monte Carlo

66

Electromagnetic Probe

2 22 2 2 2 2 2

2 1 1 2

1( , ) 2 tan ( , ) ctg ( cos ) ( , ) ( , )

' 2 2 2Mott

d d QW x Q W x Q E E G x Q G x Q

d dE d M

Lepton scattering off a nucleon is the cleanest probe of nucleon internal structure.

electron beamwith energy E

detected electronat angle with momentum E’

producedhadronic systemof mass squared

2 2Q q

,q k k q

2 2

2 2

q Qx

qP M

22 2 2 11W P q M Q

x

,0P M

virtual photon and target four-momenta:

Lorentz invariants:

Electromagnetic current inclusive cross section:

One PhotonExchange

approximation

refers to aligned (anti-aligned) spins of incident electron and target nucleon

(k)

(k’)

67

Inclusive Kinematical Domains

elastic peakepe’p’

nucleonresonances

•Elastic scattering

•Inelastic scattering:

•W<2 GeV - Resonance region

•W>2 GeV - Deep Inelastic Scattering (DIS)

•Q2<1 GeV2 † - Non-perturbative

•Q2>1 GeV2 † - Perturbative

Elastic and resonance peaks are due to formation of intermediate particles with a given mass M<2 GeV.

inelasticregion

†Running coupling constant of the strong interaction S(Q2) becomes ~0.3 at Q2=1 GeV2. Furthermore, higher twists are suppressed by powers M2/Q2.

Unpolarized electron-protonscattering

68

Perturbative DIS

21 1( , ) ( )M G Q g x

22 2( , ) ( )W Q F x

2 ,Q Bjorken limit: and x-fixed

1 2

1( ) ( )

2F x F x

x

1

2 1 1( ) ( ) ( )x

dyg x g x g y

y

2 22 2( , ) ( )G Q g x

21 1( , ) ( )MW Q F x

•Scaling:

•Parton spin flipping contributions vanish:

Callan-Gross Wandzura-Wilczek

22 ( ) ( )i i

i

F x x e q x 21

1( ) ( )

2 i ii

g x e q x •Parton distribution functions

•Fraction of proton momentum carried by struck parton

Neglect partonand targetmasses.

valence

sea

•Valence and sea partons and flavor Singlet and Non-Singlet combinations

( ) ( ) ( )i ii

x q x q x ( ) ( ) ( )ij i jx q x q x

2 2 2

1( )

3NS p n

udF F F x x

•Incoherent elastic scattering of partons

B

px x

P

69

Detector CLAS

70

Kin

em

ati

cal C

overa

ge

of

E1

-6a r

un

71

Mean transverse momentum

2 2 2 2Tp p k z

Parton model predicts simple z-dependence of measured mean transverse momentum:

Kinematical constraints cut transverse momentum distributions at low-z: 22 2max

T Tp p z

72

Q2-dependence at z=0.5

73

Leading Particle Effect

2( )ht q p

target jet directioncurrent jet

direction

22 2 max(| | )TH p H t

Upper limit of 5% on the leading target fragmentation contribution was estimated at lowest z=0.07 where |t|=|t|max is kinematically allowed.

Q2=2 GeV2

x=0.24z=0.18

Approximate integration:

74

Soft Target Fragmentation1. Most of hadrons have xF~0 regardless energy of

the experiment. No separate peaks for target or current fragmentation.

2. Current fragmentation pQCD fails at backward CM angles

EMC, E=280 GeV

2 CM

F

px

W

CLAS, Ee=6 GeV

LO pQCD

75

Interplay between variables

22

2

14

2 2F FT

H F F

x xpz x x

W

( 0) 0H Fz x

Standard SIDIS variable squeezes backward going hadrons into the very low-z region, where z0 divergence dominates the total cross section:

1. Commonly used zH variable is not suitable for target fragmentation analysis,

2. Definition of the hadron direction with respect to virtual photon is frame dependent.

forward

backward

( 0)H F Fz x x

76

Mean transverse momentum

2 2 2 2Tp p k z

Parton model predicts simple z-dependence of measured mean transverse momentum:

Kinematical constraints cut transverse momentum distributions at low-z: 22 2max

T Tp p z

77

Data vs. pQCD (Q2) -

x=0.34 z=0.5

78

Data vs. pQCD (x,z) -

Q2=2.4 GeV2 Q2=2.4 GeV2

79

Q2-dependence at x=0.34 +

80

x-dependence at Q2=2.4 GeV2 +

81

z-dependence at Q2=2.4 GeV2 +

82

<cosφ> vs. pT

Cahn effect calculations (using k┴

2=0.20 GeV2 and p┴

2=0.25 GeV2 from M.Anselmino et al., PRD71) do not reproduce measured <cos> and the inclusion of Berger effect contribution does not improve the agreement significantly.

<Q2>=2.2 GeV2

Data are integrated over x and Q2 in DIS region.

83

<cos2φ> vs. pTCahn and Berger effect compensate each other to give zero <cos2> moment. Within systematic errors the data are also compatible with zero, except for low-z.

Data are integrated over x and Q2 in DIS region.

<Q2>=2.2 GeV2

84

xF-behavior -