The Role of Semi Inclusive DIS Data

in Determining Polarized PDFs

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

Saclay, Paris, 17 September 2010

OUTLINE

A combined NLO QCD analysis of inclusive and semi inclusive DIS world data is presented

Summary

The recent COMPASS data on A1p and A1dπ(+/-), A1d

K(+/-) are included

Impact of SIDIS on polarized PDFs and higher twist

A quark flavor decomposition of the polarized sea

The higher twist corrections (HT) to g1 are accounted for (in contrast to the other analyses)

The main goal to answer the question how the helicity of the nucleon is divided up among its constituents:

Sz = 1/2 = 1/2 (Q2) + G (Q2) + Lz (Q2)

= ssdduu

the parton polarizations q and G are the first moments

12 2

0Δq(Q ) ( , )dx q x Q

1

0

22 ),()ΔG(Q QxGdx

of the helicity densities: ),( ,),(),,( 222 QxGQxuQxu

To determine the shape of the polarized parton densities

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

2222 10 4 , 41 GeVWGeVQ

preasymptotic region

Inclusive DIS Cross Section Asymmetries

Measured quantities ,||

dd

ddA

dd

ddA |

)()()(2121 | ||

, , , ggAAAA where A1, A2 are the virtual photon-nucleon asymmetries

If A|| and are measured 11 /Fg

If only A|| is measured

| | 2 1

1

(1 )A g

D F

2 2 2 24 /M x Q - kinematic factor

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

A the best quantity to test QCD and to determine PDFs

Theory In QCD 2 2 21 1 , 1g ( , ) g ( , ) g ( , )LT TMC HTx Q x Q x Q

)4

4

(Q

ΛO2221 /),(h),(g QQxQx HT

2 22 2

1

1 ( ) ( )( , ) [( ) (1 ) ]

2 2 2

fN

s s GLT q q

q f

Q Q Cg x Q e q q C G

N

functionst coefficien , WilsonCC Gq

In NLO pQCD

dynamical HT power corrections (=3,4)=> non-perturbative effects (model dependent)

polarized PD evolve in Q2

according to NLO DGLAP eqs.

2 42 2 2

1 , 1 2 4g ( , ) g ( , ) ( , ) ( )TMC

LT TMC LT

M Mx Q x Q h x Q O

Q Q

Nf (=3) - the number of flavors

target mass corrections which are calculable in QCDA. Piccione, G. Ridolfi

logarithmic in Q2

2 22 2

1

1 ( ) ( )( , ) [( ) (1 ) ]

2 2 2

fN

s s GLT q q

q f

Q Q Cg x Q e q q C G

N

can be determined from polarized inclusive DIS data !

)( qq

IMPORTANT

Due to the lack of the charged current neutrino data only

the sums

2222 10 4 , 41 GeVWGeVQ

The HT corrections to g1 are NOT negligible in the preasymptotic region and have to be accounted for

An important difference between the kinematic regions of the unpolarized and polarized data sets

)/( 22 QO

preasymptotic region

A half of the present inclusive data are at moderate Q2 and W2:

LSS, Phys. Rev. D75 (2007) 074027

x-Q2 range of F2 and g1 structure functions

Polarized data

f

f

h

hh

F

gQzxA

~),,(

1

121

ef2 qf(x,Q2) Df

h (z,Q2)

ef2 qf(x,Q2) Df

h (z,Q2)

Semi-inclusive processes

Fragmentation functions

In LO QCD

In NLO QCD the Wilson coefficients have to be included

qallow to separate and q

z)(x,ijΔC

22 1 2

11

( , , )h h

hh

g gA x z Q

F

NLO1

NLO1

1

11

),(

),(

),(

),(),(

2

2

2

22

expexp

QxF

Qxg

QxF

QxgQxA h

h

h

hh

Fit to the data

Inclusive DIS

Semi-inclusive DIS

expexp )(

)()(

1

11

1

1 HTTMCNLO

F

gg

F

g

N.B. It is NOT known at present how to account for the HT and TMC corrections in SIDIS processes. Fortunately, they should be less important due to the kinematic region of the present SIDIS data.

2χ

2χ

0.0031.269 ))(Δ(Δ)Δ(Δ 223 DFQdd)(Quuga

A

0.0250.585=3))((2 ))(())(( 2228 DFQssQddQuua

Sum

Rules

Input parton densities at Q20 = 1 GeV2

(more general expressions than those in our previous analyses)

)1()1(),(

)1()1(),( )(

)1(),(

)1()1(),(

)1()1(),)((

)1()1(),)((

20

20

20

20

20

5.020

xxxAQxG

xxxAQxsss

xxAQxd

xxxAQxu

xxxAQxdd

xxxxAQxuu

GGG

G

sss

s

ddd

uuu

u

ddd

d

uuuu

u

, ; ( 02)quu u s Gdd d

MRST

16 free parameters

f

f

h

hh

F

gQzxA

~),,(

1

121

ef2 qf(x,Q2) Df

h (z,Q2)

ef2 qf(x,Q2) Df

h (z,Q2)

For the fragmentation functions Dqh(z, Q2) the DSS

(de Florian, Sassot, Stratmann) ones have been used

The inverse Mellin transformation method has been used to calculate g1N(x, Q2), g1N

h (x, z, Q2) and F1Nh (x, z, Q2) from

their moments.

DATA

Inclusive DIS – 841 experimental points

Semi inclusive DIS – 202 experimental points

Total – 1043 exp points

Nr of the free parameters – 26 (16 for PDFs and 10 for HT)

The systematic errors are added quadratically to the statistical ones

The positivity constraints on polarized PDFs are imposed

Unpolarized NLO MRST’02 PDFs have been used to calculate F1Nh

A good description of both the DIS and SIDIS data

Fit to the data

DIS:2 0.85NrP SIDIS:

2 0.90NrP

Results:Longitudinal polarized PDFs and higher twist

LSS’10 PDFs – this fit, LSS’06 – a fit to DIS data alone (PR D75, 2007)

A flavor decomposition of the polarized sea due to SIDIS data

are determined without additional assumptions

and Δ Δu( ) d( )x x

Changing in sign very unexpected

( )s x

Changing in sign ΔG(x) - such a solution has been already found from inclusive DIS data N.B. In the QCD analyses of inclusive DIS data:

sea sea 2 Δu Δu Δd Δd (Δs+Δs) /Flavor symmetric sea :convention

Error bands Δχ2 = 1

∆s(x)

Our s(x) differs from that one obtained by DSSV (less negative at x<0.03 and less positive for large x). Note that DSSV have used the assumption for s(x)

ds In contrast to a changing in sign s(x) coming from SIDIS, in all the QCD analyses of inclusive DIS data a negative [s(x)+ s(x)]/2 for any x in the measured region is obtained

The determination of s(x) from SIDIS strongly depends on FFs (COMPASS – PL B680 (2009) 217) and the new FFs (de Florian, Sassot, Stratmann) are crucially responsible for the unexpected behavior of s(x)Obtaining a final and unequivocal result for s(x) remains a challenge for further research on the internal spin structure of the nucleon

¯

¯¯

May be the assumption ∆s(x)=∆s(x) in SIDIS is not correct ?

∆s(x) is controversial !

ΔG(x, Q2)

The present polarized DIS and SIDIS data cannot rule out the solution with a positive gluon polarization

2 20 0.888 0.883( ) ( )DF DFG node Gx x

The sea quark densities obtained in the fits with positive and node xΔG are almost identical.

SIDIS data do NOT help to constrain better the gluonpolarization.

1. Via Open Charm production (q=c) c D0 K-p+ and D*+D0p+

COMPASS: ΔG/G = -0.08 +/- 0.21 +/- 0.11 at <xg>=0.11 and <µ2> = 13 GeV2

LO treatment. All deuteron data included (C. Franco, DIS 2010, Florence)

2. Via High-pt hadron pairs (q=u,d,s) - Detect 2 hadrons (mostly pions) COMPASS, HERMES - 2 determinations:

• Q2 > 1 GeV2

• Q2 < 1 GeV2

g qq

Photon- Gluon Fusion

Determination of ∆G from direct measurements

∆G/G – two methods, three measurements

Unfortunately, the direct measurements give us information on G in narrow range of x

Comparison with directly measured G/G

ΔG/G from high pt hadron pairsµ2 = 3 GeV2

ΔG/G from open charm production

The most precise values of G/G, the COMPASS ones, are consistent with both of the polarized gluon densities determined in our combined QCD analysis

Both of our solutions for ΔG/G are also in agreement with the COMPASS experimental value, especially the changing in sign xΔG.

The direct measurements of ΔG/G at COMPASS cannot distinguish between the positive and node xΔG(x) obtained from our QCD analysis

As expected the SIDIS data do not influence essentially the sums

already well determined from the inclusive DIS data.

Our densities are well consistent with those obtained by DSSV.

( ) and ( ) u u d d

Higher twist effects

g1N = (g1

N )LT,TMC + hN(x)/Q2

Compared to HT(LSS’06): The values of HT(p) are practically not changed while the new values of HT(n) are smaller and almost compatible with zero within the errors for x > 0.1 . We consider this change of HT(n) as a result of the new behavior of Δs(x), positive for x > 0.03. In addition, the new A1

p COMPASS data impact on the smallest x point of HT(p,n).

The first moments of higher twist

Thanks to the very precise inclusive DIS CLAS data the first moments of HT corrections are also well determined.

np,N ,)( 75.0

0045.0

xhdxh NN

In agreement with the instanton model predictions and the values obtained from the analyses of the first moment of g1

(p-n) (Deur et al., PR D78, 032001, 2008. ; R. Pasechnik et al. PR D78, 071902, 2008)

2 )005.0028.0( GeVhp

2 (0.018 0.008) n

h GeV

2 ( 0.046 0.009) p n

h h GeV 2 ( 0.011 0.009) p n

h h GeV

In agreement with 1/NC expansion in

QCD (Balla et al., NP B510, 327, 1998)|| ||

npnphhhh

0 np

hh

Higher twist vs TMC

Sidorov, Stamenov: Mod. PL A21, 1991 (2006)

LSS10 predictions for the COMPASS A1pπ+(-) and A1p

K+(-) data2 35.67 / 48 0.74NrP

After the fit including the COMPASS A1pπ+(-) and A1p

K+(-) data2 34.84 / 48 0.72 (0.74)NrP

Impact of SIDIS COMPASS/p data on PDFs uncertainties

Impact of the future DIS CLAS12 data on PDFs uncertainties

Using the 11 GeV highly polarized electron beam of the energy-upgraded CEBAF at JLab very accurate data in 0.075 ≤ x ≤ 0.775, 1.01 ≤ Q2 ≤ 12.05

A significant improvement of the data accuracy do NOT impact on Δs errors?!

Impact of the future SIDIS CLAS12 data on PDFs uncertainties

Kinematic region: 0.04 ≤ x ≤ 0.76, 1.01 ≤ Q2 ≤ 10.16 GeV2

Spin sum rule for the nucleon

s G a0 = MS

LSS’06 (node xG) -0.058 ± 0.006 0.034 ± 0.490 0.235 ± 0.045

LSS’10 (node xG) -0.055 ± 0.006 -0.396 ± 0.431 0.254 ± 0.042

LSS’10 (xG pos) -0.063 ± 0.004 0.255 ± 0.187 0.207 ± 0.034

Sz = ½ = ½ (Q2) + G (Q2) + Lq (Q2) + Lg(Q2)

= - 0.27 (0.36) +/- 0.43 (0.19) + Lq (Q2) + Lg(Q2)

To be determined from forward

extrapolations of generalized PDFs

Q2 = 4 GeV2

Due to the ambiguity of the gluon polarization the quark-gluon spin contribution to the total spin of the nucleon is still not well determined.

First moments of Δs(x), ΔG(x) and ΔΣ(x) at

SUMMARY

The SIDIS data, as well the direct measurements of ΔG/G, cannot help to distinguish between the positive and changing in sign solutions for ΔG(x) – the ambiguity of the form of ΔG(x) remains still large.

A combined NLO QCD analysis of inclusive and semi inclusive world DIS data is presented

In contrast to the other analyses the target mass and higher twist corrections to the spin structure function g1 are taken into account

Due to SIDIS data

Changing in sign Δs(x), but different from the DSSV one - less negative at x < 0.03 and less positive for x > 0.03

Δs(x)SIDIS differs essentially from a negative Δs(x)DIS obtained from all the QCD analyses of inclusive DIS data. This behavior strongly depends on the kaon FFs used. A model independent extraction of kaon FFs would help to solve this inconsistency.

The sea quark densities Δu and Δd are determined¯ ¯

¯

¯ ¯

Additional slides

0.21-0.1

1

17

g 1.32 0

f0. 5

KTeV experiment Fermilab: PRL 87 (2001) 13201

e 0

-decay

SU(3)f prediction for the form factor ratio g1/f1

Experimental result

1A

1

g g 1.269 .003

f

A good agreement with the exact SU(3)f symmetry !

From exp. uncertainties SU(3) breaking is at most of order 20%

NA48 experiment at CERN g1/f1 = 1.20 +/- 0.05 (PLB 645 (2007) 36)

Kinematatic factor 2 = 4M2x2/Q2 cannot be neglected for most of the data sets (JLab, SLAC, HERMES)

The approximation A1th

≈ (g1/F1)th used by some of the

groups in the preasymptotic region is not reasonable !

Which inclusive data to chose for QCD fits – A1 or g1/F1 ?

A1= g1/F1 - 2 g2/F1

The QCD treatment of g2 is not well known

The best manner to determine the polarized PDFs is to perform QCD fits to the data on g1/F1

N.B.

(g1)QCD = (g1)LT + (g1)HT+TMC (F1)QCD = (F1)LT + (F1)HT+TMC

LT(LO, NLO) 1/ln(Q22 2/Q2, TMC M2/Q2

There are essentially two methods to fit the data (accounting or not accounting for the HT corrections to g1)

2 21 1

2 21 1exp

g (x,Q ) g (x,Q )

F (x,Q ) F (x,Q )

LT

LT

OK in pure DIS region where HT can be ignored

11 1

1 1 expexp

( ) ( )

( )

g g g

F F

LT HT+TMC

The two methods are equivalent in the pre-asymptotic region only if the (HT+TMC) terms cancel in the ratio g1/F1

PDFsGRSV, DSSV, LSS

LSS 2x(F1)exp = (F2)exp(1 + γ2)/(1+ Rexp)

21 1 1 1

21 1 1 1exp

( , ) ( ) ( ) ( )1

( , ) ( ) ( ) ( )

g x Q g g F

F x Q F g F

LT HT+TMC HT+TMC

LT LT LT

1 1

1 1

( ) ( )( ) ( )

g Fg FHT+TMC HT+TMC

LT LT is fulfilled

Fits to g1/F1 data using for the ratio

1 1 1

1 1 exp

( ) ( ) ( ) or

( ) ( )LT LT HT TMC

LT

g g g

F F

will lead to the same results if the condition

If not (which is the case), the ignored HT terms in g1 and F1, according to the Ist method, will be absorbed into the extracted PDFs

Pre-asymptotic region

LSS’06 vs DSSV

11 1

1 1 expexp

( ) ( )

( )

g g

F

g

F

LT/N HT+TMCLOLSS

21

21

2 21 1exp

gg (x, (xQ )

F (x,Q ) F (x

,Q )

,Q )

L

LT

T/NLO

/NLO

DSSV

In the DSSV analysis the TM and HT corrections are not taken into account for both g1 and F1 structure functions

F1(x, Q2)LT/NLO was calculated using the NLO MRST’02 PDFs

DSSV: A first NLO global analysis of DIS, SIDIS and RHIC polarized pp scattering data

The difference between F1(exp) and F1(MRST)LT is a measure of the size of

TMC and HT corrections which cannot be ignored in the pre-asymptotic region

As expected, the curves corresponding to g1tot(LSS)/F1(exp) and

g1LT(DSSV)/F1

LT (MRST) practically coincide (an exception for x > 0.2 !)

although different expressions for g1 and F1 were used in the fit

proton

Surprisingly g1LT(LSS) and

g1LT(DSSV) coincide for x > 0.1

although the HT+TMC, taken into account in LSS and ignored in the DSSV analysis, do NOT cancel in the ratio g1/F1 in the

pre-asymptotic region

PUZZLE ???

2 21 1

2 21 1exp

g (x,Q ) g (x,Q )

(1+F (x,Q ) F ( )) x,Q

LT/NLO2

LT/NLO

1 1

1 1

( ) ( )1 )

( ) ( )

g F

g F 2HT+TMC HT+TMC

LT LT

γ

In the DSSV fit, a factor is introduced for the data in the pre-asymptotic region (CLAS, JLab/Hall A and SLAC/E143). There is NO rational explanation for a such correction !! Except for the fact that it is impossible to achieve a good description of these data, especially for the CLAS one, without this correction.

???

It turns out that accidentally more or less (4-18%) accounts for the TM and HT corrections to g1 and F1

in the ratio g1/F1 ONLY for x > 0.1

2(1 γ )

2 2 2 2γ 4 /NM x Q2(1 γ )