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

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

COMPASS muon program Purpose and features Nucleon spin Spin sum rule quark spin contribution Nucleon spin Spin sum rule 0.3 ? Small? 0? ・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 structure as well as quark spin structure function.

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

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

History of DATA TAKING 2002 - 2007 2002 160 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%)

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)

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

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..

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

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

HIGH PT HADRON PAIRS : Q2<1 GeV2 Resolved photon processes 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.)

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

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

DG/G FROM OPEN CHARM DG/G = - 0.57 ± 0.41 (stat) ± (syst ≤ stat) 0.17 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

Indirect measument of DG 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

COMPASS g1D WITH NLO QCD FIT Indirect measument of DG Two equally possible solutions: DG>0 and DG<0 solutions : DG > 0 DG < 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

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.

DG/G SUMMARY |DG| not large (0.2-0.3) 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

Valence quark distribution

Polarised valence quark distribution from Semi-Inclusive DIS Inclusive measurement measured 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 μ d μ’ 特定せず Semi-Inclusive measurement 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 μ d μ’ 特定する

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！

Deuteron標的のAh+, Ah-の測定 μ d μ’ hadrons 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

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

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.

バレンスクォーク分布の核子スピンへの寄与

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

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。 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

まとめ 今後 ・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、 本日の報告はAeXiv:0707.4077v1 ・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±0.05 at 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。

Transverse distribution

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） ?

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 transversity in (1) Collins asymmetry and Sivers asymmetry (2) SSA in two hadron correlation.

TRANSVERSE SPIN EFFECTS Transversity PDF quark with spin parallel to the nucleon spin in a transversely polarized nucleon DTq(x) = q↑↑(x) - q↑↓(x) h1q(x), dq(x), dTq(x) 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

SINGLE HADRON ASYMMETRIES SIDIS cross-section for transv. PT Collins Sivers 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）

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

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

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

Partile identified Collins & Sivers asymmetrie p±, K± ASYMMETRIES 2003-2004 same DIS event selection and hadron definition as before plus PID based on RICH 3% protons 12% kaons 77% pions 5% no RICH information 100% hadrons after all cuts final sample positive all leading pions 5.3 M 3.4 M kaons 0.9 M 0.7 M negative all leading pions 4.2 M 2.8 M kaons 0.6 M 0.4 M neutral all leading kaons 0.26 M 0.18 M new

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

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

K0 Collins & Sivers Asymmetries 2002-2004 Leading hadrons All hadrons

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

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/