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Transversity New Results from COMPASS

Christian Schill Universit ät Freiburg. Transversity New Results from COMPASS. Graduiertenkolleg Mainz, 7. Nov. 2007. Contents. Introduction: Spin Structure of the Nucleon The COMPASS experiment COMPASS results on asymmetries Transversity distribution function

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Transversity New Results from COMPASS

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  1. Christian Schill Universität Freiburg Transversity New Results from COMPASS Graduiertenkolleg Mainz, 7. Nov. 2007

  2. Contents • Introduction: Spin Structure of the Nucleon • The COMPASS experiment • COMPASS results on asymmetries • Transversity distribution function • Sivers distribution function • Other TMD distribution functions • Conclusions

  3. Deep-Inelastic Scattering Investigation of the proton structure 1955 Hofstadter: Radius 0,8 fm Nobel Prize 1961 1968 Friedman, Kendall, Taylor: Quarks in the proton Nobel Prize 1990 DESY: highest Q² Quarks and gluons are the elementary constituents Q² = negative transferred four-momentum squared

  4. Deep-Inelastic Scattering P inclusive hadrons semi-inclusive scattering: detection of final hadrons y = relative energy loss of scattered lepton Q² = negative four-momentum transfer squared x = Momentum fraction of the proton carried by the quark

  5. Cross-Section in Deep-Inelastic Scattering P inclusive hadrons y = relative energy loss of scattered lepton Q² = negative four-momentum transfer squared x = Momentum fraction of the proton carried by the quark

  6. Structure functions partons are point-like particles quark carries 1/3 of momentum

  7. Structure functions partons are point-like particles parton carries all momentum quark carries 1/3 of momentum x = Fraction of momentum carried by the parton

  8. Structure functions partons are point-like particles parton carries all momentum quark carries 1/3 of momentum x = Fraction of momentum carried by the parton

  9. Structure functions partons are point-like particles parton carries all momentum gluons reduce quark momentum contribution quark carries 1/3 of momentum with sea-quarks x = Fraction of momentum carried by the parton

  10. Structure functions partons are point-like particles parton carries all momentum gluons reduce quark momentum contribution quark carries 1/3 of momentum with sea-quarks x = Fraction of momentum carried by the parton

  11. Structure functions larger Q² better Resolution more Gluons and see-quarks Q² dependence is described by QCD scattering on spin ½ particles Scale invariance scattering on point-like objects x

  12. Parton Distribution Functions Parton model: Parton Distribution Functions:

  13. Polarized Deep Inelastic Scattering Experimental Asymmetry: g1: Spin structure function Δqi: Polarized parton distribution function

  14. Polarized Parton Distribution Functions Parton model:

  15. Transverse Spin Physics At leading order, the inner structure of the nucleon can be described with three Parton Distribution Functions: q(x)Momentum distribution Well known – Unpolarized DIS Δq(x)Helicity distribution known – Polarized DIS ΔTq(x)Transversity distribution Largely unknown

  16. Transversity Distribution Function DTq(x) = q↑↑(x) - q↑↓(x) q=uv, dv, qsea quark with spin parallel to the nucleon spinin a transversely polarized nucleon • Properties: • probes the relativistic nature of quark dynamics • positivity(Soffer) bound • sum rule for transverse spin Bakker, Leader, Trueman, PRD 70 (04)

  17. How to Measure Transversity? Optical theorem: leptonic hadronic Imaginary part of amplitude of forward Compton scattering: Cross-section of inclusive deep- inelastic scattering: * + N  X * + N  * + N

  18. Structure Functions in Forward Compton Picture + + - - + + + + + + + - - - + + + + + - + - F1(x)  g1(x)  not possible in inclusive deep-inelastic scattering because of quark helicity flip ΔTq(x) 

  19. Measuring Transversity hadron(s) FF quark quark DTq(x) proton proton Only in Semi-inclusive deep-inelastic scattering Fragmentation process into hadrons responsible for quark spin flip Measured in COMPASS

  20. Measuring Transversity Can be measured in semi-inclusive deep-inelastic scattering on a transversely polarized target via “quark polarimetry”: “Collins” asymmetry “Collins” Fragmentation Function Two-hadron asymmetry “Interference” Fragmentation Function Λ polarization Fragmentation Function of q↑Λ

  21. Collins Fragmentation - Model http://cerncourier.com/main/article/44/8/19/1 Collins Effect in String Fragmentation (X. Artru)

  22. Collins Fragmentation - Model

  23. Collins Asymmetry SIDIS on a transversely polarized target: l N l´h X Fragmentation of a transversely polarized quark into hadrons azimuthal asymmetry: The Collins angle Coll is defined as:

  24. Collins Asymmetry The measured asymmetry AColl gives access to thetransversity distribution times the Collins fragmentation function: f: Dilution factor Dnn: Depolarization factor Dnn=2(1-y)/(1+(1-y)2) PT: Target polarization Transversity distribution Collins fragmentation function (measured in e+e- at BELLE)

  25. Contents • Transverse spin physics • The COMPASS experiment • COMPASS results on asymmetries • Transversity distribution function • Sivers distribution function • Other TMD distribution functions • Conclusions

  26. The COMPASS experiment COmmon Muon Proton Apparatus for Structure and Spectroscopy (270 physicists, 25 institutes, 11 countries) • high luminosity: ~ 4 ٠ 1032 cm-2 s -1 • fixed target • 160 GeV µ+ beam Investigation of the spin structure of the nucleon: LHC COMPASS SPS

  27. The COMPASS spectrometer μ beam Target μFilter Calorimeters 50 m Ring Imaging Cherenkov detector Straws MWPC Gems coverage of wide kinematical range: SciFi Drift chambers 10-5 < x < 0.5 10-3 < Q2 < 100 GeV2 Micromegas Silicon from Germany: FR, MZ, ER, BN, BO, M, BI

  28. The polarized 6LiD-Target 3He – 4He dilution refrigerator Superconducting Dipole (0.5 T) Two 60 cm long target cells with opposite polarization Vertex distribution: T=50mK Transverse target polarization: Reversed once a week Polarization 50 % Dilution factor 0.38

  29. Ring Imaging Cherenkov Detector 3 m 6 m Mirror wall 5 m CsI MWPC Radiator: C4F10 Identification of π, K and protons Cherenkov thresholds: π ≈ 3 GeV/c K ≈ 9 GeV/c p ≈ 17 GeV/c 2σ π/K separation at 43 GeV/c

  30. Transversity Data Sample transversely polarized deuteron target ~ 20% of the running time 2002 2002 11 days 11 days of data taking (19), of data taking 2 periods trigger (large x, Q2) + PID (ECAL, RICH) 2003 2003 9 days 9 days of data taking (14), of data taking 1 period 2004 2004 14 days 14 days of data taking (24), of data taking 2 periods reconstructed reconstructed 10 Mill. DIS events DIS events DIS events (10 (10 ) ) 6 6

  31. Contents • Transverse spin physics • The COMPASS experiment • COMPASS results on asymmetries • Transversity distribution function • Sivers distribution function • Other TMD distribution functions • Conclusions

  32. COMPASS Results: Collins Effect Deuteron target  preliminary K only statistical errors shown (systematical errors considerably smaller)

  33. Interpretation • Parton model, valence region: isospin-symmetric deuteron target D1: favored FF D2: disfavored FF HERMES (DESY): Proton asymmetries  0 BELLE (KEK-B): Fragmentation functions  0 Small asymmetries  cancellation ΔTu(x) ≈ -ΔTd(x)

  34. Collins: Interpretation Global fit (COMPASS, HERMES, BELLE): COMPASS data Anselmino et al. hep-ph/0701006

  35. Collins: Global Fit Global fit (COMPASS, HERMES, BELLE): HERMES data Anselmino et al. hep-ph/0701006

  36. Collins: Global Fit Global fit (COMPASS, HERMES, BELLE): BELLE data Anselmino et al. hep-ph/0701006

  37. Results for Transversity global fit Soffer bound Anselmino et al. hep-ph/0701006

  38. Collins Fragmentation Function Favored and unfavored FF with opposite sign Anselmino et al. hep-ph/0701006

  39. Measuring Transversity Can be measured in semi-inclusive deep-inelastic scattering on a transversely polarized target via “quark polarimetry”: “Collins” asymmetry “Collins” Fragmentation Function Two-hadron asymmetry “Interference” Fragmentation Function Λ polarization Fragmentation Function of q↑Λ

  40. Transversity in Hadron-Pair Production Collins-Angle replaced by: RS = R + S - π R= angle between lepton scattering plane and two-hadron plane (A. Bacchetta, M. Radici, hep-ph/0407345) (X. Artru, hep-ph/0207309)

  41. Azimuthal Asymmetry for Hadron-Pair Production Target single spin asymmetry ARS(x,z,Mh2): z=z1+z2 (X. Artru, hep-ph/0207309) Two-hadron interference fragmentation function presently unknown can be measured in e+e- (BELLE) expected to depend on the hadron pair invariant mass

  42. Hadron Pairs Invariant Mass Spectra all hadron pairs: 5.3 M

  43. COMPASS Results for Hadron Pairs systematic uncertainty considerably smaller than statistical error

  44. COMPASS Result for All Hadron Pairs deuteron target

  45. Interpretation Two-hadron Asymmetry: On a deuteron target: Independent measurement from Collins asymmetry with different fragmentation functions. Data suggest as well:ΔTuv(x) = - ΔTdv(x)

  46. Model Calculations Model calculations for COMPASS kinematics (M. Radici, QCDN 06, hep-ph/0608037): Model for transversity: • Soffer, Stratmann, Vogelsang, • P.R. D65 (02) 114024 • Korotkov, Nowak, Oganessian, • E.P.J. C18 (01) 639 • Schweitzer et al., • P.R. D64 (01) 034013 • Wakamatsu • P.L. B509 (01) 59 ΔTq(x) xBj Prediction for COMPASS: • small asymmetries on the deuteron ARS Mh

  47. Model Predictions for a Proton Target COMPASS kinematics Proton Target A.Bacchetta, M.Radici PRD74(2006)114007 Model for Di-Hadron Fragmentation Function new data on a proton target have been already taken this year!

  48. Contents • Transverse spin physics • The COMPASS experiment • COMPASS results on asymmetries • Transversity distribution function • Sivers distribution function • Other TMD distribution functions • Conclusions

  49. The Sivers Distribution Function most famous transverse momentum dependent parton distribution function describes an intrinsic asymmetry in the parton transverse momentum distribution induced by the nucleon spin transverse nucleon spin x nucleon momentum • it is related to the parton orbital • angular momentum in a transversely • polarized nucleon quark density M. Burkardt, PRD, 66, 114005(2002)

  50. Measurement of Sivers Asymmetry The “Sivers angle” is • S = h - S Independent from Collins angle, possible to measure both effects in the same data h,,sazimuthal angles of the hadron, transverse spin of the initial quark

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