1. 1 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The challenge to extract  G/G from HERMES data

2. 2 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer HERA: e + /e - (27GeV) - proton collider HERA @ DESY Polarized Deep Inelastic Scattering HERMES @ HERA self-polarised electrons: e ~ 53 ± 2.5 % 27.5 GeV (e  /e  ) ~ 53 ± 2.5 % 1 H → ~ 85 ±3.8 % 2 H → ~ 84 ±3.5 % 1 H ~ 74 ±4.2 % pure nuclear-polarized atomic gas, flipped at 90s time intervals

3. 3 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The HERMES Spectrometer Kinematic Range: 0.02 1 GeV 2 and W > 2 GeV Reconstruction:  p/p < 2%,  < 1 mrad Particle ID:  TRD, Preshower, Calorimeter a 1997: Cherenkov, 1998 a : RICH + Muon-ID Internal Gas Target: unpol: H 2,D 2,He,N,Ne,Kr, Xe He, H, D, H

4. 4 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer hadron/positron separation combining signals from: TRD, calorimeter, preshower, RICH Aerogel; n=1.03 C 4 F 10 ; n=1.0014 hadron separation Dual radiator RICH for , K, p Particle Identification  K

5. 5 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The golden channels Idea: Direct measurement of  G Isolate the photon gluon fusion process (PGF) Open Charm production HERMES = 7.2GeV HERMES = 7.2GeV too low count rates too low count rates high p t hadrons or pairs of hadrons go to low Q 2 increase statistics scale of hard sub-processes Data on tape: polarized proton data 50pb -1 polarized deuterium data 140pb -1

6. 6 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer What is needed to get  G/G Double spin asymmetries for high p t hadrons and pair of hadrons A theoretical model describing all underlying sub-processes all underlying sub-processes fragmentation fragmentation two possibilities: QCD calculation a la B. Jaeger, M. Stratmann, W. Vogelsang hep-ph/0505157 Advantage: can be done to order  s 2 Disadvantage: to include detector effects (acceptance,..) difficult difficult Monte Carlo simulation (PYTHIA-6) Advantage: detector effects can easily be included Disadvantage: max. order  s 1

7. 7 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Asymmetries Inclusive hadron double spin asymmetries: 2 kinematical regions: “Photo-production”: anti-tagging of scattered lepton “Photo-production”: anti-tagging of scattered lepton Event kinematics unknown Event kinematics unknown p t vs beam-axis p t vs beam-axis “Transition region”: tagging of scattered lepton p t defined relative to virtual photon direction p t defined relative to virtual photon direction Q 2 > 0.1 GeV 2 Q 2 > 0.1 GeV 2 high p t pairs of hadrons “Photo-production” + “Transition region”: p t vs beam-axis p t vs beam-axis Event kinematics unknown; only 10% events have e’ Event kinematics unknown; only 10% events have e’

8. 8 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Asymmetries („Photo-production“) P-asym.’s > 0 D-asym.’s ~ 0 at small p t Positive h have positive asym. negative h have 0 or negative asym. at large p t  Blue: Proton data Red: Deuteron data Red: Deuteron data  All hadrons  Pions  Kaons

9. 9 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Asymmetries („Transition“)  Blue: Proton data Red: Deuteron data Red: Deuteron data  All hadrons  Pions  Kaons At p t >1 GeV: Q 2  1.5 GeV 2, x  0.05 A  relatively flat in p t Follows average behavior in SIDIS Small difference of positive and negative h Statistics at p t >1 GeV limited

10. 10 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Asymmetries (pairs of hadrons) Proton Deuteron A  relatively flat in  p t 2 Proton asym. > 0 for all  p t 2 Deuteron asym. 2 GeV Statistics at  p t 2 > 2 GeV limited Define:

11. 11 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Model in PYTHIA-6 VMDdirect anomalous photon „Soft“ VMD: Elastic, diffractive, non-diffractive („minimum bias“, „low-p T “) processes Hard VMD: QCD 2  2 processes QCD- Compton PGF LO DIS (virtual photons) Splitting of   qq QCD 2  2 processes Model: Mix processes with different photon characteristics Small Q 2 : VMD+anomalous (=„resolved“) photon dominate Large Q 2 : LO DIS dominates Choice of hard process according to hardest scale involved: If all scales are too small: „soft“ VMD (diffractive or „low-pT“) The „resolved“ part is modeled to match the world data on  (  p)

12. 12 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Challenges Intrinsic k T  0.4 GeV p T from fragmentation  0.35 GeV Q 2 small  expect contribution from  expect contribution from VMD processes VMD processes Small scales (O(1 GeV 2 ))  Important:  Important: non-perturbative contributions, non-perturbative contributions, NLO corrections NLO corrections Fraction of hard gluon initiated processes small  large background  large background All effects are folded with acceptance Fixed target energy : Measured p T 1-2 GeV High energy:

13. 13 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Adapting Pythia to Hermes Kinematics Check PYTHIA VMD model to exclusive  0 production In “Transition” region as full kinematics known; Q 2 > 0.1GeV 2 Default PYTHIA:  (PYTHIA) ~ 6 *  (HERMES) Changes: The Q 2 slope of the total (resolved)  *p-cross section of world data The parametrisation of The  -VM couplings The angular distribution of the  decay products

14. 14 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Adapting Pythia to Hermes Kinematics The exclusive  0 cross section data-MC agrees now within 10% Diffractive contribution ~10% Diffractive contribution ~10% The PYTHIA  0 cross section also matches the “photo-production” data well

15. 15 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Fragmentation DATA: unpolarised p-target Q 2 > 1GeV 2, W 2 >10 GeV 2, z>0.2, 2 1GeV 2, W 2 >10 GeV 2, z>0.2, 2<p h <15GeV Tuning of JETSET FF parameters to multiplicities in acceptance MC: PYTHIA in combination with JETSET; PDF:CTEQ-6     KKKK KKKK KKKK KKKK pp

16. 16 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Fragmentation-Purities Proton target purities K-K-K-K- K+K+K+K+ ++++ ----u 4*s d

17. 17 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Contamination from excl. VM Exclusive VM production different process than SIDIS estimate the contribution from Pythia-6  large contribution at high z K: moderate contribution vs. z  contribution growing with x B decreasing x B decreasing

18. 18 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Experimental Multiplicities systematic uncertainty mainly from hadron PID correction Q 2 > 1GeV 2, W 2 > 10GeV 2 EMC: Fragmentation Function (Nucl. Phys. B321 (1989) 541)

19. 19 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Cross Section vs Q 2 and z Agreement in < 20% How are things looking vs p t ? three critical variables intrinsic k t of parton in photon or nucleon (PARP 91 / 99) p t from fragmentation p t from fragmentation (PARJ 21) (PARJ 21) Implement QED radiative corrections into PYTHIA using RADGEN Cross section for “Transition” region Q 2 > 0.1GeV 2 green curve relevant one

20. 20 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Cross Section vs p t HERMES standard values: M. Anselmino et al. Phys. Rev. D71,074006 Cross section for “Transition” region Q 2 > 0.1GeV 2 Has the cross section from PYTHIA and Data to agree PYTHIA and Data to agree at p t > 1GeV ???

21. 21 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Cross Section vs p t (II) Process fractions for “Transition” region Q 2 > 0.1GeV 2 : p t > 1GeV: (  s 1 ) process start dominating what about (  s 2 ) corrections ???

22. 22 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer NLO Corrections Polarized and unpolarized cross sections and k factors Scale dependence of polarized cross section at LO and NLO Calculations from B. Jaeger et al. hep-ph/0505157 for HERMES: “Photo-production” kinematics big NLO corrections

23. 23 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer k-factors and PYTHIA Cross section vs pt in “Photo-production”: The cross section from PYTHIA and Data have can not agree PYTHIA and Data have can not agree at p t > 1GeV !!! PYTHIA includes only  s 1 processes

24. 24 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer The Method Measured asymmetry is an incoherent superposition of different sub-process asymmetries: Signal: Gluon of the nucleon in the initial state Background: all other sub-processes The gluon polarization is then: Asymmetry of the hard sub-process

25. 25 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer PYTHIA itself gives only unpolarized xsec Calculate asymmetry weight for each event Takes kinematical distribution into account Asymmetries of hard processes known Correlation of p t and hard p t for p t > 1 GeV Assume something about Polarization of partons in resolved photon Asymmetry of „soft“ VMD processes Results – MC Asymmetries Averaged sub-process asymmetries for QCD 2  2 processes (hard VMD- und anomalous photon processes) LO DISQCDCPGF ? LO/NLO DIS processes, in „Transition“ region

26. 26 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Results – MC Asymmetries Soft VMD (low-p t ) dominates (40-70%) LO DIS dominates (50-90%) Soft VMD (low-p t > 60%, diffractive 10-40%) dominates Asymmetries vs. x in „Transition“ region Asymmetries vs. p t in „Photo-production“ region (small p t ) Large uncertainty in assigning asymmetry to low-p t Large uncertainty in assigning asymmetry to low-p t process process If it is VMD, it should not have an asymmetry If it is VMD, it should not have an asymmetry If it has an asymmetry, it should not be VMD If it has an asymmetry, it should not be VMD

27. 27 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Photon PDFs Anomalous and hard VMD processes enter in background q(photon)+q(nucleon)  2 „jets“ and in signal q(photon)+g(nucleon)  2 „jets“ g(photon) negligible Only maximal and minimal scenarios for Δq/q (photon) available using Δq/qmax=1 and Δq/qmin=-0.6 Δq/qmin=-0.6 Large part of total uncertainty, scales with central value M. Glück et al., Phys. Lett. B503

28. 28 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Results  G/G Proton Deuteron DIS suppressed at high  p t 2, <10% PGF+hard g ~ 3-4*QCDC (~10%)  p t 2 >2.5 GeV  p t 2 >2.5 GeV „soft“ VMD dominates at low  p t 2 Hard VMD processes ~15%,  p t 2 >2 GeV “Photo-production” high p t hadron pairs “Photo-production” high p t hadron pairs

29. 29 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Results – Sub-process Fractions „Transition“ Region „Transition“ Region „Photo-production“ DIS rises and dominates at high p t PGF+hard g ~ 2-3*QCDC, ~25%, p t >1 p t >1 GeV, Hard g ~ 40% of signal „soft“ VMD dominates at small p T, ~40%, p T  1 GeV Hard VMD processes 10%, p T >1 GeV DIS suppressed at high p t, 20% PGF+hard g ~ 2-3*QCDC, ~10-25% p t >1 GeV p t >1 GeV „soft“ VMD ~15%, p T  1 GeV Hard VMD processes ~10%, p T >1 GeV

30. 30 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Results – ΔG/G „Photo-production“ reg „Photo-production“ reg. Scale Q 2  1.25 GeV 2, x  0.15 At p T <1.5 GeV results for Proton > Deuteron „Transition“ region Scale Q 2  1.77 GeV 2, x  0.16 2.8  difference between h + and h - Deuteron 4 independent data sets (p, d, h ± ) 4 independent data sets (p, d, h ± )

31. 31 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Results - ΔG/G “Photo-production” “Photo-production” combined data sets combined data sets Combined data in both regions Combined data in both regions “Transition” “Transition” only Deuteron data; p t > 1 GeV only Deuteron data; p t > 1 GeV “Photo-production”; p t > 1.35 GeV “Photo-production”; p t > 1.35 GeV

32. 32 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Open Points Very wide correlation between p t and x g Very wide correlation between p t and x g Can the mean value theorem be used to calculate  G/G Can the mean value theorem be used to calculate  G/G depends strongly on shape of if not, redo last step of analysis with different formalism if not, redo last step of analysis with different formalism Pythia calculates only unpolarised kinematics Pythia calculates only unpolarised kinematics unpol. kinematics = / = polarized kinematics unpol. kinematics = / = polarized kinematics only solution polarized MC only solution polarized MC/

33. 33 Workshop on ‘Contribution of the Gluon Spin to the Proton Spin’ – RIKEN 05 P.Liebing / E.C. Aschenauer Conclusion Hermes can extract ΔG/G from tagged and anti-tagged high-p t hadron asymmetries with good statistics and Big model (MC) dependence not so small estimated systematic uncertainties within one model Not yet accounted for: Large NLO corrections to pol. and unpol. cross sections Statistical uncertainties of pol. and unpol. PDF used (including g(x)) Analysis of high-p t hadron pairs consistent Find solution to open points For less model dependent measurements: Higher energy (collider) – need high luminosity For ep or  p: Measure pol. photon PDFs Clean process (prompt photon at RHIC?) and/or heavy quarks (open charm?)