1. First Measurement of the Collins fragmentation function at Belle M. Grosse Perdekamp (University of Illinois and RBRC) K. Hasuko (RIKEN/RBRC) S. Lange (Frankfurt University) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC) for the Belle Collaboration QCDN06 June 14 th, Frascati, Italy (see hep-ex/0507063 for details, accepted by PRL)

2. Measurement of the Collins fragmentation function at BELLE2 QCDN06, June 14 th J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation with of a quark q with spin s q into a spinless hadron h carries an azimuthal dependence: Collins effect in quark fragmentation

3. Measurement of the Collins fragmentation function at BELLE3 QCDN06, June 14 th The Collins Effect in the Artru Fragmentation Model π + picks up L=1 to compensate for the pair S=1 and is emitted to the right. String breaks and a dd-pair with spin -1 is inserted. A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation:

4. Measurement of the Collins fragmentation function at BELLE4 QCDN06, June 14 th SIDIS experiments (HERMES and COMPASS) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function Important input for global Transversity Analysis RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x) There are always 2 unknown functions involved which cannot be measured independently The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function ! Universality appears to be provenin LO by Collins and Metz: [PRL93:( 2004)252001 ] +most recent work from Amsterdam Group

5. Measurement of the Collins fragmentation function at BELLE5 QCDN06, June 14 th KEKB: L>1.5x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e - + 3.5GeV e +  s = 10.58GeV (  (4S)) e + e -   S    Off-resonance: 10.52 GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: >600 fb -1 >45fb -1 => off-resonance Belle detector KEKB

6. Measurement of the Collins fragmentation function at BELLE6 QCDN06, June 14 th Good tracking and particle identification!

7. Measurement of the Collins fragmentation function at BELLE7 QCDN06, June 14 th e-e- e+e+ Jet axis: Thrust = 6.4 Near-side Hemisphere: h i, i=1,N n with z i Far-side: h j, j=1,N f with z j  Event Structure at Belle e + e - CMS frame: Spin averaged cross section:

8. Measurement of the Collins fragmentation function at BELLE8 QCDN06, June 14 th Collins fragmentation in e + e - : Angles and Cross section cos(     ) method       2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins  e + e - CMS frame: e-e- e+e+ [D.Boer: PhD thesis(1998)]

9. Measurement of the Collins fragmentation function at BELLE9 QCDN06, June 14 th Collins fragmentation in e + e - : Angles and Cross section cos(2   ) method  2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins  Independent of thrust-axis Convolution integral I over transverse momenta involved e + e - CMS frame: e-e- e+e+ [Boer,Jakob,Mulders: NPB504(1997)345]

10. Measurement of the Collins fragmentation function at BELLE10 QCDN06, June 14 th Applied cuts, binning Off-resonance data –60 MeV below  (S) resonance –29.1 fb -1 Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –Ntrack  3 –Thrust > 0.8 –Z 1, Z 2 >0.2 Hemisphere cut Q T < 3.5 GeV z1z1 z2z2 0123 4 5 6 78 9 0.2 0.3 0.5 0.7 1.0 0.20.30.50.71.0 5 86 1 2 3 = Diagonal bins

11. Measurement of the Collins fragmentation function at BELLE11 QCDN06, June 14 th Examples of fits to azimuthal asymmetries D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0 No change in cosine moments when including sine and higher harmonics Cosine modulations clearly visible 22     )

12. Measurement of the Collins fragmentation function at BELLE12 QCDN06, June 14 th Methods to eliminate gluon contributions: Double ratios and subtractions Double ratio method: Subtraction method: Pros: Acceptance cancels out Cons: Works only if effects are small (both gluon radiation and signal) Pros: Gluon radiation cancels out exactly Cons: Acceptance effects remain 2 methods give very small difference in the result

13. Measurement of the Collins fragmentation function at BELLE13 QCDN06, June 14 th Testing the double ratios with MC Asymmetries do cancel out for MC Double ratios of         compatible with zero Mixed events also show zero result Asymmetry reconstruction works well for  MC (weak decays) Single hemisphere analysis yields zero  Double ratios are safe to use uds MC (UL/L double ratios) uds MC (UL/C double ratios) Data (         )

14. Measurement of the Collins fragmentation function at BELLE14 QCDN06, June 14 th Small double ratios in low thrust data sample Low thrust contains radiative effects Collins effect at least smeared for low thrust  Strong experimental indication that double ratio method works A0A0 A 12

15. Measurement of the Collins fragmentation function at BELLE15 QCDN06, June 14 th Results for e + e -   X for 29fb -1 Significant non-zero asymmetries Rising behavior vs. z cos      double ratios only marginally larger First direct measurement of the Collins function Integrated results: –cos(2   ) method (3.06±0.57±0.55)% –cos(2     ) method (4.26±0.68±0.68)% z1z1 z2z2 Systematic error A0A0 A 12 Final results

16. Measurement of the Collins fragmentation function at BELLE16 QCDN06, June 14 th Unlike-sign pion pairs (UL): (fav x fav + unf x unf) Like-sign pion pairs (L): (fav x unf + unf x fav)  ±   pairs (fav + unf) x (fav + unf) charged  pairs are similar (C): (P.Schweitzer([hep-ph/0603054]): (fav + unf) x (fav + unf) Other Favored/Unfavored Combinations  charged pions or   Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.  Build new double ratios:  Unlike-sign/ charged  pairs (UL/C) UL/L UL/C ~ fav 2 + unf 2 - 2 fav x unf ~ -2 fav x unf (oversimplified)

17. Measurement of the Collins fragmentation function at BELLE17 QCDN06, June 14 th Systematic errors Tau contributions PID systematics  MC double ratios Charged ratios (           Higher order terms Double ratio-subtraction method  taken from UL/L analysis Further studies: Reweighting asymmetries:  underestimation of cos      asymmetries Correlation studies:  statistical errrors rescaled by 14% Beam polarization studies  consistent with zero

18. Measurement of the Collins fragmentation function at BELLE18 QCDN06, June 14 th Final charm corrected results for e + e -   X (29fb -1 of continuum data) Significant non-zero asymmetries Rising behavior vs. z cos(   +   ) double ratios only marginally larger UL/C asymmetries about 40- 50% of UL/L asymmetries First direct measurements of the Collins function Final results Preliminary results

19. Measurement of the Collins fragmentation function at BELLE19 QCDN06, June 14 th What about the data under the resonance? Almost 600 fb -1 of on_resonance data  (4S) is just small resonance More than 75% of hadronic cross section

20. Measurement of the Collins fragmentation function at BELLE20 QCDN06, June 14 th Why is it possible to include on_resonance data? Different Thrust distributions e + e -  q  q (u d s) MC  (4S)  B + B - MC  (4S)  B 0  B 0 MC Largest systematic errors reduce with more statistics Charm-tagged Data sample also increases with statistics

21. Measurement of the Collins fragmentation function at BELLE21 QCDN06, June 14 th e + e -  (  +  - ) jet1 (  -  + ) jet2 X Stay in the mass region around  -mass Find pion pairs in opposite hemispheres Observe angles  1  2 between the event-plane (beam, jet-axis) and the two two-pion planes. Transverse momentum is integrated (universal function, evolution easy  directly applicable to semi-inclusive DIS and pp) Theoretical guidance by papers of Boer,Jakob,Radici and Artru,Collins Early work by Collins, Heppelman, Ladinski Interference Fragmentation – thrust method  2   1

22. Measurement of the Collins fragmentation function at BELLE22 QCDN06, June 14 th Different model predictions for IFF Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of  - phaseshift analysis  sign change at  mass - originally no predictions on actual magnitudes - Tang included some for RHIC-Spin Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channel  no sign change observed (updated model has Breit- Wigner like asymmetry) PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96

23. Measurement of the Collins fragmentation function at BELLE23 QCDN06, June 14 th What would we see in e + e - ? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m1  m2  “ Jaffe ”“ Radici ”

24. Measurement of the Collins fragmentation function at BELLE24 QCDN06, June 14 th Summary and outlook Double ratios: double ratios from data most systematic errors cancel Analysis procedure passes all null tests Systematic uncertainties understood  Significant nonzero asymmetry with double ratios are observed UL/C about half as large UL/L double ratios Data can be used for more sophisticated analysis Paper with UL/L double ratios (hep-ex/0507063) is accepted Leading order fits ongoing On resonance  >10 x statistics  long paper on Collins results Interference fragmentation function analysis started Include Vector Mesons into Collins analysis:  Possibility to test string fragmentation models used to describe Collins effect Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS,  Polarimetry) Summary: Outlook:

25. Measurement of the Collins fragmentation function at BELLE25 QCDN06, June 14 th

26. Measurement of the Collins fragmentation function at BELLE26 QCDN06, June 14 th Spin composition of the nucleon: –Contribution of quark spin small –Contribution of gluon spin also small? –Orbital angular momentum? Sivers effect? Single spin asymmetries small in pQCD –…but large and nonzero! –Understandable by gauge link contributions Sivers effect: –Unpolarized quarks in transversely polarized nucleon –Non-centered quark distribution in impact parameter space  Rescattering creates left-right asymmetry Boer-Mulders effect: Transversely polarized quarks in unpolarized nucleon Vacuum polarization effect? Collins effect: Fragmentation of transversly polarized quark into unpolarized hadron Connects microscopic quantitiy (transverse spin) to macroscopic quantity (azimuthal asymmetries) QCD: the right theory, but many surprises especially in spin …

27. Measurement of the Collins fragmentation function at BELLE27 QCDN06, June 14 th Fits to our UL/L data: Efremov, Goeke, Schweitzer: [hep-ph/0603054] : Taking reasonable transversity from  QSM Gaussian intrinsic transverse momentum dependence  HERMES, COMPASS and Belle results are consistent with each other However: Fit errors on Collins function still large  Probably improvement by UL/C data (not yet included)  Can we do better?

28. Measurement of the Collins fragmentation function at BELLE28 QCDN06, June 14 th What do we see? I: events Animation of an event lepton tracks, thrust axis and all particle momenta in the CMS frame P h1 =P 1 +P 2 P h2 =P 3 +P 4 Plane defined by leptons and thrust Planes defined by hadron pairs

29. Measurement of the Collins fragmentation function at BELLE29 QCDN06, June 14 th Typical hadronic events at Belle

30. Measurement of the Collins fragmentation function at BELLE30 QCDN06, June 14 th What is the transverse momentum Q T of the virtual photon? In the lepton CMS frame e - =-e + and the virtual photon is only time-like: q  =(e -  +p +  )=(Q,0,0,0) Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame where P h1 +P h2 =0  q  ’ =(q ’ 0,q ’ ) Inclusive Cross section for radiative events (acc. to D.Boer): P h1 e+e+ e-e- P h2 e-’e-’ e+’e+’ q’ P’ h1 P’ h2 qTqT Lepton-CMS Hadron-CMS

31. Measurement of the Collins fragmentation function at BELLE31 QCDN06, June 14 th Raw asymmetries vs Q T      Q T describes transverse momentum of virtual photon in  CMS system Significant nonzero Asymmetries visible in MC (w/o Collins) Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs uds MC (  ) Unlike sign pairs uds MC (  ) Like sign pairs

32. Measurement of the Collins fragmentation function at BELLE32 QCDN06, June 14 th Experimental issues Cos2  moments have two contributions: –Collins  Can be isolated either by subtraction or double ratio method –Radiative effects  Cancels exactly in subtraction method, and in LO of double ratios Beam Polarization zero?  Cos(2  Lab ) asymmetries for jets or  False asymmetries from weak decays  Study effect in  decays, constrain through D tagging False asymmetries from misidentified hemispheres  Q T or polar angle cut False asymmetries from acceptance  Cancels in double ratios, can be estimated in charge ratios, fiducial cuts Decaying particles  lower z cut

33. Measurement of the Collins fragmentation function at BELLE33 QCDN06, June 14 th Take simple parameterization to test sensitivity on favored to disfavored Ratio Favored/Disfavored contribution  Sensitivity c b

34. Measurement of the Collins fragmentation function at BELLE34 QCDN06, June 14 th Similar to previous method Observe angles  1R  2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation – “   “ method  R2  R1