M. J. Varanda DESY

1. Measurement of the Spin Structure Function g1 and of the Strange Helicity ΔS from Inclusive and Semi-inclusive DIS data at HERMES M. J. Varanda DESY

2. Deep Inelastic Scattering - DIS is exact in QED Spin 1

3. Inclusive Cross-Section & Asymetries kinematic factors kin. fact. param. measured param. Measured at Hermes Deuterium only: PZZ=0.83±0.03 Azz~0.01 Inclusive Double Spin Asymmetry T

4. Longitudinal Target Data used for g1 The cut at Q2 = 1 GeV2 identifies the DIS region DIS Pbeam ~ (53 ± 1.8)% Pbeam ~ (53 ± 1.0)% Full analysis can be found in Phys. Rev. D75(2007)012007 Event Selection: kinematical Cuts & bin selection

5. Unfolding of radiative corrections • Measured events have to be corrected for: • Background tail (radiation from (quasi)-elastic) • Radiation from DIS and detector smearing • The smearing of events is simulated through a MonteCarlo which includes a full detector description and a model for the cross-section

6. Unfolding of radiative corrections Error inflation due to unfolding • Before unfolding → observed asymmetry data points are correlated • After unfolding → the statistical errors on the unfolded data points are correlated, systematic error correlations removed The correction for the systematic effect introduces statistical correlations

7. Born Double Spin Asymmetries • Measured and Born Spin asymmetries calculated for the 46 (x,Q2) bins • The Born Asymmetries depend strongly on Q2 for the same x-bin: dependence of the virtual photon polarization on the lepton kinematics • For the g1 extraction: • The unpolarized cross-section extracted using the parameterizations ALLM97 for F2 and R1990 for R = σL/σT

8. Extraction of g1/F1 • Extraction of g1 from parameterizations to A2 and F1: • A2 from fits to available proton and deuteron data • F1 based on F2 parameterizations and on the ratio F2n/F2p measured by NMC • The multiple measurements at different Q2 values evolved using a NLO-QCD fit to all available g1 data, and assuming

9. g1 Results: Proton+Deuteron Proton: Low-x region: central values of SMC larger then those of Hermes reflecting the expected Q2 evolution Deutron: X < 0.04: Hermes Data compatible with zero, consistent with COMPASS while SMC data Favors negative values (at Q2 > 1 GeV2)

10. g1 Results: Neutron ωD= 0.05 ± 0.01 • g1 negative everywhere except at • very high-x • In Q2 < 1GeV2 regime the Hermes data tends to zero at lower x values

11. g1 results; neutron and NS The new measurements constrains the x-dependence of g1 much better than before Differences between Hermes (Q2<1) and SMC(Q2>1) deuteron data are reflected in NS the results

12. First Moment of g1 The g1 first moment was calculated for proton and deuteron data in the DIS range: 0.021 ≤ x ≤ 0.9 Saturation in the deuteron integral is observed g1 vanishes for x→1: contribution from 0.9 ≤ x ≤ 1 @ Q2 = 5GeV2 estimated fitting (1-x)α(1+βx) to HERMES data The Non-Singlet and Neutron integrals from Proton and Deuteron data (use only Q2>1GeV2 data)

13. Integral from Deuteron data Q2=5 GeV2, NNLO in MS scheme -0.085 0.013 0.008 0.009 from hyperon beta decay (a8=0.586±0.031) (SU(3) symmetry assumed) From neutron beta decay a3=1.269±0.003 theory theory ωD=0.05±0.01

14. Semi-inclusive DIS (SIDIS) q h New approach: Strange quark helicity (ΔS) has been extracted from Double Spin asymmetries from K± events produced in a Isoscalar Deuterium Target (isoscalar method) Semi-Inclusive DIS events where a hadron (h) is detected in coincidence with the DIS Lepton allows to probe the flavour content of the nucleon because the detected hadron should be correlated with the struck quark q

15. The Isoscalar method can be applied to isoscalar targets (Deuteron) where the fragmentation process can be described without any assumptions regarding isospin Aside the isospin symmetry between proton and neutron the only symmetry used is charge conjugation invariance Since strange quarks carry no isospin, the strange quark sea is identical in the proton and neutron The isoscalar method is based on the measurement of the inclusive polarized asymmetry A1d(x,Q2) and on the Semi-inclusive polarized charged Kaon asymmetry A1dK±(x,Q2) measured on a deuterium target The fragmentation functions needed in the analysis are directly extracted from the SAME Hermes data ΔS: Isoscalar Method

16. ΔS extraction • Analysis performed in LO • Different systematics from inclusive extraction • No assumption of SU(3) symmetry • It is necessary the knowledge of the Inclusive Purities (PQ and PS) and Semi-Inclusive Purities (PQK and PSK) which are extracted from Monte Carlo

17. Isoscalar Method SIDIS events with K± detected in coincidence with the DIS lepton in a deuterium target where ΔQ/Q and ΔS/S are the Non-Strange and Strange quark Polarizations

18. Kaon Asymmetry for Deuterium • Inclusive and Semi-Inclusive double spin Born asymmetries • Data Selection: • Q2 ≥ 1 GeV2, W2 ≥ 10 GeV2, y < 0.85 • 0.2 < z < 0.8, xF > 0.1, 2.0 GeV < p < 15 GeV • QED radiation, instrumental smearing, detector acceptance

19. Unpolarized Kaon yields ò ò + K K Q ( x ) D ( z ) dz S ( x ) D ( z ) dz K dN ( x ) / dx - non strange strange = + DIS 5 Q ( x ) 2 S ( x ) dN ( x ) / dx Preliminary The Non-Strange and Strange Fragmentation Functions can be extracted from a fit to the Data using the CTEQ6L PDFs

20. Strange Polarisation Hermes Preliminary (Analysis still in progress) The non-strange helicity is in good agreement with the derived from the 5-component flavour decomposition of the Proton helicities

21. Strange Polarization The first momentum of ΔQ is in excellent agreement with the value previously measured ΔQ 0.391 ± 0.019(stat) ± 0.014(sys) ΔS 0.036 ± 0.035(stat) ± 0.007(sys) Δq8 0.319 ± 0.073(stat) ± 0.020(sys) • The first momentum for ΔS(x) is consistent with zero in the measured region 0.02 < x < 1.0 (@ Q2 = 2.5 GeV2) • The octet combination: Δq8(x) = ΔQ(x) - 3ΔS(x) -> First Moment smaller then the axial charge a8=Δq8 = 0.526±0.031 (from hyperon constants assuming SU(3) symmetry)

22. HERMES has measured g1 for proton and deuteron for 0.004 < x < 0.9 and 0.18 GeV2 <Q2<20 GeV2 (0.02 < x < 0.9 for Q2 > 1) Measured results are correlated no longer systematically but statistically Integrals provide a fair comparison for the statistical accuracy of various experiments: Proton data precision is comparable with CERN and SLAC Deuteron data is the most precise so far The deuteron integral is observed to saturate a0 = 0.330 ± 0.011(theor) ± 0.025 (exp) ± 0.028 (evol) at 5GeV2 The extracted strange helicity from the first moment of g1d over the meaured DIS region and assuming SU(3) symmetry is negative by about 4σ Hermes Semi-Inclusive Kaon analysis gives a strange helicity value consistent with zero over the measured x-range, extracting the strange and Non-strange fragmentation functions from a fit to the data. It gives an octet combination different from the axial charge a8 Conclusions

23. EXTRA SLIDES

24. Integrals provide a fair comparison of the accuracies of various experiments (all correlations taken into account) Proton data comparable with SLAC and CERN expts. Deuteron data is the most precise so far Comparisons (*): integrals re-calculated in a smaller x range, to match HERMES

25. The HERMES Spectrometer Kinematic Range:0.02 < x < 0.8 at Q2 > 1 GeV2 and W > 2 GeV Reconstruction:dp/p < 2%, dq < 1 mrad Internal Gas Target: unpol: H2, D2, He, N, Ne, Kr, Xe , He , H , D , H Particle ID: TRD, Preshower, Calorimeter --- 1997: Cherenkov, 1998: RICH: Identification of K±/π±/protons in 2 ≤p≤15GeV