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Transverse Spin Physics

Transverse Spin Physics. Some Comments on Hard Scattering Transverse Spin Puzzle and Solutions QCD @ high energies  small transverse spin asymmetries Experiment  observe large transverse spin asymmetries Solutions: (I) correlation between proton spin and intrinsic

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Transverse Spin Physics

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  1. Transverse Spin Physics Some Comments on Hard Scattering Transverse Spin Puzzle and Solutions QCD @ high energies  small transverse spin asymmetries Experiment  observe large transverse spin asymmetries Solutions: (I) correlation between proton spin and intrinsic quark transverse momentum kTquark: Sivers effect (II) correlation between the struck quark spin and transverse momentum kThadron of final state hadron: Collins effect (III) quark-gluon correlations in the initial or final state Koike, Qiu & Sterman M. Grosse Perdekamp University of Illinois and RBRC PHENIX Collaboration Meeting, Boulder, July 11th, 2007

  2. Optical Theorem in Hard Scattering e- current quark jet e- spectator system proton Forward Elastic Scattering Amplitude Cross Section 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? Operator product expansion in twist parameter t, t=d-nu..v Wilson coefficient Operator matrix element Transverse Spin

  3. 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

  4. 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

  5. Observations Concerning Transversity Transversity distributions are the last unknown leading twist, t=2, nucleon distribution functions. 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, Interesting properties: chiral odd, does not mix with gluons under evolution For non-relativistic quarks : Difference provides information on quark dynamics in the nucleon. Soffer’s bound: not small! Possibly S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433 Transverse Spin

  6. Transversity: Inclusive vs Semi-Inclusive Processes q chirality unchanged by strong interaction or electromagnetic current Does not contribute in leading twist inclusive DIS J.C. Collins, Nucl. Phys. B396, 161(1993) Collins fragmen- tation function Higher twist contributions are suppressed by Semi-inclusive DIS with chiral odd frag- mentation function: Transverse Spin

  7. Transverse Spin Asymmetries vs QCD 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

  8. 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

  9. 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

  10. NL- NR AN= = 0 NL+ NR q π sq sq q q π Collins Effect in the Quark- fragmentation into the Final State NR : pions to the right Collins Effect NL : pions to the left Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence: Simple process: Fundamental test case for QCD at low energies (Dennis Sivers) Transverse Spin

  11. 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 up. u-quark absorbs photon/gluon and flips it’s Spin. Transverse Spin

  12. Measurements of Quark Transversity Distributions and Collins Fragmentation Functions (I) SIDIS New HERMES results for Collins Asymmetries Diefenthaler, DIS 2007, Lu INPC 2007 Collins Asymmetries in semi- inclusive deep inelastic scattering e+p  e + π + X ~ Transversity (x) x Collins(z) AUT sin(f+fs) Transverse Spin

  13. Measurements of Quark Transversity Distributions and Collins Fragmentation Functions (II) e+e- New Belle Collins Asymmetries Seidl, DIS 2007 Collins Asymmetries in e+e- annihilation into hadrons e++e- π++ π- + X ~ Collins(z1) x Collins (z2) PRELIMINARY j2-p e- Q j1 e+ A12 cos(f1+f2) Transverse Spin

  14. First Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e+e- Fit includes: HERMES SIDIS + COMPASS SIDIS + Belle e+e- transversity dist. + Collins FF Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 Transverse Spin

  15. 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

  16. Sivers Effect (Initial State) Sivers Effect: kT distribution of the quarks depends on the transverse spin direction of the protons Sp Sivers function: 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

  17. Sivers Asymmetries at HERMES and COMPASS • implies non-zero Lq p+/- K+/- Transverse Spin

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

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

  20. Fundamental Theoretical Work Sivers’ Effect and Questions of Universality and Factorization Annual number of publications on transverse spin in SPIRES vs time. The total number of pulications is about ~750, about 15% are experimental. Transverse Spin

  21. Soft Gluon Interaction in the Initial and Final State of Hard Scattering Processes Integrate final state gluon radiation: gauge link and insert gauge link in hard scattering matrix element Integrate initial state gluon radiation: gauge link and insert gauge link in hard scattering matrix element Transverse Spin

  22. What new do we have we learned ? The Sivers effect arises from soft gluon interactions in the final state (SIDIS) or initial state (Drell Yan). Need to modify naïve concepts of factorization which reduce hard scattering to partonic processes and neglect soft gluon interactions in the initial or final state: hard scattering matrix elements are modified with gauge link integrals that account for initial and final state soft gluon exchange. A modified concept of universality has been obtained which shows how the presence of initial or final state interactions can impact transverse momentum dependent distribution; eg. the Sivers function changes sign between SIDS and Drell Yan! There may be exciting applications elsewhere, eg. the understanding nuclear effects in hard scattering or the passage of quarks and gluons in colored media. Transverse Spin

  23. Application for Gauge Link Formalism Elsewhere? (I) Modification of hard scattering matrix elements in cold nuclear matter (Stan Brodsky @ the 1st Urbana Study Group on Transverse Spin, 03-2003) Can we understand the modifi- cation of hard scattering matrix elements and therefore parton distributions functions quanti- tatively?  initial state in Au-Au! G(x) GA(x) x Transverse Spin

  24. Application for Gauge Link Formalism Elsewhere? (II) Passage of quarks on gluons through colored media (Collins, Qiu: private communication, April 2007) Can we understand the passage of quarks and gluons using the gauge formalism? Transverse Spin

  25. Transverse Spin Drell Yan at RHIC vsπ-SiversAsymmetry in Deep Inelastic Scattering Important test at RHIC of the fundamental QCD prediction using gauge link formalism of thenon-universality of the Sivers effect! requires very high luminosity (~ 250pb-1) Transverse Spin

  26. Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory ! Simple QED example: Drell-Yan: repulsive DIS: attractive Same inQCD: As a result: Transverse Spin

  27. Drell Yan at RHIC Large x  forward rapidity (Les Bland) Heavy flavor background (Ming Liu) Drell Yan yield in arbitrary units ϒ-states J/Ψ charm bottom Ψ’ FVTX enables DY measurement by rejecting heavy flavor background: • Measurement: 4 GeV < Q < 10 GeV Transverse Spin

  28. Experiment SIDIS vs Drell Yan: Sivers|DIS= − Sivers|DY *** TestQCD Prediction of Non-Universality *** HERMES Sivers Results RHIC II Drell Yan Projections 0 Sivers Amplitude Markus Diefenthaler DIS Workshop Műnchen, April 2007 0 0.1 0.2 0.3 x Transverse Spin

  29. Sensitivity to Sivers Effect for Anti-Quarks Sensitive to valence quark Sivers at large x and sea quark Sivers distributions at small x. dashed line: Collins et al. Phys. Rev.D73:094023,2006 dependence on quark sea sea quark Sivers x~0.02 valence quark Sivers x~0.5 Transverse Spin

  30. Our Ultimate Goal What is the nucleon wave function in terms of quarks and gluons? eg. quark spin – proton spin coupling quark spin – quark orbital momentum coupling proton spin –proton spin – quark orbital momentum coupling How can QCD be used to carry out ab initio calculations of the nucleon wave function? Transverse Spin

  31. Transversity vs Sivers vs 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 Transverse Spin

  32. Transversity vs Sivers vs 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

  33. Transverse Spin Physics in PHENIX Inclusive AN: hadrons  CA, MuA, MPC, NCC photons  CA, NCC Transversity: IFF  CA, MPC Collins effect in jets  NCC Sivers: AN in D-production  FVTX+MuA, VTX+CA AN for di-hadrons back-to-back  MPC, NCC AN for jets  NCC AT in Drell-Yan  MuA, FVTX Transverse Spin

  34. Summary First evidence that Collins’ and Sivers’ effects create sizable single transverse spin asymmetries in hard scattering reactions. Gauge link formalism makes it possible to account for the presence of Sivers asymmetries. Fundamental Tests possible in Drell Yan in PHENIX. Possible connection between Sivers asymmetries and orbital angular momentum. Many complementary channels to explore transverse spin phenomena in PHENIX. Unique Sivers and transversity x Collins signatures! Transverse Spin

  35. Muon Piston Calorimeter Upgrade Physics Transverse spin in polarized p-p ΔG at low x Saturation/low-x in d-Au Technology  ALICE(PHOS) PbWO4 avalanche photo diode readout 3.1 < η < 3.65, 0 < φ < 2π Schedule MPC south commissioned in run 2006 MPC north commissioned in fall 2007 MPC south upgrade in summer 2007 Collaboration BNL, Colorado, Hiroshima, Kurchatov Institute, ORNL, RIKEN, Stony Brook, UCR, UMass, UIUC

  36. 0AN at High xF p+p0+X at s=62.4 GeV/c2 p+p0+X at s=62.4 GeV/c2 3.0<<4.0 Mickey Chiu, INPC, Tokyo PLB 603,173 (2004) process contribution to 0, =3.3, s=200 GeV • Large asymmetries at forward xF • Valence quark effect? • xF, pT, s, and  dependence provide quantitative tests for theories

  37. First attempt at lower x: ALL(2π0) from Les Bland (for STAR FMS) Measure ALL for neutral pion pairs: one in the central arm the second in the MPC  0.1 > x  0.001 Theory Framework available from Marco Stratmann MPC Transverse Spin

  38. Current Work Hardware: new MPC south arrived from UIUC parts for new light distribution system in prodution at UMass and UIUC Upgrade: south acceptance, light distribution system scheduled for July/August 2007 Analysis: di-hadron ALL(2π0)     John  ALL(π0) 62 GeV         Aaron  62 GeV π0 x-section Seishi, Mickey  pi0 ALL(π0) 200 GeV       Seishi/John  200 GeV π0 x-section   John/Seishi  Sivers back-to-back     Nathan, MickeyMore tentative possibilities:  Doug et al on kT asymmetry butwith MPC π0, Beau might be working on an IFF study. Transverse Spin

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

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

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