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Transverse Spin Physics

Transverse Spin Physics. PHENIX Focus Seminar March 21, 2006 Brookhaven National Laboratory, Upton NY. M. Grosse Perdekamp (University of Illinois and RBRC). Transverse Spin Physics. Motivation Spin dependence of QCD cross sections Extract transversity distributions from

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Transverse Spin Physics

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  1. Transverse Spin Physics PHENIX Focus Seminar March 21, 2006 Brookhaven National Laboratory, Upton NY M. Grosse Perdekamp (University of Illinois and RBRC)

  2. Transverse Spin Physics • Motivation • Spin dependence of QCD cross sections • Extract transversity distributions from QCD analysis: SIDIS + pp + e+e- • Sivers function measurements • Orbital angular momentum? • Transverse Spin Measurements • pp fixed target • SIDIS • Polarized pp collider • Future (RHIC II, PAX) • Summary Transverse Spin

  3. Motivation: What is the structure of matter in the Universe? First ideas by Greek philosophers: for example Leukipp and Demokrit (~ 450-400 bc) formulated the atomic hypothesis: There are small particles, atoms, of which all matter is made and which cannot be divided in smaller parts Transverse Spin

  4. Some 2400 years later Richard Feynman: If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms - little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied. (The Feynman Lectures on Physics) Transverse Spin

  5. Example I: Hydrogen as Fundamental Bound State of the EM-Interaction  QED pioneers QFT! Lamb Doppler free saturation spectroscopy hydrogen atom Quantum Electro Dynamics Lamb shift Tomonaga, Feynman, Schwinger Transverse Spin

  6. Our Example: The Nucleon as Fundamental Bound State of the Strong Nuclear Force Polarized DIS, pp Nucleon Quantum Chromo Dynamics Proton Structure Fundamental QCD tests Transverse Spin

  7. Modern experimental tools make quantitative studies of the atomic hypothesis possible!

  8. Spin Dependence of QCD Cross Sections: Longitudinal Spin aLL Gluon Compton: q+g  q+gamma Cross section for anti-parallel quark and gluon spin Annihilation: q+q  q +gamma Transverse Spin

  9. Measuring ΔG: We exploit aLL at RHIC… Knowledge of the aLL (from theory!) is absolutely critical before we can learn anything about proton spin structure at RHIC  should be fine, we know that pQCD works at sufficiently high energy scales. It surely will get the spin dependence of cross sections right! the unknown we would like to extract! measured at RHIC known from deep inelastic lepton-proton scattering experiments  “DIS” perturbative QCD (pQCD) ? Transverse Spin

  10. Cross Sections for Transverse Spin QCD: Asymmetries for transverse spin are small at high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) ) Experiment (E704, Fermi National Laboratory): π+ QCD Test ! π0 π- Is QCD the correct theory of the strong interaction? Transverse Spin

  11. Inspect Factorized Expression for Cross Section fragmentation process Proton Structure Can initial and/or final state effects generate large trans-verse spin asymmetries? (ALL ~10-1) Hard Scattering Process Jet e+e- pQCD Proton Structure small spin dependence (aLL~10-4) Transverse Spin

  12. Transverse Spin in QCD: Two Solutions (I) Transversity quark-distributions and Collins fragmentation Correlation between proton- und quark-spin and spin dependent fragmentation π+ π0 π- (II) Sivers quarkdistribution Correlation between proton-spin and transverse quark momentum Transverse Spin

  13. Collins Effect in the Quark- fragmentation into the Final State NL- NR AN= = 0 NL+ NR π sq sq q q π NL : pions to the left Collins Effect NR : pions to the right Simple process: Fundamental test case for QCD at low energies (Dennis Sivers) Transverse Spin

  14. Artru Model for Collins Fragmentation A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: String breaks and a dd-pair with spin 1 is inserted. Proton spin is pointing up! L = -1 π+ picks up L=-1 to compensate for the pair S=1 and is emitted to the right. u-quark absorbs photon/gluon and flips it’s Spin. Transverse Spin

  15. Sivers Effect (Initial State) Sivers Effect: kT distribution of the quarks depends on the transverse spin direction of the protons Sp Sivers vunction: proton D. Sivers 1990 proton Sp J. Collins, 1993 : Sivers function is forbidden by symmetry properties (T-odd) Brodsky, Hwang and Schmidt 2002: Sivers function can arise from interference with diagrams with soft final state gluon exchange. Transverse Spin

  16. Sivers: Connection to Orbital Angular Momentum? M. Burkardt xqis blue/red shifted! Transverse Spin

  17. Sivers Effect: Final State Interaction • Final state soft gluons ? • What happens to factorization and universality ?? Transverse Spin

  18. Transversity, Sivers and Boer Mulders Transversity : correlation between transverse proton spin and quark spin Sivers : correlation between transverse proton spin and quark transverse momentum Boer/Mulders: correlation between transverse quark spin and quark transverse momentum Sp– Sq – coupling ? Sp-- Lq– coupling ??? Sq-- Lq– coupling ?? ? Transverse Spin

  19. Optical Theorem in Hard Scattering e- current quark jet e- spectator system proton Cross Section Forward Elastic Scattering Amplitude Optical Theorem initial state final state photon, gluon pQCD, hard scattering quark Factorization? q(x,Q2), G(x,Q2) proton Process independent quark and gluon distri- butions  Universality? Transverse Spin

  20. Helicity Amplitudes in Hard Scattering Forward Scattering Amplitude initial state final state hard probe: gluon, photon Quark, hi Quark, hf proton, Hf proton, Hi Hi hi Hf hf Helicity is conserved helicity average helicity difference helicity flip transversity quark distributions h: quark helicity H: proton helicity In initial and final state Transverse Spin

  21. Quark Distributions quark distrb. helicity amplitudes structure functions: Helicity flip! Probability to probe a quark of flavor i and momentum fraction x that contributes to the spin of a transversely polarized proton proton spin q probe spectators Transverse Spin

  22. Observation Helicity flip amplitude  no gluon transversity  pure quark observable avoid complicated coupling between gluon- and quark degrees of freedom we observe for longitudinal polarization: Lattice results suggest that the transverse quark spin sum is large. For example, S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433 Transverse Spin

  23. First AN Results from PHENIX and STAR PHENIX AN(π0) and AN(π0), |η|<0.35 Phys.Rev.Lett.95:202001,2005 STAR AN(π0) at 3.4<η<4.0 Phys.Rev.Lett.92:171801,2004 and (hep-ex/0502040) In PHENIX: Aidala, Bauer, Makdisi, Okada, Perdekamp Transverse Spin

  24. Compare Experiment, Collins- and Sivers-Effect Theory: Collins Theory: Sivers Anselmino et al. Anselmino et al. AN AN π+ π+ π0 AN cannot distinguish between Collins & Sivers … π0 π- π- Transverse Spin

  25. BRAHMS: AN for charged pions AN for pions: AN= +0.05 +- 0.005 +- [0.015] pT vs XF AN= -0.08 +- 0.005 +- [0.02] in 0.17 < xF < 0.32 xF x 100 • o From the Brahms 2005 run the • statistical errors will be reduced • by a factor 6-7 • o New absolute RHIC polarimeter will • reduce the systematic error by a factor 4 • What can be learned from confronting model calculations with precision data on AN? xF x 100 Transverse Spin

  26. AN for Protons from BRAHMS BRAHMS preliminary e • Proton AN is compatible with 0 • AN will be available for pions, kaons and protons from run 2005 • What do we learn from comparing AN for different fragmentation functions? Transverse Spin

  27. Sivers Function in PHENIX from Run 6 Data … • Precise measurement of AN in forward direction (MPC and EMC). • 2) Measurement of the Sivers function through AN in hadron- • hadron correlationen, neutrale pionen pairs (MPC and EMC) • (Boer and Vogelsang Phys.Rev.D69:094025,2004) AN Jets Hadron Paare ∫Ldt = 0.35pb-1 (Run 3) Similar in STAR…. Transverse Spin

  28. APD PbWO4 The Muon Piston Calorimeter (MPC) Forward EM Calorimeter: 2.2x2.2x18 cm3 , 20 X0, PbWO4 crystals for ALICE, LHC from Kurchatov ALICE: PbWO4 outer radius r=22.5 cm beam pipe r=5 cm PHENIX Muon Tracker Station I 3<η<3.5 Transverse Spin

  29. Transverse Aymmetries in Deep Inelastic Scattering Hermes Proton Target COMPASS, Deuteron Target Sivers Asymmetries Transversitiy x Collins Asymmetries QCD: Sivers Asymmetrie hat negatives Vorzeichen in p-p (Drell Yan)! Fraktorisierung und Universalität für kT-abhängige Verteilungen + FFs Analyse, Vogelsang and Yuan (Phys.Rev.D72:054028,2005) Transverse Spin

  30. A Program for the Study of Transverse Proton Spin Structure RBRC Workshop, 9-2000 factorization + universality? Belle Transversity Tensor Charge Theory + Bakker-Leader-Trueman Sum Rule Lattice QCD: Tensor Charge RBRC Transverse Spin

  31. Best Approach to Transversity for PHENIX?! Interference Fragmentation Jian Tang , Thesis MIT, June 1999 R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920 Jet X. Ji, Phys. Rev. D49 (1994)114 IFF J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565 Proton Structure Hard Scattering Process Jet measure in e+e- from DIS pQCD extract Transverse Spin

  32. Interference Fragmentation Asymmetries at RHIC (Tang, Thesis, MIT) Maximum Asymmetry 200 GeV 500 GeV Transverse Spin

  33. Projected Asymmetry (PHENIX) for 32pb-1 ) Small aymmetry below 5% but good rate! Transverse Spin

  34. Collins (+ Interference Fragmentation) in e+e- Annihilation at Belle KEK B-factory Asymmetric Collider 8 GeV e- + 3.5 GeV e+ 60 MeV below Ύ(4S): 10.52 GeV e+e-qq (u,d,s,c) High luminosity: ~ 500 fb-1 ~ 45fb-1 for off-resonance data set Belle Detector KEKB Belle Detector excellent track reconstruction and particle identification Transverse Spin

  35. Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation of a quark with transverse Spin into a hadron h with the following azimuthale distribution: Transverse Spin

  36. General Form of the Fragmentation Function Dhq is the probability to find a hadron with momentum z1 and transverse momentum phT: unpolarized FF Collins FF Transverse Spin

  37. Event-Structure in Belle e+e- SBS: J-Hemisphere: hi , i=1,Nn mit zi e- <Nh+,-> = 6.4 Q e+ Jet Axis: Thrust Cross section for Hadron Pairs: D-Hemisphere: hj , j=1,Nf with zj Transverse Spin

  38. Collins Fragmentation: Angles and Cross Section e+e- SBS: j2-p e- Q j1 j2 j1 e+ Cross Section for inclusive Hadron Pairs: Collins FF Transverse Spin

  39. z2 1.0 3 6 8 9 0.7 2 5 7 8 0.5 1 5 4 6 0.3 0 1 2 3 0.2 z1 0.2 0.3 0.5 0.7 1.0 Azimuthal Correlation in 10 (z1 – z2) Quark-Momentum Bins Azimuthal Distribution of Hadron-Pairs Bins in Quark Momentum N(f)/N0 D1 : Spin averaged Fragmentation Function H1: Collins Fragmentation Function Transverse Spin

  40. Collins Asymmetries forπ+π- Pairs • Experimental method to remove acceptance effects and asymmetries from QCD radiative processes. • First direct measurement of the Collins function. • First QCD analysis (Anselmino et al.) for Hermes and Belle data show good agreement between Belle FF and Hermes z1 z2 Transverse Spin

  41. HERMES Asymmetries (Transversity x Collins) and Belle Asymmetries (Collins)(Mauro Anselmino and Alexei Prokudin) BELLE PRELIMINARY Preliminary analysis, COMPASS week in Prag, August-2005 Common fit to the Hermes asymmetries (Transversity x Collins) and theBelle asymmetries (Collins)  Good agreement! Transverse Spin

  42. Measurement of Transversity- and Sivers-Distributions in Hadron-Hadron Collisions RHIC Luminosity? AN excellent! AN(Hadron-Korrelationen) good (Sivers signature!) AT (Collins FF) just enough AT (Interferenz FF) just enough AT (Drell Yan) no ATT( Drell Yan) no ATT( Drell Yan) pp Need Collins and Interefence FFs! RHIC II Luminosities (from 2012) GSI/PAX (anti-protons  Transversity for valence-quarks! Transverse Spin

  43. Transversity vs Sivers vs Boer-Mulders in Drell Yan Transversity : correlation between transverse proton spin and quark spin Sivers : correlation between transverse proton spin and quark transverse momentum Boer/Mulders: correlation between transverse quark spin and quark transverse momentum Transverse Spin

  44. Sivers-Asymmetrien, AT in Drell Yan für RHIC II Luminositäten Pojektionen für STAR for 125pb-1 hep-ph/0511272 Collins, Efremov, Goeke, Grosse Perdekamp, Menzel, Meredith, Metz, Schweitzer Neues Drell Yan Experiment 1250 pb-1 (“Vollzeit” transverse running + weite Akzeptanz, Vertex Fokusiermagnete) Transverse Spin

  45. Sivers-Asymmetrien, AT in Drell Yan für PAX und COMPASS PAX COMPASS Transverse Spin

  46. Summary o Much progress in resolving the origin of large transverse spin phenomena in QCD o Studying questions of factorization and universality leads to improved understanding of theoretical tools to apply pQCD at low scales. o Learn about quark spin and possibly quark orbital angular momentum contributions to the proton spin. Transverse Spin

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