Measurement of polarized distribution functions at HERMES

1. Measurement of polarized distribution functions at HERMES Alessandra Fantoni (on behalf of the HERMES Collaboration) • The spin puzzle & the HERMES experiment • Polarised quarks distributions • Transversity 13th International QCD Conference Montpellier 03-07 July 2006

2. HERa MEasurement of Spin (DESY) 180 Researchers from 30 Institutions of 12 Countries • Study of nucleon structure • double spin asymmetries • (inclusive, seminclusive) • single spin asymmetries • (seminclusive, transversity and exclusive processes) Data taking since 1995

3. The Nucleon Spin DS Polarised Deep Inelastic Scattering (DIS) HERMES (√s=7 GeV): Q2max = 20 GeV2

4. 27.5 GeV (e+/e-) <Pb>~ 53±2.5 % 1H→ <|Pt|> ~ 85 % 2H→ <|Pt|> ~ 84 % 1H <|Pt|> ~ 74 % gaseus atomic target, high polarisation, non diluited Characteristiques of the HERMES experiment • resolution: • dp/p~2%, dq<1 mrad • PID: leptons with • e~98%, contam. <1% • hadronsdual RICH:p, K,p • 2<Eh<15 GeV Stern-Gerlach separation

5. hadron/positron separation combining signals from: TRD-Calorimeter-Preshower-RICH Aerogel; n=1.03 p C4F10; n=1.0014 K Particle Identification hadron separation Dual radiator RICHfor p, K, p

6. Polarized quark distributions Inclusive DIS: Measurements of g1 onp,d,3Heprovides PDF through the Q2 evolution

7. Measured Q2 Polarised Structure Functions : g1 g1(x) world data (at measured Q2) • g1 corrected for instrumental smearing (unfolded) and QED radiative effects • measured on neutron (3He, 1995), proton and deuteron targets • Better precision for g1n from g1d-g1p • Data can be used in NLO QCD fits to obtain polarized PDFs • Two methods will be used • g1 and QCD fit papers under preparation

8. Flavor tagging p+ ud K- us p- ud Fragmentation Function (FF) Partonic Distribution Function (PDF) z=Eh/(E-E’) Polarised semi-inclusive DIS

9. Polarised Quark Distribution Functions Polarised Parton Distribution Functions Dqf(x)=q+(x)-q-(x) Hadronic asymmetries to be measured Extract Dq by solving known quantities Purity Functions

10. statistics sufficient for 5 parameter fit: Measured Asymmetries Deuteron Proton

11. in measured range (0.023 – 0.6) : seaquarks (u, d, s, s):compatibile with 0 - - - First direct 5-flavor separation of polarised PDFs Polarised Quark Distribution Functions [PRL92(2004), PRD71(2005)] u quarks: large positive polarisation dquarks: negative polarisation

12. transversely polarised quarks and nucleons dq(x): helicity flip tensor charge measuring ! • unpolarised quarks • and nucleons • q(x): spin averaged • vector charge well known longitudinally polarised quarks and nucleons Dq(x): helicity difference axial charge known Nucleon quark structure

13. Peculiarities of Transversity dq NOT allowed in e.m. & strong interactions Single helicity flip chiral-odd DF Double helicity flip chiral-odd DF x chiral-odd FF “Collins” FF

14. DIS + SIDIS cross section Chiral-odd Distribution Function High sensitivity to the valence quark polarization q and q have opposite sign. _ Relativistic nature of quark. In absence of relativistic effects h1(x)=g1(x) Q2 -evolution. Unlike for g1p(x), the gluon doesn’t mix with quark in h1p(x) Tensor charge: first moment of h1. Calculable by lattice QCD. Peculiarity of • Chiral-even naïve T-odd DF • Related to parton orbital momentum • Violates naïve universality of PDF • - Different sign of in DY (Collins) (Sivers)

15. Transversity asymmetry[PRL94(2005)]  transversity x Collins FF  Sivers DF x FF unpolarised Sivers DF connected to quark angular momentum

16. Angles and Asymmetries Definitions Separation DF and FF weighting the events with their phT No other assumption necessary !! Convolution Integral on initial quark transverse momentum pT and final k T Bi-dimensional fit of A(f, fs)

17. Ferving activities STAR PHENIX Hall A CLAS COMPASS BELLE • Significant non zero asymmetries • Ap+>0, Ap-<0 • |Ap-| > |Ap+| ? • Possible evidence • First measurement of naïve T-odd DF in DIS • ? • . Transversity Asymmetries[PRL94(2005)] • p+positivo e p- negativo

18. Transversity Asymmetries on Kaons • A k+ > 0, Ak-≈ 0 • Systematic uncertainty: • PID, Acceptance, Smearing, • Unpolarised cosine moments • No Significant non zero amplitudes • Systematic uncertainty: • PID, Acceptance, Smearing, • Unpolarised cosine moments

19. Transversity Asymmetries on Kaons-Pions • Ak+ consistent with Ap+ • u quarks dominance • Collins FF similar for p and k ? • Ak+ larger than Ap+ in some bins • u quarks dominance • Sea quarks contribution to Sivers moment important ?

20. Conclusions • Polarised Structure Functions: • Precise and complete measurement of g1 • Polarised Quark Distributions: • First complete separation of pPDFs w/o assumption on sea polarization • No hint of negative strange sea • Transversity: • First measurements of Collins and Sivers moments for pions in SIDIS • First measurements of Collins and Sivers moments for kaons in SIDIS • 2005 data will double the statistics • Collins function estimation will allow extraction • of the transversity distribution • 5. Sivers function will be extracted in the next • few years at HERMES