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The spin structure function g 1 and QCD fits to the g 1 world data

The spin structure function g 1 and QCD fits to the g 1 world data. Lara De Nardo TRIUMF/DESY. Outline. Definition of g 1 Review of recent g 1 data HERMES COMPASS CLAS Review of recent fits to g 1 LSS AAC BB COMPASS Some ideas Conclusions.

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The spin structure function g 1 and QCD fits to the g 1 world data

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  1. The spin structure function g1 and QCD fits to the g1 world data Lara De Nardo TRIUMF/DESY

  2. Outline • Definition of g1 • Review of recent g1 data • HERMES • COMPASS • CLAS • Review of recent fits to g1 • LSS • AAC • BB • COMPASS • Some ideas • Conclusions

  3. Inclusive Deep Inelastic Scattering is exact in QED in LO QCD

  4. Inclusive Deep Inelastic Scattering is exact in QED in LO QCD

  5. Measured Inclusive Asymetries kinematic factors kin. fact. param. measured param. Measured at HERMES, with Pzz=0.83±0.03 Azz~0.01 measured DIS cross section inclusive asymmetry:

  6. g1 World Data P,D D

  7. HERMES results • 0.0041 < x < 0.9 • 0.18 GeV2 < Q2 < 20 GeV2 • Correction for smearing and radiative effects introduces statistical correlations • Statistical uncertainties are diagonal elements of covariance matrix • Systematic unc. are dominted by target and beam polarization Phys.Rev.D75(2007)012007

  8. Integrals Q2=5 GeV2, NNLO in MS scheme Saturation in the deuteron integral is assumed • Use only deuteron data! from hyperon beta decay (a8=0.586±0.031) theory theory ωD=0.05±0.01 (use only Q2>1GeV2 data) from neutron beta decay a3=1.269±0.003

  9. COMPASS results 2002-2003 data Q2<1 GeV2 0.0005<x<0.02 • At low Q2only measurements from SMC and COMPASS • 10 times lower statistical error than SMC Phys.Lett.B647(2007)330

  10. COMPASS results • 2002-03-04 data • 89M events 0.78GeV2 < <Q2> < 55.3GeV2 0.003<x<0.7 a0= 0.35 ± 0.03(stat) ± 0.05 (syst) at 3GeV2 • A1 compatible with zero for x<0.05 • No tendency towards negative values at low x (as in SMC) Phys.Rev.D75(2007)012007

  11. Data on g1n • g1nnegative everywhere except at very high-x • Recent HERMES results indicate that low-Q2 data tends to zero at low-x • does not support earlier conjecture of strong decrease for

  12. A1 World Data

  13. CLAS E155fit CLAS fit at Q2=10GeV2 • 400 points for p and 1654 for d! (633 for Q2>1GeV2 and W>2GeV) • Clear decrease of asymmetries with decreasing Q2 Phys.Lett.B641(2006)11

  14. g1 QCD fits minimize (for HERMES data) minimize DS, DqpNS, DqnNS, DG or Duv, Ddv, Dq, DG (need assumption on the sea) Start from model at initial Q2=Q20: DGLAP: to go fromQ20toQ2data Calculate g1fit at the Q2 of all data points: • g1 QCD fits are models for Dq(x,Q2) obtained by fitting inclusive world data on g1 : get

  15. Evolution of Statistical Uncertainties X-space Statistical uncertainties are given by: • Calculable exactly at Q20 since the functional form of Dq is known at Q20. • The derivatives of the distributions evolve just like the distributions! • One has to take into account the fact that e.g. DG does not depend • on the DS parameters only at Q20! • For details on the unc. calculations in Mellin space see BB paper

  16. COMPASS’06 x space Mellin space x space Mellin space • Positivity imposed to Ds and Dg (asym. errors) Q2=3GeV2 • A negative Dg is needed at low-x in order to represent data

  17. LSS’06 • New data: • Low Q2 CLAS data • COMPASS data (large Q2) Initial parameterization: Higher twist terms included in the fit: i=1,…,5: 10 parameters +6 for PDs (=8-2 for sum rules) E.Leader et al.,Phys.Rev.D75(2007)074027

  18. LSS06: Impact of CLAS data Number of data points: 190 823 • Low-Q2 data increases precision in the determination of HT • PDF accuracy is also improved • (it has to be noted that other groups (BB) have not found such a strong signal for HT) Plots from D.Stamenov’s talk at DIS07

  19. CLAS12 expectations x(Du+Du) x(Dd+Dd) CLAS12 LSS06(with EG1) Q2=2.5GeV2 LSS05 xDG xDs 12 GeV upgrade EG1: 0.05 <Q2<3.5GeV2(2001) EG12: 0.5<Q2<7 GeV2(2012?) • EG1 improves • Du, Dd, Ds, DG • CLAS12 will particularly improve DG K.Griffionen, DIS07

  20. LSS06: Impact of COMPASS data Number of data points: 823 826 Old:Phys.Lett.B612(2005)154 New:Phys.Lett.B647(2007)8 (2.5 times larger statistics) • Data at large Q2 does not impact HT Differently from what found by COMPASS, g1d is almost insensitive to the sign of Dg, but depends on the HT terms • Effect of new data is negligible

  21. LSS06 vs COMPASS06 DG>0 DG>0 DG<0 DG<0 Same c2 for the three solutions LSS’06 • The solution with DG>0 is pushed to zero at low-x, in order to explain g1d data almost zero (it would make g1d more negative) • Differences between the two fits interpreted as due to HT terms missing in COMPASS06

  22. Impact of HERMES data Without HERMES g1d With HERMES g1d (test done with BB code, Nucl.Phys.B636(2002)225) • DG=0.32±0.47 0.22 ±0.39 (stat). • The effect on the other parton distributions is much less visible • ∆S =0.22 ± 0.11 ± 0.05(exp) ± 0.06(theo) Thanks to H.Böttcher

  23. AAC06 • Positivity imposed • 11 free parameters • Error bands with Fit A: DIS A1 + PHENIX data Fit B: DIS A1 • Hermes data is described better (red) when DG is included in g1 • DG should be positive in the region 0.033<x<0.065 • Remaining discrepancies described by LSS with HT: M.Hirai et al., Phys.Rev.D74(2006)014015

  24. AAC06 Resulting distributions compared to previous analyses

  25. AAC-low-x is dominated by gg scattering at small pT It depends on no sign dependence! Fit 3: allow for negative Dg in the low-x region • To explain the negative at pT=2.38GeV a negative gluon is needed for 0.06<x<0.2 • No change is observed in the quark distributions • The negative Dg does not reside in the Fit-1 error band! • The uncertainties depend on the error band!! • Error due to functional form not included in uncertainties

  26. Comparisons with existing DG measurements AAC06 LSS06 COMPASS06 • The precision of the data is not yet able to discriminate among various functions New HERMES analysis that supercedes the old one will be presented by N.Bianchi

  27. (Not so) Random issues on QCD fits

  28. Results Stability • Up to three minima have recently been seen with similar values ofc2. • Test the stability and accuracy of the methods using MonteCarlo pseudo-data generated from a chosen set of polarised parton distributions • compare then with the fit results. LSS’06

  29. Statistical Uncertainties c2 Dc2 pj pi • At least two groups (BB and AAC) report statistical uncertainties inflated by • They cannot be directly compared to those of other groups. (These inflated uncertainties do not correspond to what is normally understood as statistical uncertainty, obtained as the standard deviation of the distribution of results derived by fitting a large number of MC data sets resembling the experimental data sets, but with each data point fluctuating independently according to the experimental statistical uncertainty) • Dc2=1 defines the 1s uncertainty for single parameters • Dc2~NPAR is the 1s uncertainty for the NPAR parameters to be simultaneously located inside the hypercontour • (normally used for unknown systematics, see CTEQ, MRST….) NPAR=number of parameters

  30. Normalization Uncertainties One can get even more fancy and consider the experimental systematic uncertainties: Si can also be calculated analytically at each step • Some groups attempt to account for the (substantial) syst. unc. common to an entire data set for one experiment by adding it incoherently in quadrature to the uncertainty in each data point. • It can be accounted for correctly with ac2 penalty term, see BB: Fitted normalization Norm. unc. quoted by expt. • The normalizations can also be calculated analytically at each step, without increasing the number of parameters in the fit:

  31. Symmetric Sea Assumption: new results from COMPASS HERMES, Q2=2.5GeV2 • The estimated v is 2.5stat away • from the symmetric sea scenario

  32. Conclusions • The new g1 data from HERMES, COMPASS and CLAS provide new insights into the polarised quark distributions. • At the moment still other data (like for AAC or semi-inclusive asymmetries for De Florian et al.) has to come in aid of QCD fits in order to pin down the gluon distribution • For more precise data on DG from scaling violations of g1, proposed e-p colliders e-LIC and eRHIC • The latest QCD fits look at various aspects of Dq (AAC:gluon, LSS:HT…) • It would be nice to have one comprehensive analysis with all these features: • HT calculation • Statistical error band calculation • explicitely state which Dc2 choice was made and possibly provide results with the two choices • Propagation of systematic uncertainties • Fit NS to test the Bjorken Sum Rule • Fit as • …… • And last by not the least, I’d like to thank all the people that knowingly or not provided me with their plots!

  33. as(M 2Z ) • QCD fits are a powerful way to extract as(M2Z ). • While a variety of results exist in unpolarised DIS (up to N3LO), only sparse information is available from fits to g1 data, with large errors J.Blümlein et al.,Nucl.Phys.B774(2007)182

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