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

3. introduction What spins in the nucleon? 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 Inclusive spin-dependent DIS –EMC, SMC, COMPASS –E142,E143,E154,E155 –HERMES –Jlab-Hall A, B(CLAS) Semi-inclusive DIS Semi-inclusive DIS –SMC, COMPASS –HERMES Polarized pp collisions Polarized pp collisions –RHIC PHENIX & STAR PHENIX & STAR

5. QCD analysis done by many groups (experimental and theoretical) input: DIS inclusive data g 1 (x,Q 2 ) for p, d, 3 He QCD fits to all inclusive measurements QCD fits to all inclusive measurements information on  g(x) from evolution (indirect) information on  g(x) from evolution (indirect) as gluons do not couple to photon, but influence Q 2 evolution as gluons do not couple to photon, but influence Q 2 evolution method: method: assume functional form for parton distributions at selected Q 0 2 assume functional form for parton distributions at selected Q 0 2 calculate expected values of g 1 at every (x,Q 2 ) point where measured using calculate expected values of g 1 at every (x,Q 2 ) point where measured using look for parameters giving best description of the data look for parameters giving best description of the data first only inclusive DIS, more inputs  later first only inclusive DIS, more inputs  later g(x,Q 0 2 ) is parametrized, important is the selected Q 0 2 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, Q 0 2 of the fit is important functional form and also first moment depend on it

7. Gluon is a natural candidate to carry spin of the nucleon it carries about 50% of the proton momentum it can contribute also to spin fits with different inputs fits with different inputs (changing with time) (changing with time)  more precise  more precise assumptions 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) LSS three solutions with very similar comparison of LSS and Compass fit (same input data) Differences: functional form higher twists positivity constraints more data did not reduce uncertainty it showed that functions for g(x,Q 2 0 ) were too simple !!! |  G|  0.2 - 0.3

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 fits to DIS inclusive data Precise determination of quark polarization Precise determination of quark polarization Improvements in flavour decomposition with inclusion of semi-inclusive data in the fit Improvements in flavour decomposition with inclusion of semi-inclusive data in the fit No clear answer concerning higher twists in proton and neutron g 1 No clear answer concerning higher twists in proton and neutron g 1 Gluon not well constrained 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 Additional information needed to resolve this ambiguity Options: Options: –Measurement of processes directly sensitive to gluons being done in lepton-nucleon and proton-proton being done in lepton-nucleon and proton-proton –Much bigger Q 2 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 n D0 = 37398n D* = 8675 Compass data: Thick target, no D 0 vertex reconstruction selection: decay angle, momentum fraction z(D 0 ) & RICH PID D* tagging : cut on 3body invariant mass weighting with S/B depending on event kinematics improves precision No D* tagging Asymmetries for signal from D 0 +D* in z,p T bins available

13.  G/G from Compass (LO)  from Neural Network trained on MC (AROMA): input variables : Q 2, x bj, y, p T, z D Correlation ~80% In LO approximation from Compass data Work on NLO interpretation of this result in progress Where NLO has to be taken into account? Calculation of a LL Definition of S/(S+B) because in NLO light quark can emmit gluon because in NLO light quark can emmit gluon and contribute to PGF and contribute to PGF (but not bring information about gluon polarization)

14. PGF with light quarks high p T hadrons or hadron pairs 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): First results (published): –Hermes PRL 84(2000)2584  g/g= 0.42+/-0.18+/-0.03 at =0.17  g/g= 0.42+/-0.18+/-0.03 at =0.17 in photoproduction region in photoproduction region –SMC PRD 70(2004)012002  g/g= -0.20+/-0.28+/-0.10 at =0.08  g/g= -0.20+/-0.28+/-0.10 at =0.08 in DIS region (Q 2 >1GeV 2 ) in DIS region (Q 2 >1GeV 2 ) –Compass –Compass PLB 633 (2006) 25-32  g/g=0.024+/-0.089+/-0.057  g/g=0.024+/-0.089+/-0.057 Q 2 <1 GeV 2 (nonperturbative region) Q 2 <1 GeV 2 (nonperturbative region) Now more precise information from Hermes and Compass Now more precise information from Hermes and Compass high p T is more likely with two partons in the final state  select PGF and QCD Compton  suppresses diminant process of photon absorption

15. Compass – high p T pairs 3 basic processes, PGF probes gluons in the nucleon Q 2 >1 GeV 2 gives perturbative scale, resolved photon small a LL and R from MC (using NN) for every event A LL 2h and A 1 from measurements in Compass 3 processes contribute to both A 1 and A LL 2h but with different fractions

16. Evaluation of gluon polarization 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..) For each event we get (from NN) probability for 3 processes Comparing results with true probability from MC Gives confidence in the NN classification a LL is a ratio of partonic spin dependent and spin Independent cross sections for sub-processes

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

18. Hermes –  g/g Hermes –  g/g R sig and R bg taken from Pythia MC A bg model 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 Consistency between: samples, targets, charges Dominating sample is from untagged h on deutron Combining h + and h -

19. Hermes –  g/g  method II Hermes –  g/g  method II +0.127 -0.105 (sys-model) data Assumes functional form for  g/g(x) only small range in p T average x of measurement Fit: find  g(x)/g(x) such that Difference between functions is a systematic uncertainty =1.35 GeV 2 =0.22

20.  g/g results from lepton-nucleon scattering Value small Value small Possibly =0 Possibly =0 at least at x~0.1 at least at x~0.1 Compass high-p T Open charm Hermes high-p T New (not published) Compass low Q 2, updated

21. Extracting  G/G from pp scattering of composite objects, scattering of composite objects, accessing gluons through kinematic selections accessing gluons through kinematic selections Very many nice measurements, appology that only few will be shown here Very many nice measurements, appology that only few will be shown here (selection is for illustration, not choosing most important) (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 p T 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 a LL, changing with event kinematics  competing requirements: sensitivity to gluons, hard scale and analyzing power

23. underlyingprocesses, many contributions 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. Steps towards gluon polarization Check consistency of the measured cross-sections, correlations and fragmentation funct. with assumptions Check consistency of the measured cross-sections, correlations and fragmentation funct. with assumptions Get estimates for effects of approximations and corrections Get estimates for effects of approximations and corrections Extract asymmetries for different processes from the data Extract asymmetries for different processes from the data Use them with tested assumptions to get preferable  g(x) (parametrization, limitations) Use them with tested assumptions to get preferable  g(x) (parametrization, limitations) What can be expected: from gluon distributions to asymmetries p T is related to the x g

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

26. NLO describes high p T processes in many reactions safe to study underlying partonic kinematics but it is not easy for  0.. Uncertainty can arise also from the fragmentation functions here it is larger than scale uncertainty and reflects in the predictions for A LL

27. What is the data telling us:  0 asymmetries both experiments very consistently measure asymmetries consistent with zero this conclusion holds for both measured energies the range of probed x g shifts Extention towards low x g can be achieved with more forward  0 or with higher energy (difficult)

28. Photons – „golden chanel” clean signal linear in  G two contributing processes, q-g dominates in pp Selection by photon „isolation” Background from  0

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

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

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

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

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

34. NLO fit DSSV what it says about gluon polarization? Gluons are treated in a special way: -single truncated moment is dominated by x around x min -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 Q 0 2 at 1 GeV 2

35. DSSV PDF – gluon what constrains it? Future prospects: Future prospects: –Precision for jets and pions –Dijets asymmetries –Direct photons –Inclusion of open charm asymmetries –W production asymm. (RHIC@500GeV) –Q 2 range with EIC Present precision and effect from Inclusion of specific data sets  G is close to zero, but value of of about +/-0.2 not excluded

36. Plans,scenarios? how to use data to get  g/g? Global analysis vs. extraction from single measurement Global analysis vs. extraction from single measurement even with much simplified assumptions 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 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 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 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  S 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  G point to a rather small gluon contribution … but still two scenarios remain possible: 1.Gluons give about 0.2-0.3 (enough to make nucleon spin) 2.Gluons are unpolarized  additional contribution from orbital momenta (likely of gluons if quarks do not contribute, as lattice results suggest) With small  G, as observed, anomalous contribution to axial charge a 0 is small and cannot explain „spin crisis”

39. Thank you! Many thanks to all people who contributed to the selection of results Many thanks to all people who contributed to the selection of results I was using results from paralell sessions presentad by 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