1. Determination of the gluon polarisation at HERMES N. Bianchi on behalf of: The HERMES Collaboration & The main analyzers (P.Liebing, E.Aschenauer, R.Fabbri, V.Mexner, …) N.Bianchi, Pacific SPIN07, Vancouver BC

2. How to measure G: indirect N.Bianchi, Pacific SPIN07, Vancouver BC For fixed target exp. small x-Q 2 lever arm: g (and q) very badly determined : G 0,5 1

3. How to measure G: direct (general) N.Bianchi, Pacific SPIN07, Vancouver BC Method: Photon-Gluon-Fusion t h/2m q Charm-production : PGF dominated and hard scale by the mass of c-Quarks Open charm: clean process (no charm quarks in the nucleon wave function)

4. How to measure G: direct (high p t ) N.Bianchi, Pacific SPIN07, Vancouver BC (Pairs of) hadrons with high transverse momenta (Hard scale: p t = 1 – few GeV range) Open charm needs very high energy to access to charm production (CERN, RHIC experiments) At HERMES hidden charm (J/ ) is produced and identified : low statistics less clean channel due to VMD contribution and FSI Best direct way for HERMES to measure G:

5. First HERMES measurement N.Bianchi, Pacific SPIN07, Vancouver BC First longitudinal double spin asymmetries for 2 hadrons Historical plot : first HERMES data and future projections A. Airapetian et al, Phys. Rev. Lett. 84 (2000) 2584

6. Old HERMES data N.Bianchi, Pacific SPIN07, Vancouver BC Following SLAC pioneristic measurement on un-tagged single hadron asymmetry.. HERMES preliminary 2001 …. the differences between the curves (BBS) are less than the differences between any of the curves and the data. This makes it impossible to draw any conclusions about G(x). ….The present data will provide valuable experimental constraints on such models, and perhaps lead to constraints on the gluon polarization in the nucleon in the future. (E155 - Phys.Lett.B458 (1999) 536) Proton Deuteron

7. New HERMES data N.Bianchi, Pacific SPIN07, Vancouver BC improved statistics both H and (high statistics) D longitudinally polarized target new anti-tagged analysis improved a lot the MC knowledge and tuning systematic studies different channels (anti-tagged, tagged, pairs)

8. Asymmetries (anti-tagged) N.Bianchi, Pacific SPIN07, Vancouver BC Anti-tagged data: Scattered lepton not in acceptance p t measured with respect to beam axis for p t >1.05 GeV : 1272k(419k) for deuteron (proton) sample Curves from MC +asymmetry model using: Δg/g(x)=0 : central Δg/g(x)=-1 : upper Δg/g(x)=+1 : lower Δg/g(x)=0 asymmetry is due to quarks (DIS at large Q 2 and x at large fake p T ) Gluons become important for above p t 1 GeV

9. Asymmetries (tagged) N.Bianchi, Pacific SPIN07, Vancouver BC Tagged data: Scattered lepton detected in acceptance p t measured with respect to virtual photon Q 2 >0.1 GeV 2, W 2 >4 GeV 2 for p t >1 GeV : 53k (19k) for deuteron (proton) sample Curves from MC +asymmetry model using: Δg/g(x)=0 : central Δg/g(x)=-1 : upper Δg/g(x)=+1 : lower Δg/g(x)=0 : large and stable asymmetry is due to quarks in DIS events averaged in the HERMES acceptance

10. Asymmetries (hadron pairs) N.Bianchi, Pacific SPIN07, Vancouver BC Anti-tagged data for pairs of charged-hadrons: No regards on scattered lepton (10% are detected) p t measured with respect to beam axis p t (h1,h2) > 0.5 GeV for >2 GeV 2 :60k (20k) for deuteron (proton) sample plotted vs. lower cut on: Curves from MC+asymmetry model using: Δg/g(x)=0 : central Δg/g(x)=-1 : upper Δg/g(x)=+1 : lower

11. Extraction (general) N.Bianchi, Pacific SPIN07, Vancouver BC Measured asymmetry is an incoherent superposition of different hard and soft subprocess asymmetries: Signal: Gluon of the nucleon in the initial state Background: all other sub-processes MC Lepto : LO and NLO DIS but no photoproduction Pythia : DIS but also non perturbative model for photoproduction

12. MC Models N.Bianchi, Pacific SPIN07, Vancouver BC MC model PYTHIA 6.2,tuned and adapted for HERMES data fragmentation process, intrisic k t, exclusive ρ 0 cross section (VMD) Provides kinematics of the hard subprocess relative contributions f i of the background and signal subprocesses in the relevant pt range background asymmetries and the hard subprocess asymmetries -weight calculated for every MC event -PDFs (unpol/pol): Hard process CTEQ5L/GRSV2000 (nucleon) Hard resolved photon processes SaS2/GRS (photon) -Asymmetry assumptions for soft processes: A=0 for exclusive/diffractive processes A~A1(low x) from world data for soft nondiffractive (low- pT) Vary PDFs/assumptions for syst. error

13. Subprocesses N.Bianchi, Pacific SPIN07, Vancouver BC

14. Subprocesses N.Bianchi, Pacific SPIN07, Vancouver BC VMD (elast.+diffr., soft low-pT): decreasing with p TDIS: increasing (dominating) with p T QCD2->2(q): QCDC/QCD2->2(q): increasing with p T Signal processes are PGF and QCD2>2(g) (resolved photon) Antitagged, Charge combined, Deuteron data

15. Asymmetries of Subprocesses N.Bianchi, Pacific SPIN07, Vancouver BC Antitagged, Charge combined, Deuteron data DIS increasing with p T (x): positive QCD2->2 QCDC/QCD2->2,VMD: flat and small but important for background asymmetry! |PGF| increasing with p T |PGF| increasing with p T :negative QCD2->2(g): opposite to PGF, small

16. g/g extraction: methods I and II N.Bianchi, Pacific SPIN07, Vancouver BC Method I: –Factorize –Assumes No sign change in â(x) flat g/g(x) –No information on of measurement –Gives average g/g over covered x range (0.07<x<0.7) Method II: –Fit: find a g/g(x) such that –Assumes functional form for g/g(x) –Only small range in p T –Gives g/g(x) and average x of measurement

17. G from method I N.Bianchi, Pacific SPIN07, Vancouver BC h +,h - antitagged: 4 points between 1.05<p T <2.5 GeV h +,h - tagged: 1 point for p T >1 GeV Pairs: 1 point for GeV 2 Assuming g(x)/g(x) const over x : Only statistical errors are shown Results for different data samples (diff. mixtures) agree within statistics Consistency between the two hadron charges and the two targets Dominating sample: Deuteron antitagged -> Used for Method II and syst. error analysis (charge combined)

18. G from method II N.Bianchi, Pacific SPIN07, Vancouver BC Light shaded area: range of all data Dark shaded area: fit center of gravity (span of the 4 p t bins) Several test functions Final 2 functions used are polynomials with 1(2) free parameters Fix: - g/g x for x 0 - g/g 1 for x 1 | g/g(x)|<1 for all x Difference between functions is a systematic uncertainty (Anti-tagged only)

19. G from method II N.Bianchi, Pacific SPIN07, Vancouver BC 2/ndf 5 mainly due to highest p T point Model systematic is not included in fit 1-2 parameter function is too smooth function 1 used as default and function 2 for systematics

20. Model systematic N.Bianchi, Pacific SPIN07, Vancouver BC PYTHIA 6.2 has been tuned: fair agreement in tagged region (see plot vs kinematic variables) less agreement in anti-tagged region some failures in p t dependence checks with LO pQCD (collinear) Uncertainties from each group –PYTHIA params. –PDFs –low-p T asym. summed linearly to Models uncertainty Experimental (stat.+syst.) added in quadrature –syst. uncertainty (beam&target) from 4% scaling uncertainty to 14% on g/g

21. Results vs world data N.Bianchi, Pacific SPIN07, Vancouver BC Black and blue curves: pQCD fits to g1 Black data points: CERN exp results Red data point: Prel. HERMES Method I Red curves Prel. HERMES Method II: fit Δg(x)/g(x) with 2 functions such that

22. Conclusions N.Bianchi, Pacific SPIN07, Vancouver BC g/g(x, 2) = 0.071 ± 0.034(stat) ± 0.010 (sys-exp) (sys-model) g/g(x, 2) = 0.078 ± 0.034(stat) ± 0.011 (sys-exp) (sys-model) g/g has been extracted by HERMES using two different methods Method I Method II +0.125 -0.082 -0.105 -0.127 Syst. model uncertainties still dominating (PDFs, PYTHIA model) G/G is likely small G/G is unlikely to solve the puzzle of the nucleon missing spin

23. Back up slides N.Bianchi, Pacific SPIN07, Vancouver BC