1. The Role of Semi Inclusive DIS Data in Determining Polarized PDFs
Saclay, Paris, 17 September 2010
The Role of Semi Inclusive DIS Data in Determining Polarized PDFs
E. Leader (London), A. Sidorov (Dubna), D. Stamenov (Sofia)

2. OUTLINE
A combined NLO QCD analysis of inclusive and semi inclusive DIS world data is presented
The recent COMPASS data on A1p and A1dπ(+/-), A1dK(+/-) are included
The higher twist corrections (HT) to g1 are accounted for (in contrast to the other analyses)
Impact of SIDIS on polarized PDFs and higher twist
A quark flavor decomposition of the polarized sea
Summary

3. Sz = 1/2 = 1/2 DS(Q2) + DG (Q2) + Lz (Q2)
The main goal to answer the question how the
helicity of the nucleon is divided up among its constituents:
Sz = 1/2 = 1/2 DS(Q2) + DG (Q2) + Lz (Q2)
DS =
the parton polarizations Dq and DG are the first moments
of the helicity densities:
To determine the shape of the polarized parton densities

4. Inclusive DIS DIS regime ==> Q2 >> M2, n >> M
one of the best tools to study
the structure of nucleon
Q2 = -q2 = 4EE`sin2 (q/2) l` k`
x = Q2/(2Mn)
n = E – E` l k q g*
DIS regime ==> Q2 >> M2, n >> M N P
Fi(x, Q2) gi(x, Q2)
preasymptotic region
unpolarized SF
polarized SF

5. Inclusive DIS Cross Section Asymmetries
Measured quantities
where A1, A2 are the virtual photon-nucleon asymmetries
the best quantity to test QCD and to determine PDFs
If A|| and are measured
If only A|| is measured
- kinematic factor
NB. g cannot be neglected in the JLab,
SLAC and HERMES kinematic regions

6. Theory polarized PD evolve in Q2 according to NLO DGLAP eqs. In QCD
dynamical HT power corrections (t =3,4)
=> non-perturbative effects (model dependent)
target mass corrections
which are calculable in QCD
A. Piccione, G. Ridolfi
In NLO pQCD
logarithmic in Q2
polarized PD evolve in Q2
according to NLO DGLAP eqs.
Nf (=3) - the number of flavors

7. Due to the lack of the charged current neutrino data only the sums
IMPORTANT
Due to the lack of the charged current neutrino data only
the sums
can be determined from polarized inclusive DIS data !

8. An important difference between the kinematic regions of the unpolarized and polarized data sets
A half of the present inclusive data are at moderate Q2 and W2:
preasymptotic region
The HT corrections to g1 are NOT negligible in the preasymptotic region and have to be accounted for
LSS, Phys. Rev. D75 (2007)

9. x-Q2 range of F2 and g1 structure functions
Polarized data

10. Semi-inclusive processes
allow to separate and
Fragmentation functions
ef2 Dqf(x,Q2) Dfh (z,Q2)
In LO QCD
ef2 qf(x,Q2) Dfh (z,Q2)
In NLO QCD the Wilson coefficients have to be included

11. Fit to the data Inclusive DIS Semi-inclusive DIS
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.

12. Input parton densities at Q20 = 1 GeV2
(more general expressions than those in our previous analyses)
Sum
Rules
16 free parameters

13. ef2 Dqf(x,Q2) Dfh (z,Q2)
ef2 qf(x,Q2) Dfh (z,Q2)

14. Nr of the free parameters – 26 (16 for PDFs and 10 for HT)
For the fragmentation functions Dqh(z, Q2) the DSS (de Florian, Sassot, Stratmann) ones have been used
Unpolarized NLO MRST’02 PDFs have been used to calculate F1Nh
The inverse Mellin transformation method has been used to calculate g1N(x, Q2), g1Nh (x, z, Q2) and F1Nh (x, z, Q2) from their moments.
The positivity constraints on polarized PDFs are imposed
Nr of the free parameters – 26 (16 for PDFs and 10 for HT)
The systematic errors are added quadratically to the statistical ones
DATA
Inclusive DIS – 841 experimental points
Semi inclusive DIS – 202 experimental points
Total – 1043 exp points

15. Fit to the data
A good description of both the DIS and SIDIS data
DIS:
SIDIS:

16. Results:Longitudinal polarized PDFs and higher twist

17. LSS’10 PDFs – this fit, LSS’06 – a fit to DIS data alone (PR D75, 2007)
Error bands Δχ2 = 1
A flavor decomposition of the polarized sea due to SIDIS data
are determined without additional assumptions
Changing in sign very unexpected
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:

18. ∆s(x)
Our Ds(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 Ds(x)
In contrast to a changing in sign Ds(x) coming from SIDIS, in all the QCD analyses of inclusive DIS data a negative [Ds(x)+ Ds(x)]/2 for any x in the measured region is obtained
∆s(x) is controversial !
May be the assumption ∆s(x)=∆s(x) in SIDIS is not correct ?
The determination of Ds(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 Ds(x)
Obtaining a final and unequivocal result for Ds(x) remains a challenge for further research on the internal spin structure of the nucleon

19. ΔG(x, Q2)
The present polarized DIS and SIDIS data cannot rule out the solution with a positive gluon polarization
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 gluon
polarization.

20. Determination of ∆G from direct measurements
∆G/G – two methods, three measurements
1. Via Open Charm production (q=c)
c  D0  K-p+ and D*+D0p+
COMPASS: ΔG/G = / /- 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
Photon- Gluon Fusion
Unfortunately, the direct measurements give us information on DG in narrow range of x

21. Comparison with directly measured DG/G
µ2 = 3 GeV2
ΔG/G from high pt hadron pairs
The most precise values of DG/G, the COMPASS ones, are consistent with both of the polarized gluon densities determined in our combined QCD analysis
ΔG/G from open charm production
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

22. 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.

23. g1N = (g1N )LT,TMC + hN(x)/Q2
Higher twist effects
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 > We consider this change of HT(n) as a result of the new behavior of Δs(x), positive for x > In addition, the new A1p COMPASS data impact on the smallest x point of HT(p,n).
g1N = (g1N )LT,TMC + hN(x)/Q2

24. 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.
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, , ; R. Pasechnik et al. PR D78, , 2008)
In agreement with 1/NC expansion in QCD (Balla et al., NP B510, 327, 1998) 

25. Higher twist vs TMC
Sidorov, Stamenov: Mod. PL A21, 1991 (2006)

26. LSS10 predictions for the COMPASS A1pπ+(-) and A1pK+(-) data

27. After the fit including the COMPASS A1pπ+(-) and A1pK+(-) data

28. Impact of SIDIS COMPASS/p data on PDFs uncertainties

29. 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 ≤ x ≤ 0.775, ≤ Q2 ≤ 12.05
A significant improvement of the data accuracy do NOT impact on Δs errors?!

30. Impact of the future SIDIS CLAS12 data on PDFs uncertainties
Kinematic region: ≤ x ≤ 0.76, ≤ Q2 ≤ GeV2

31. Spin sum rule for the nucleon

32. Sz = ½ = ½ DS(Q2) + DG (Q2) + Lq (Q2) + Lg(Q2)
First moments of Δs(x), ΔG(x) and ΔΣ(x) at
Q2 = 4 GeV2 Ds DG
a0 = DSMS
LSS’06 (node xDG)
± 0.006
0.034 ± 0.490
0.235 ± 0.045
LSS’10 (node xDG)
± 0.006
± 0.431
0.254 ± 0.042
LSS’10 (xDG pos)
± 0.004
0.255 ± 0.187
0.207 ± 0.034 
Sz = ½ = ½ DS(Q2) + DG (Q2) + Lq (Q2) + Lg(Q2)
= (0.36) +/ (0.19) + Lq (Q2) + Lg(Q2)
To be determined from forward
extrapolations of generalized PDFs
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.

33. SUMMARY
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
The sea quark densities Δu and Δd are determined
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 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.

34. Additional slides

35. KTeV experiment Fermilab: PRL 87 (2001) 13201 SU(3)f prediction for
b-decay
SU(3)f prediction for
the form factor ratio g1/f1
Experimental result
A good agreement with the exact SU(3)f symmetry !
SU(3) breaking is
at most of order 20%
From exp. uncertainties
NA48 experiment at CERN  g1/f1 = / (PLB 645 (2007) 36)

36. Which inclusive data to chose for QCD fits – A1 or g1/F1 ?
A1= g1/F1 - g2 g2/F1
Kinematatic factor g2 = 4M2x2/Q2 cannot be neglected for most of the data sets (JLab, SLAC, HERMES)
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
The approximation A1th ≈ (g1/F1)th used by some of the groups in the preasymptotic region is not reasonable !
N.B.

37. There are essentially two methods to fit the data
(accounting or not accounting for the HT corrections to g1)
(g1)QCD = (g1)LT + (g1)HT+TMC (F1)QCD = (F1)LT + (F1)HT+TMC
LT(LO, NLO)  1/ln(Q2/L2) HT  L2/Q2, TMC  M2/Q2
PDFs
GRSV, DSSV, LSS
OK in pure DIS region where HT can be ignored
The two methods are equivalent in the pre-asymptotic region only if the (HT+TMC) terms cancel in the ratio g1/F1
LSS
2x(F1)exp = (F2)exp(1 + γ2)/(1+ Rexp)

38. Pre-asymptotic region
Fits to g1/F1 data using for the ratio
will lead to the same results if the condition
is fulfilled
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

39. LSS’06 vs DSSV
LSS
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

40. As expected, the curves corresponding to g1tot(LSS)/F1(exp) and g1LT(DSSV)/F1LT (MRST) practically coincide (an exception for x > 0.2 !) although different expressions for g1 and F1 were used in the fit
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
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 ???

41. 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