Gluons’ polarization in the nucleon

1. Gluons’ polarization in the nucleon Summary of results and ideas where we are and where we go Ewa Rondio, A. Soltan Institute for Nuclear Studies Warsaw, Poland

2. plan • Introduction • Early information from QCD fits • Need for „direct measurements” • Present results from DIS • Important contribution from pp • Fit in NLO including DIS and pp data • Complementarity of Dg/g results

3. What spins in the nucleon? introduction It all started 20 years ago (1988/89) from this measurement EMC measurement of cross section asymmetries on polarized proton extended towards low x and showed that: Quark contribution is not enough to explain spin of the proton • What are the other candidates? • gluons • orbital angular momentum • of quarks and gluons

4. Remarkable experimental progress in QCD spin physics in the last 20 years • Inclusive spin-dependent DIS • EMC, SMC, COMPASS • E142,E143,E154,E155 • HERMES • Jlab-Hall A, B(CLAS) • Semi-inclusive DIS • SMC, COMPASS • HERMES • Polarized pp collisions • RHIC • PHENIX & STAR

5. QCD analysis done by many groups (experimental and theoretical)input: DIS inclusive data g1(x,Q2) for p, d, 3He QCD fits to all inclusive measurements information on Dg(x) from evolution (indirect) as gluons do not couple to photon, but influence Q2 evolution method: assume functional form for parton distributions at selected Q02 calculate expected values of g1 at every (x,Q2) point where measured using look for parameters giving best description of the data first only inclusive DIS , more inputs  later g(x,Q02) is parametrized, important is the selected Q02 functional form and also first moment depend on it, flexibility is an issue

6. Early phase of analysis Many efforts in the past have been made - Ball, Forte, Ridolfi (1994) • Gluck, Reya, Stratmann, Vogelsang (2001) • Blumlein and Bottcher (2003) • Leader, Sidorov, Stamenov (2006) • Hirai, Kumano, Saito (2006) • ….. Weak constraints from the data, only very simple gluon functions were possible, Q02 of the fit is important functional form and also first moment depend on it

7. Gluon is a natural candidateto carry spin of the nucleon it carries about 50% of the proton momentumit can contribute also to spin • fits with different inputs (changing with time)  more precise • assumptions functional form flexible positive negative with sign change higher twists ………… Spread getting smaller with time, but still large Let’s look at the latest results Polarized gluon distributions from QCD fits all presently available (also historical)

8. Gluon polarization form fits (DIS data) Differences: comparison of LSS and Compass fit (same input data) functional form higher twists positivity constraints more data did not reduce uncertainty it showed that functions for g(x,Q20) were too simple !!! LSS |DG|  0.2 - 0.3 three solutions with very similar

9. LSS – higher twists and influence of data sets ACC - with additional data and DIS only Small effect on g(x) but big reduction of the uncertainty

10. Status from QCD fitsto DIS inclusive data • Precise determination of quark polarization • Improvements in flavour decomposition with inclusion of semi-inclusive data in the fit • No clear answer concerning higher twists in proton and neutron g1 • Gluon not well constrained • With better data more freedom in functional form resulted in much bigger spread of possible solutions • Positive, negative and changing sign forms all give acceptable solutions in the fits • Additional information needed to resolve this ambiguity • Options: • Measurement of processes directly sensitive to gluons being done in lepton-nucleon and proton-proton • Much bigger Q2 range (lepton-proton collider)  far future

11. How gluon can be accessed in DIS in pp colissions DIS

12. Signal of gluon polarization D meson from PGF Compass data: Thick target, no D0 vertex reconstruction selection: decay angle, momentum fraction z(D0) & RICH PID No D* tagging D* tagging : cut on 3body invariant mass nD0 = 37398 nD* = 8675 weighting with S/B depending on event kinematics improves precision • Asymmetries for signal from D0+D* in z,pT bins available

13. DG/G from Compass (LO)  from Neural Network trained on MC(AROMA): input variables : Q2, xbj, y, pT, zD Correlation ~80% • Where NLO has to be taken into account? • Calculation of aLL • Definition of S/(S+B) • because in NLO light quark can emmit gluon • and contribute to PGF • (but not bring information about gluon polarization) In LO approximation from Compass data Work on NLO interpretation of this result in progress

14. PGF with light quarkshigh pT hadrons or hadron pairs • high pT is more likely with • two partons in the final state • select PGF and QCD Compton • suppresses diminant process of photon absorption • R.D.Carlitz, J.C.Collins and A.H.Mueller, Phys.Lett.B 214, 229 (1988) • Revisited by A.Bravar,D.von Harrach and A.Kotzinian, Phys.Lett.B 421, 349 (1998) • Applied by SMC, HERMES and COMPASS • First results (published): • Hermes PRL 84(2000)2584 Dg/g= 0.42+/-0.18+/-0.03 at <x>=0.17 in photoproduction region • SMC PRD 70(2004)012002 Dg/g= -0.20+/-0.28+/-0.10 at <x>=0.08 in DIS region (Q2>1GeV2) • Compass PLB 633 (2006) 25-32 Dg/g=0.024+/-0.089+/-0.057 Q2<1 GeV2 (nonperturbative region) • Now more precise information from Hermes and Compass

15. Compass – high pT pairs 3 processes contribute to both A1 and ALL2h but with different fractions 3 basic processes, PGF probes gluons in the nucleon Q2>1 GeV2 gives perturbative scale, resolved photon small ALL2h and A1 from measurements in Compass aLL and R from MC (using NN) for every event

16. Evaluation of gluon polarization For each event we get (from NN) probability for 3 processes Comparing results with true probability from MC Gives confidence in the NN classification aLL is a ratio of partonic spin dependent and spin Independent cross sections for sub-processes The analysis are done in LO approximation – NLO effects are partially taken into account via parton shower concept in MC. Dominant systematic error is from MC (data description, PS, parameters..)

17. Hermes – hadron production at high pT looking at tagged, antitagged samples (with e,without e), h+, h-, pairs Asymmetries compared with prediction from model assumptions on gluons

18. Hermes – Dg/g h+,h- antitagged: 4 points between 1.05<pT<2.5 GeV h+,h- tagged: 1 point for pT>1 GeV Pairs: 1 point for Rsig and Rbg taken from Pythia MC Abg model Dominating sample is from untagged h on deutron Combining h+ and h- Consistency between: samples, targets, charges

19. +0.127 (sys-model) -0.105 Hermes – Dg/g method II Fit: find Dg(x)/g(x) such that • Assumes functional form for Dg/g(x) • only small range in pT • average x of measurement data <m2>=1.35 GeV2 <x>=0.22 Difference between functions is a systematic uncertainty

20. Dg/g results from lepton-nucleon scattering New (not published) • Value small • Possibly =0 at least at x~0.1 Compass high-pT Hermes high-pT Compass low Q2, updated Open charm

21. Extracting DG/G from pp • scattering of composite objects, • accessing gluons through kinematic selections • Very many nice measurements, appology that only few will be shown here (selection is for illustration, not choosing most important) Double longitudinal spin asymmetry Combined effect of several processes

22. How we access gluons in pp scattering? Simplified picture at leading order gluons are probed in gluon-gluon and gluon-quark scattering quark-quark is a background contribution of processes depends on the event characteristics for example it is a function of jet pT Collider allows wide range of CM energy scales But it is not easy to extract signal/scale from complicated event structure (even more in NLO) Sensitivity to gluon polarization depends on the analyzing power aLL, changing with event kinematics  competing requirements: sensitivity to gluons, hard scale and analyzing power

23. underlying processes, many contributions Partonic kinematics determination from final states Requires knowledge of fragmentation function only average partonic kinematics allows reconstruction of partonic kinematics …. But statisticaly limited additional difficulty is background from p0 heavy flavour production - tagged gluon-gluon

24. What can be expected: from gluon distributions to asymmetries Steps towards gluon polarization • Check consistency of the measured cross-sections, correlations and fragmentation funct. with assumptions • Get estimates for effects of approximations and corrections • Extract asymmetries for different processes from the data • Use them with tested assumptions to get preferable Dg(x) (parametrization, limitations) pT is related to the xg

25. PHENIX (p, g)  good description of s over many orders of magnitude, NLO important STAR (jets) Interpretation in pQCD* first step  show that this is a good way to describe the processes in question PRL 97,252001 Phys.Rev.D76,051105 Direct photons Run5, preliminary

26. but it is not easy for p0.. Uncertainty can arise also from the fragmentation functions NLO describes high pT processes in many reactions safe to study underlying partonic kinematics here it is larger than scale uncertainty and reflects in the predictions for ALL

27. What is the data telling us:p0 asymmetries both experiments very consistently measure asymmetries consistent with zero • this conclusion holds for both • measured energies • the range of probed xg shifts • Extention towards low xg can be • achieved with more forward p0 • or with higher energy (difficult)

28. Photons – „golden chanel” clean signal linear in DG two contributing processes, q-g dominates in pp Selection by photon „isolation” Background from p0

29. Next to Leading Order vs. Next to Leading Logarithms An alternative way is to compare with another approximation: how does it affect the asymmetries? scale uncertainty Possible way to estimate role of missing terms, factor 2 inscale is arbitrary

30. Moving beyond inclusive probes It is also important to understand more fine structure of events(to check description used) Here ALL predictions are LO, would be interesting to compare with NLO (work in progress)

31. Jets with high pT effects smearing jet pT needed to be corrected for fraction of energy In the cone for a jet Jet selection algorithm optimal cone size dependent on pT

32. how to quantify the conclusions? and the best option just become available… Many results were presented in terms of (CL) as a funct. of or (better) better to use all PDF’s and compute CL for asymmetries comparison with measurements But by now we know that GRSV does not describe DIS data, so less bias way is

33. NLO fit by de Florian, Sassot, Stratmann andVogelsang (hep-ph/0804.0422) in which pp collision jet data are included for the first time. (Technicallychallenging!) Input data:

34. NLO fitDSSV what it says about gluon polarization? • Gluons are treated in a special way: • single truncated moment is dominated • by x around xmin • Low x is very badly constrained by data •  split calculations in 3 egions: • 0.001 – 0.05 – small x • 0.05 – 0.2 - „RHIC” region • 0.2 – 1.0 - large x in the region covered by RHIC data  gluon polarization is small, crosses zero? for Q02 at 1 GeV2

35. DSSV PDF – gluonwhat constrains it? • Future prospects: • Precision for jets and pions • Dijets asymmetries • Direct photons • Inclusion of open charm asymmetries • W production asymm. (RHIC@500GeV) • Q2 range with EIC Present precision and effect from Inclusion of specific data sets DG is close to zero, but value of of about +/-0.2 not excluded

36. Plans,scenarios? how to use data to get Dg/g? • Global analysis vs. extraction from single measurement even with much simplified assumptions • each of them is needed • this is a cross check of our understanding – not competition • Global analysis should have as much input as possible • uniform treatment • most up-to date theoretical achievements • Experimentalists should be encouraged to go as far as they can with interpretation of the data • best understanding of corrections, systematics • pushes toward improvements of experimental techniques and of data analysis • consistency checks allowing better control of systematic effects • comparison of several results gives measure of precision • more channels can be used (without full theoretical treatment)

37. We can see such complementarity in aS determination  important for a check of systematic effects • Lesson from this example for analysis of gluon polarization: • For experimentalists • Measure more and try • interpretation (even if • simplified) • For theorists • Include as much as possible • to the combine fits • Introduce alternative • approach to the existing one

38. Summary and conclusions – decomposition of nucleon spin? • Quarks give about 1/3 of what is needed • Results on DG point to a rather small gluon contribution • … but still two scenarios remain possible: • Gluons give about 0.2-0.3 (enough to make nucleon spin) • Gluons are unpolarized  additional contribution • from orbital momenta (likely of gluons if quarks do • not contribute, as lattice results suggest) • With small DG, as observed, anomalous contribution to axial charge a0 is small and cannot explain „spin crisis”

39. Thank you! • Many thanks to all people who contributed to the selection of results • I was using results from paralell sessions presentad by • Hermes and Compass collaboratios on DIS • PHENIX and STAR on pp • LSS, AAC and DSSV grops on QCD fits