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Azimuthal asymmetries in hadron production at e+e- collider and

Azimuthal asymmetries in hadron production at e+e- collider and chiral odd fragmentation function. Ogawa Akio Penn State Univ. / BNL (STAR) Daniel Boer Riken BNL Research Center (Theorist) Matthias G. Perdekamp Riken BNL Research Center(PHENIX)

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Azimuthal asymmetries in hadron production at e+e- collider and

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  1. Azimuthal asymmetries in hadron production at e+e- collider and chiral odd fragmentation function Ogawa Akio Penn State Univ. / BNL (STAR) Daniel Boer Riken BNL Research Center (Theorist) Matthias G. Perdekamp Riken BNL Research Center(PHENIX) From RHIC Spin Collaboration

  2. Outline • Introduction • What is Collins Fragmentation Function • What is Interference Fragmentation Function(IFF) • Measurement at e+e- • Applications • Transversity • Single spin asymmetries • Conclusion

  3. Fragmentation Function(FF) “Probability of a parton to hadronize into a specific final state” Factorization theorem ensures universality Collins FF & 2 pion interference FF Initial parton with transverse spin - chiral odd Azimuthal asymmetry in hadron final state Currently unknown Theoretical Interests : Q2 evolution is as fundamental as PDF Polarized DIS & pp experiment can measure FF*Transversity Unpolarized e+e-experimentcan measure FF*FF

  4. HERMES result on azimuthal asymmetry l p Non-zero transverse polarization! Results shows that both Collins Function and Transversity are non zero, and rather large

  5. Collins Fragmentation Function : H h s s kT A = q q kT h s h q Z = Eh / Eq f = angle between S and kT around quark (jet) axis

  6. 2 pion interference fragmentation function : F s s A = q r q r s q Zpair = (Ep+ +Ep- ) / Eq m = invariant mass of 2 pions f = angle between s and r The same thing for KK around f

  7. A model of Interference Fragmentation Function S- p wave interference around mass Spin average, difference FF Strong interaction phase shifts Non-vanishing “Analyzing power” above and below mass and flip sign Requires mass Resolution Great for systematic study Bin + Bin - P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301

  8. n jet2 jet1 Spin of quarks are 100% correlated! n Without using jet axis

  9. n jet2 jet1 Spin of quarks are 100% correlated!

  10. In e+e- At Belle Jet production from light quark Off resonance data Exclude b fragments High enough energy to produce jet Finding jet to apply pQCD s~100GeV2 But not too high energy FF decreases as energy increases s(Belle) << s(LEP) Observing Q2 evolution is interesting Avoid extra complication from Z pole √s(Belle) < Mz Requires good detector: Wide acceptance Momentum/mass resolution great PID capability The beauty of e+e- isH*H and F*F can be measurd!

  11. Leading twist quark distribution Well measured at DIS,pp Momentum Helicity average - Helicity difference DVCS? - Helicity flip Well measured at pol. DIS RHIC,Compass,Hermes... Transversity is the last missing piece at leading twist quark distribution

  12. The transversity function Helicity flip amplitude = Chiral odd function not accessible in (inclusive) DIS Naively for non-relativistic quarks Relativity breaks rotation symmetry. Soffer’s bound: Need not to be small! Possibly Gluon (spin1) cannot flip proton (spin1/2) helicity does not mix with gluons under evolution Non-relativistic Relativistic First Lattice QCD result S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433 More recently: S. Capitani et.al. Nucl. Phys. B (Proc. Suppl.) 79 (1999) 548

  13. Nucleon Transversity at p p Jet F Jet Interference Fragmentation Proton Structure Hard Scattering Process Jian Tang , Thesis MIT, June 1999 R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920 X. Ji, Phys. Rev. D49 (1994)114 J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565

  14. The Relativistic Heavy Ion Collider at Brookhaven National Laboratory RHIC accelerates heavy ion (Au) up to 100 A GeV and polarized proton up to 250 GeV PHENIX STAR 2000 run was successful!

  15. STAR detector Au on Au Event with CM Energy 130 GeV*A Heavy Ion physics Spin physics Photon/pomeron physics L3 Event Display June 25, 2000.

  16. p+ K+ p The PHENIX Detector Beam-Beam Counter EM Calorimeter Muon Tracking Chambers Time Expansion Chamber Central Arms Muon ID Panels Pad Chambers North Muon Arm Multiplicity/Vertex Detector Drift Chambers Time of Flight Panels South Muon Arm Ring Imaging Cerenkov

  17. Inclusive pion single spin asymmetry at p p ( p C) BNL E925 22GeV Fermi Lab E704 200GeV xF xF There is not fully satisfactory explanation Collins effect?Twist 3? RHIC STAR (BRAHMS?) will measure at

  18. Future Transversity Measurements at Polarized pp & polarized DIS BNL - Star/Phoenix/Phobos DESY-Hermes & CERN-Compass(BNL eRHIC, DESY Tesla-N) Requires H*H & F*F measurement from e+e-

  19. Conclusion • There are interesting and currently unknown fragmentation functions : Collins FF and IFF • We propose to analyze existing Belle data to extract these FF. • Large interests • CERN-LEP-DELPHI analysis on the same FF at different energy • BNL-STAR & PHENIX Experiments (BRHAMS & PHOBOS) • CERN-SPS-COMPASS, DESY-HERMES • (BNL eRHIC, DESY Tesla-N) • “Workshop on transverse spin physics” • at DESY-Zeuthen, Germany 2001 July 9-11th

  20. Helicity Amplitudes Three independent helicity amplitudes: Deep Inelastic Scattering Proton Proton Scattering helicity flip! quark helicity Proton helicity

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