CERN NA 58 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 C ，宮崎大 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 spectroscopy • Common spectrometer • High intensity muon and hadron beams COMPASS NA 58 1. Muon program 2002～ 2007 2. Hadron program 2008～ LHC SPS
COMPASS muon program Purpose and features quark spin contribution Nucleon spin Spin sum rule 0. 3 ? Small? 0? ・COMPASS experiment has been studied nucleon spin structure using 160 Ge. V spin polarized muon beam and polarized target. (cf. HERMES 27. 6 Ge. V electron (positron)-beam） COMPASS covers the kinematical region at lower x and high Q 2. ・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’ μ d Trigger-hodoscopes Beam: 160 Ge. V polarised μ+ 2. 108 µ/spill (4. 8 s/16. 2 s) ECal & HCal μ Filter 50 SM 2 Polarization: • μBeam: ~80% MWPC • Li. D Target: <50%> Straws RICH SM 1 6 Li. D Target μ V Ge 0 16 Sci. Fi Silicon m Gems Drift chambers Micromegas TWO STAGE SPECTROMETER: Polarized beam and target SAT, LAT, PID 0. 003 < x < 0. 5 10 -3 < Q 2 < 10 Ge. V 2
ーCompass 6 Li. D Polarized targetー 動的偏極法（DNP) Target dilution factor: ~40% 3 He – 4 He 希釈冷凍機 Maximum Polarization: +57% Longitudinal & transverse pol. Longitudinal orientation beam Longitudinal Transverse orientation
History of DATA TAKING 2002 - 2007 § 2002 160 Ge. V m beam & 6 Li. D Long. /Transv. Pol. § 2003 ditto (Long. /Transv. = ~80%/20%) § 2004 test run with hadron beam § 2005 NO SPS beam (Several upgrades) § 2006 160 Ge. V m beam & 6 Li. D only Long. Pol. (Long. /Transv. = 100%/0%) § 2007 160 Ge. V m beam & NH 3 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 from high p. T hadron pairs low Q 2 (02 -03 data, published in 2006) (04 data, preliminary) G/G from high p. T hadron pairs high Q 2 (02 -03 data, preliminary) open charm (02 -04 data, preliminary) g 1 D, new COMPASS QCD fit, G evaluation (02 -04, published in 2007) Quark helicity distribution g 1 D at low x and low Q 2 (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) (New) Neutral Kaon asymmetries (02 -04 data, preliminary)
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 p. T HADRON PAIRS” 2 hadrons with high p. T 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 SIGNAL extracted BACKGROUND Monte Carlo(LO) + Photon Gluon Fusion Leading Order DIS QCD compton Resolved g Q 2 < 1 (Ge. V/c)2
HIGH PT HADRON PAIRS : Q 2>1 Ge. V 2 • • p. T 1, p. T 2 > 0. 7 Ge. V/c, Σp. T 2 > 2. 5 (Ge. V/c)2 0. 1 < y < 0. 9 small x : small A 1 d LODIS and QCDC neglected • LEPTO Monte Carlo low Q 2 high Q 2 2002 -2003 data result: (prelim. ) systematic error: false asymmetry mainly contributes
HIGH PT HADRON PAIRS : Q 2<1 Ge. V 2 Resolved photon processes photon PDFs : unknown point like: perturbative(calculable) VMD: non-pertarbative extream scenarios M. Gluck et al. , Eur. Phys. J. C 20: 272(2001) 2002 -2004 data result: (prelim. )
DG/G from Open charm Photon Gluon Fusion: gg -> cc hard scale m 2 = 4 mc 2 Theory understood c Kaon ID with RICH c Combinatorial background Limited statistics Challenging measurement.
DG/G FROM OPEN CHARM BR: 68% D* tagging with slow pion BR: 4% untagged D 0 Kpp 0 D 0 Kp
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 D 0 + D* DG/G = - 0. 57 ± 0. 41 (stat) ± (syst ≤ stat) 0. 17 § 2002 – 2004 data preliminary @ xg ~ 0. 15, m 2 ~ 13 Ge. V 2 (2007)
COMPASS g 1 D (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 g 1 D WITH NLO QCD FIT Indirect measument of DG Two equally possible solutions: DG>0 solutions : G > 0 § ∫ G(x)dx = +0. 26 +0. 04, -0. 06 Previous fits do not show the trend of the data at low x § ∫ S(x)dx = +0. 28 ± 0. 01 and DG<0 G < 0 -0. 31 +0. 10, -0. 14 +0. 32 ± 0. 01 @ Q 2=3(Ge. V)2
QCD FIT & DIRECT MEASUREMENTS ∫ G(x) = 0. 3 NLO fit to g 1 Q 2 = 3 Gev 2 ∫ G(x) = -0. 3 COMPASS high PT, Q 2<1(Ge. V)2 data : good agreement with G>0 , but only 1. 3 s away from G<0.
DG/G SUMMARY § DG/G (xg ≈ 0. 1) is small from the direct measurement ( high Pt hadron pairs , Q 2<1 Ge. V 2) § Global QCD fit to g 1 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 μ μ’ measured 特定せず 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 d μ d 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 特定する －＞バレンスクォーク分布を 導き出して測定する Semi-Inclusive measurement μ’
Event selection • Kinematical cut condition Q 2>1 Ge. V 2 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！
h+ h- Deuteron標的のA , A の測定 μ d Plus charge μ’ hadrons 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 h+-h-の測定 “difference asymmetry”A 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 Q 2=10 Ge. V 2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 Q 2=10 Ge. V 2への発展 LO DNS : D. de Florian, G. A. Navarro, . Sassot, Phys. Rev. D 71(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。 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 本日の報告はAe. Xiv: 0707. 4077 v 1 ・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 Q 2=10 Ge. V 2 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. ・ q(x) is different from Tq(x) generally because rotation does not commute with Lorentz boost in relativity. ( q(x)＝ Tq(x) in non-relativity) longitudinal transverse ・ q(x) is a chiral even fuction, Tq(x) is a chiral odd function. ・ Tq(x) does not couple with gluon structure function , then it evolves with Q 2 unlike q(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) h 1 q(x), d. Tq(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 f. S = azim. angle of initial quark spin f. S’ = azim. angle of struck quark spin f. S= p- f. S’ （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 - f. S’ (= fh +f. S- p) Scattering plane • Sivers angle: Azim. angle of a hadron wrt the initial quark spin (=nucleon spin) FS= fh - f. S hadron quark direction （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 Leading hadrons z>0. 25 Kinematical condition Q 2 > 1 Ge. V 2 W 2 > 25 Ge. V 2 0. 1 < y < 0. 9 All hadrons z>0. 2 • small errors (~1%) • small asymmetries • cancellation between p and n pht > 0. 1 Ge. V/c NP B 765 (2007) 31 -70
SIVERS ASYMMETRIES FOR DEUTERON 2002 -2004 data Leading hadrons z>0. 25 All hadrons z>0. 2 • small errors (~1%) • small asymmetries • cancellation between p and n NP B 765 (2007) 31 -70
Partile identified Collins & Sivers asymmetrie p±, K± ASYMMETRIES 2003 -2004 same DIS event selection and hadron definition as before plus PID based on RICH hadrons no RICH information after all cuts leading pions 5. 3 M 3. 4 M kaons new all 0. 9 M 0. 7 M all leading 0. 26 M 0. 18 M neutral kaons 5% pions 77% kaons 12% protons final sample positive 100% negative 3% all leading pions 4. 2 M 2. 8 M kaons 0. 6 M 0. 4 M
p±, K± Collins Asymmetries All hadrons again, difficult to see an effect … 2003 -2004
p±, K± SIVERS ASYMMETRIES 2003 -2004 All hadrons
K 0 Collins & Sivers Asymmetries Leading hadrons All hadrons 2002 -2004
TRANSVERSE SPIN EFFECTS SUMMARY New deuteron data from COMPASS are available Collins and Sivers asymmetries for positive and negative hadrons, p±, K± neutral K 0 (Ks) the measured asymmetries and polarizations are very small, compatible with zero PRESENT PICTURE Collins: DT 0 D(fav. ) ~ - DT 0 D(unfav) DTd not well constrained Sivers: D 0 Tu ~ - D 0 Td
PROSPECTS • 2008/2009 – hadron program – longitudinal(+transverse) polarization run ? • 2010– DVCS measurements with muon beam & Liq. H 2 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/
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