Recent Results on Nucleon Spin Structure at COMPASS

1. CERN NA58 COMPASS実験による核子のスピン構造測定の最近の結果“Recent results on Nucleon Spin Structure at COMPASS” Tatsuro Matsuda (University of Miyazaki) • On behalf of • 山形大理A, 山形大理/Bochum大B, 中部大工C ，宮崎大工D, KEKE, CERNF • 岩田高広A ，近藤薫B ，堂下典弘B，堀川直顕C，長谷川武夫D,松田達郎D,石元茂E，堀川壮介F および • COMPASS国際共同研究グループ Czech Republic, Finland, France, Germany, India, Israel, Italy, Japan, Poland, Portugal, Russia 28 Institutes, 12 countries, ~230 physicists ＫＥＫ研究会『核子の構造関数２００８』,12 Jan. 2008

2. The COMPASS Experiment at the CERN-SPS LHC SPS COmmonMuon andProton Apparatus forStructure and Spectroscopy • Nucleon structure • Hadron structure • Hadron spectroscopy • Common spectrometer • High intensity muon and hadron beams COMPASS NA58 1.Muon program 2002～2007 2.Hadron program 2008～

3. COMPASS muon program Purpose and features quark spin contribution Nucleon spin Spin sum rule 0.3 ? 0? Small? ・COMPASS experiment has been studied nucleon spin structure using 160GeV spin polarized muon beam and polarized target. (cf. HERMES 27.6 GeV electron (positron)-beam） COMPASS covers the kinematical region at lower x and high Q2. ・COMPASS has exploited newly developed detectors and new data acquisition systems and softwares(LHC technologies) to utilize 5 times stronger beam than SMC experiment, and add the wide-angle spectrometer to detect scattered hadrons. ・COMPASS can study gluon polarization, valence quark spin structure, transverse quark spin structureas well asquark spin structure function.

4. 160 GeVμ μ’ μ SM2 d SM1 6LiD Target COMPASS実験のセットアップーCOMPASS spectrometerー Trigger-hodoscopes Beam:160 GeV polarised μ+ 2 . 108 µ/spill (4.8s/16.2s) ECal & HCal μFilter 50 m • Polarization: • μBeam: ~80% • LiD Target:<50%> RICH MWPC Straws TWO STAGE SPECTROMETER: Gems Drift chambers Polarized beam and target Micromegas SAT, LAT, PID Silicon SciFi 0.003 < x < 0.5 10-3 < Q2 < 10 GeV2

5. 3He – 4He 希釈冷凍機 ーCompass 6LiD Polarizedtargetー 動的偏極法（DNP) Target dilution factor: ~40% Maximum Polarization:+57% Longitudinal & transverse pol. beam Longitudinalorientation Longitudinal Transverse Transverse orientation

6. History of DATA TAKING 2002 - 2007 • 2002160 GeV m beam & 6LiD Long./Transv. Pol. • 2003 ditto (Long./Transv.= ~80%/20%) • 2004 ditto (Long./Transv.= ~80%/20%) • 2004 test run with hadron beam • 2005 NO SPS beam (Several upgrades) • 2006 160 GeV m beam & 6LiD only Long. Pol. (Long./Transv.= 100%/0%) • 2007 160 GeV m beam & NH3 Long. /Transv. Pol. (Long./Transv.= ~ 50%/ ~ 50%)

7. Status of analyses of nucleon spin strucutre at COMPASS Analyses based on 2002-2004 data are proceeding. (Please wait for results based on 2006 & 2007) Longitudinal (Helicity) distribution DG/G • DG/G from high pT hadron pairs low Q2 (02-03 data, published in 2006) • (04 data, preliminary) • DG/G from high pT hadron pairs high Q2 (02-03 data, preliminary) • open charm (02-04 data, preliminary) g1D, new COMPASS QCD fit, DG evaluation (02-04, published in 2007) Quark helicity distribution g1D at low x and low Q2 (02-03 data, published in 2007) polarised valence quark distribution (02-04 data, submitted in 2007) Transverse (Transversity) distribution Quark transversity distribution single-hadron asymmetries (02-04 data, published in 2007) two-hadron correlation asymmetries (02-04 data, preliminary) Kaon and Pion asymmetries (03-04 data, preliminary) Neutral Kaon asymmetries (02-04 data, preliminary) (New)

8. DG/G Almost same results as KEK 2007 meeting

9. DIRECT MEASUREMENT OF DG/G Photon Gluon Fusion:gg-> qq two ways to access DG/G q= u,d,s“HIGH pT HADRON PAIRS”2 hadrons with high pT  Large statistics physical background: „model” (MC) dependent, q= c“OPEN CHARM” charm production  less background, less MC dependent. small statistics Leading order analysis in the moment..

10. HIGH PT HADRON PAIRS measure extracted Monte Carlo(LO) SIGNAL BACKGROUND + Resolvedg Q2 < 1 (GeV/c)2 Photon Gluon Fusion Leading Order DIS QCD compton

11. HIGH PT HADRON PAIRS : Q2>1 GeV2 • pT1, pT2 > 0.7 GeV/c, • ΣpT2 > 2.5 (GeV/c)2 • 0.1 < y < 0.9 • small x : small A1d  LODIS and QCDC neglected • LEPTO Monte Carlo low Q2 high Q2 2002-2003 data result: (prelim.) systematic error: false asymmetry mainly contributes

12. Resolved photon processes HIGH PT HADRON PAIRS : Q2<1 GeV2 photon PDFs : unknown point like: perturbative(calculable) VMD: non-pertarbative  extream scenarios M.Gluck et al., Eur.Phys.J. C20:272(2001) 2002-2004 data result: (prelim.)

13. DG/G from Open charm Photon Gluon Fusion:gg-> cc hard scale m2 = 4mc2 Theory understood c Kaon ID with RICH c Combinatorial background Limited statistics Challenging measurement.

14. DG/G FROM OPEN CHARM BR:68% BR:4% D* tagging with slow pion D0Kp untagged D0Kpp0 D0Kp

15. DG/G FROM OPEN CHARM from Neural Network (parameterization) trained with AROMA Monte Carlo (full kinematics) • f : dilution factor ~0.4 • Pb : beam polarization ~0.8 • Pt : target polarization ~0.5 • S/(S+B): determined from fit AROMA MC VS. Neural Network • 2002 – 2004 data D0 + D* • DG/G = - 0.57 ± 0.41 (stat) ± (syst ≤ stat) • @ xg ~ 0.15, m2 ~ 13 GeV2 0.17 (2007) preliminary

16. COMPASS g1D(2002-2004) Indirect measument of DG precise data at low x , 3~4 better than SMC NEGATIVE TREND NOT OBSERVED PLB 647 (2007) 8-17

17. COMPASS g1D WITH NLO QCD FIT Indirect measument of DG Two equally possible solutions: DG>0 and DG<0 • solutions :DG > 0DG < 0 • ∫G(x)dx=+0.26 +0.04,-0.06-0.31 +0.10,-0.14 • ∫S(x)dx= +0.28± 0.01+0.32 ± 0.01 @ Q2=3(GeV)2 Previous fits do not show the trend of the data at low x

18. QCD FIT & DIRECT MEASUREMENTS ∫G(x) = 0.3 NLO fit to g1 Q2 = 3 Gev2 ∫G(x) = -0.3 COMPASS high PT, Q2<1(GeV)2 data : good agreement with DG>0 , but only 1.3s away from DG<0.

19. DG/G SUMMARY • DG/G (xg ≈ 0.1) is small from the direct measurement ( high Pt hadron pairs ,Q2<1GeV2) • Global QCD fit to g1 data gives two solutions. • DG>0 and DG<0 • |DG| not large (0.2-0.3) • DG>0 is in better agreement to the direct measurement. • Large DG unlikely

20. Valence quark distribution

21. μ’ μ’ μ μ d d Polarised valence quark distributionfrom Semi-Inclusive DIS Inclusive measurement 生成されたハドロンを特定しない －＞すべてのクォーク分布を 測定する measured 特定せず 生成されたleadingハドロンの 電荷が正か、負かを特定すること でもとのstruck quarkのを区別する －＞バレンスクォーク分布を 導き出して測定する Semi-Inclusive measurement 特定する

22. Event selection • Kinematical cut condition 　Q2>1GeV2 　0.1<y<0.9 　0.2<zh<0.85 • DIS事象を選ぶ • Current fragmentation regionからのハドロンを捕まえる • バックグラウンド事象の混入を少なくする • 入射ビーム飛跡は両方のターゲットセルを通る • 生成ハドロンはvertex pointから来る • ハドロンの電荷以外は同定しない 中性子もあります！

23. μ’ μ hadrons d Deuteron標的のAh+, Ah-の測定 Plus charge Miuus charge 断面積と 非対称度 パートン分布 との関係 パートン分布を引き出す際に、Fragmentation functionの情報が必要

24. Deuteron標的の“difference asymmetry”Ah+-h-の測定 但し N:測定数 a:アクセプタンス パートン分布を引き出す際に、Fragmentation functionは不要 （但しLO QCDレベル） uv+dvを掛けてやれば、Δuv+Δdvが分かる

25. 偏極バレンスクォーク分布を求める • 非偏極パートン分布を使う • Q2=10 GeV2への発展 • 重陽子のD-stateの補正 • Seaクォーク成分の少ないhigh x領域では、inclusive dataから借用する Q2=10 GeV2への発展 LO DNS : D. de Florian, G.A. Navarro, . Sassot, Phys. Rev. D71(2005)094018.

26. バレンスクォーク分布の核子スピンへの寄与

27. Discussion　簡単な方程式 また、 Inclusive dataより Hyperon decay等より より

28. を決めれば が決まる SU(3) Sea symmetry Present data 今回の結果からは　　　　　　　　　　　　　　　　　　となる。 これまでしばしば仮定してきたSU(3) symmetric seaとは2σのずれ

29. 本日の報告はAeXiv:0707.4077v1 まとめ ・準包含反応を用いて、核子（重陽子）のスピン依存バレンスクォーク分布を求めた。 ・バレンスクォークの核子スピンへの寄与として、 Σv＝0.41±0.07±0.05at Q2=10 GeV2を得た。 • この結果を用いると　　　　　　　　　が導かれる。 今後 • 2006年データを用いて統計精度を上げることが可能 • K中間子を選択して、 の測定も進行中。 • 2007年は偏極陽子標的を用いて測定中で、これを • 用いて　　　　と　　　の分離も可能。

30. Transverse distribution

31. What is Transversity？ ・Nucleon structure functions are described with 3 functions at twist 2 and they are complete at twist level 2. ・Dq(x) is different from DTq(x) generally because rotation does not commute with Lorentz boost in relativity. (Dq(x)＝DTq(x) in non-relativity) ・Dq(x) is a chiral even fuction, DTq(x) is a chiral odd function. longitudinal transverse ・DTq(x) does not couple with gluon structure function , then it evolves with Q2 unlike Dq(x). （Soffer inquality）　　　（Tensor charge）　　 （Transverse Spin SR） ?

32. How do we measure transversity? • Quark helicity is conserved in totally • Inclusive Deep Inelastic Scattering（IDIS) , • so Inclusive DIS does not access to transversity, • because transversity needs quark helicty flip • in helicity base. • In case of Semi-Inclusive Deep Inelastic(SIDIS) • it is possible to access transversity, because SIDIS allows both flip and non-flip cases. • Then we measure SIDIS events to study transversity. • If we choose phenomena with chiral odd fragmentation functions, • we can access chiral odd quark distribution functions. • We measure SIDIS including transversityin • (1) Collins asymmetry and Sivers asymmetry • (2) SSA in two hadron correlation.

33. TRANSVERSE SPIN EFFECTS DTq(x) = q↑↑(x) - q↑↓(x) h1q(x), dq(x), dTq(x) Transversity PDF quark with spin parallel to the nucleon spinin a transversely polarized nucleon from Collins asym. in SIDIS single hadron production and two hadron asym. , L transverse polarization TMD PDFs an intrinsic asymmetry in the parton Transverse Momentum Distribution induced by the nucleon spin related to orbital angular momentum of quark Sivers PDF from Sivers asym. in SIDIS single hadron production

34. SINGLE HADRON ASYMMETRIES SIDIS cross-section for transv. PT Sivers Collins fS= azim. angle of initial quark spin fS’= azim. angle of struck quark spin fS= p-fS’（due to helicity conservation) fh= azim. angle of leading hadron initial quark spin (nucleon spin) struck quark spin • Collins angle: Azim. angle of a hadron wrt the struck quark spin • FC =fh - fS’ (=fh +fS-p) • Sivers angle:Azim. angle of a hadron wrt the initial quark spin (=nucleon spin) • FS=fh - fS Scattering plane quark direction hadron （Breit frame）

35. COLLINS & SIVERS ASYMMETRIES Collins Asymmetry ± refer to the opposite orientation of the transverse spin of the nucleon PT is the target polarisation; DNNis the transverse spin transfer coefficient initial  struck quark, given by QED Transvesity Collins fragmentation function Sivers Asymmetry Sivers PDF

36. COLLINS ASYMMETRIES FOR DEUTERON 2002-2004 data Kinematical condition Leading hadrons z>0.25 • small errors (~1%) • small asymmetries Q2 > 1 GeV2 W2> 25 GeV2 0.1 < y < 0.9 pht > 0.1 GeV/c All hadrons z>0.2 NP B765 (2007) 31-70 • cancellation between p and n

37. SIVERS ASYMMETRIES FOR DEUTERON 2002-2004 data Leading hadrons z>0.25 All hadrons z>0.2 • small errors (~1%) • small asymmetries NP B765 (2007) 31-70 • cancellation between p and n

38. hadrons 100% no RICH information 5% pions 77% after all cuts kaons 12% protons 3% Partile identified Collins & Sivers asymmetrie p±, K± ASYMMETRIES 2003-2004 • same DIS event selection and hadron definition as before • plus • PID based on RICH final sample new

39. All hadrons p±, K±Collins Asymmetries 2003-2004 again, difficult to see an effect …

40. All hadrons p±, K±SIVERS ASYMMETRIES 2003-2004

41. K0Collins & Sivers Asymmetries 2002-2004 Leading hadrons All hadrons

42. TRANSVERSE SPIN EFFECTS SUMMARY New deuteron data from COMPASS are available the measured asymmetries and polarizations are very small, compatible with zero Collins and Sivers asymmetries for positive and negative hadrons, p±, K± neutral K0 (Ks) PRESENT PICTURE Collins:DT0D(fav.) ~ - DT0D(unfav) DTd not well constrained Sivers: D0Tu ~ - D0Td

43. PROSPECTS • 2008/2009 • hadron program • longitudinal(+transverse) polarization run ? • 2010- • DVCS measurements with muon beam & Liq.H2 target • Polarized Drell-Yan measurements with p- beam & pol. Target • COMPASS paper list is found at the following web site. • Please hava a look at • http://wwwcompass.cern.ch/compass/publications/papers/