1. Collins Asymmetries in Belle Measurement of Collins Asymmetries in e + e - Annihilation at the KEK B-Factory XII Workshop on High Energy Spin 2007 Joint Institute for Nuclear Research, Dubna, September 6 th M. Grosse Perdekamp. Illinois D. Gabbert Illinois and RBRC M. Grosse Perdekamp Illinois and RBRC K. Hasuko RIKEN and RBRC S. Lange Frankfurt M. Leitgab Illinois D. Mertens Illinois A. Ogawa BNL and RBRC R. Seidl Illinois and RBRC V. Siegle RBRC for the Belle Collaboration

2. Collins Asymmetries in Belle2 September 6 th ----------- Outline ------------ oMotivation  Collins FF for global QCD analysis of single transverse asymmetries in pp and SIDIS oCollins Asymmetries from e + e -  LEP first work on Delphi data in the 90s: Bonivento, Matteuzzi, Kotzinian, (DELPHI note,1995), Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74, 1999)  Experimental technique  Results oFuture Plans Spin dependent observables Precision measurement of spin averaged hadron fragmentation functions

3. Collins Asymmetries in Belle3 September 6 th o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales. o Tests of universality and factorization between e + e -, DIS and p-p collisions o Symmetry properties o Evolution is fundamental QCD prediction o Connection between microscopic and macroscopic observables:  Probe/analyzer for transverse quark spin critical input for transverse proton spin program at DESY, CERN, JLab and RHIC Why is the Collins Fragmentation Function Interesting?

4. Collins Asymmetries in Belle4 September 6 th Motivation Transversity Quark Distributions δq(x) from Collins- (CFF) and Interference-Fragmentation (IFF) Collins- and IFF- asymmetries in semi-inclusive deep inelastic scattering (SIDIS) and pp measure ~ δq(x) x CFF(z) ~ δq(x) x IFF(z) Collins- and IFF- asymmetries in e + e - annihilation are of the form ~ CFF(z 1 ) x CFF(z 2 ) ~ IFF(z 1 ) x IFF(z 2 )  global QCD analysis Latest HERMES results for Collins Asym- Metries, M. Diefenthaler, DIS 2007, Munich

5. Collins Asymmetries in Belle5 September 6 th Global Analysis: Extract Transversity Distributions Transversity, δq(x) Tensor Charge Lattice QCD: Tensor Charge Factorization + Universality ?! Theory RBRC Transversity Workshop 2000 SIDIS ~ δq(x) x CFF(z) ~ δq(x) x IFF(z) e + e - ~ CFF(z 1 ) x CFF(z 2 ) ~ IFF(z 1 ) x IFF(z 2 ) pp  jets ~ G(x 1 )xδq(x 2 ) x CFF(z) pp  h + + h - + X ~ G(x 1 )xδq(x 2 ) x IFF(z) pp  l + + l - + X ~ δq(x 1 ) x δq(x 2 )

6. Collins Asymmetries in Belle6 September 6 th First QCD Analysis of SIDIS + e + e - ! Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 HERMES SIDIS + COMPASS SIDIS + Belle e + e -  transversity dist. + Collins FF Fit includes:

7. Collins Asymmetries in Belle7 September 6 th The Preliminary DELPHI Collins Result Efremov, Smirnova, Tkachev (Nucl. Phys. Proc. Suppl. 74, 1999) Sample: 3.5 x 10 6 events at √s=M Z 0 Analysis: di-hadron correlation for leading hadrons 35<θ 2 <135 15< θ 2 <175 endcaps  First result on Collins Asymmetries in e + e -  Monte Carlo for acceptance corrections  Un-estimated (large) systematic errors  DELPHI result e + e - compatible with HERMES+ BELLE (Efremov, Goeke, Schweitzer)

8. Measurement of Collins Asymmetries In e + e - at KEK B with the Belle Phys.Rev.Lett.96:232002,2006 and update at Spin 2006 in Kyoto

9. Collins Asymmetries in Belle9 September 6 th Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence:

10. Collins Asymmetries in Belle10 September 6 th General Form of Fragmentation Functions Number density for finding hadron h from a transversely polarized quark, q: unpolarized FF Collins FF

11. Collins Asymmetries in Belle11 September 6 th o Quark spin direction unknown: measurement of Collins function in one hemisphere is not possible sin φ modulation will average out. o Correlation between two hemispheres with sin φ i Collins single spin asymmetries results in cos(φ 1 +φ 2 ) modulation of the observed di-hadron yield. Measurement of azimuthal correlations for pion pairs around the jet axis in two-jet events! Collins FF in e + e - : Need Correlation between Hemispheres !

12. Collins Asymmetries in Belle12 September 6 th q1q1 quark-1 spin Collins effect in e + e - quark fragmentation will lead to azimuthal asymmetries in di-hadron correlation measurements! Experimental requirements:  Small asymmetries  very large data sample!  Good particle ID to high moments.  Hermetic detector Collins Effect in di-Hadron Correlations In e + e - Annihilation into Quarks! electron positron q2q2 quark-2 spin z2z2 z1z1 z 1,2 relative pion momenta

13. Collins Asymmetries in Belle13 September 6 th KEKB –Asymmetric collider –8 GeV e - + 3.5 GeV e + –  s = 10.58 GeV, e + e -  ϒ  S    –Off-resonance: 10.52 GeV e + e -  q  q (u,d,s,c) –Integrated Luminosity: 547 fb -1 (on resonance) 60 fb -1 (off-resonance) Belle detector KEKB KEKB: L>1.6 x 10 34 cm -2 s -1 !! Average Trigger rates:  (4S)  BB11.5Hz q  q28 Hz  16 Hz Bhabha 4.4 Hz 2  35 Hz 1.5 x 10 9 hadronic events in analysis ~ 430 x DELPHI …

14. Collins Asymmetries in Belle14 September 6 th Luminosity vs time for 24 hours at KEKB Continuous Injection  Constant Collision Rate 24 hours high energy ring - beam current low energy ring - beam current HER lifetime LER lifetime ∫Ldt vs day time ∫Ldt =1fb -1 /day

15. Collins Asymmetries in Belle15 September 6 th Large acceptance, good tracking and particle identification!

16. Collins Asymmetries in Belle16 September 6 th Hadronic Events observed with Belle Thrust ~ 1 ~ 0.5  1.5 x 10 9 hadronic events in analysis Off resonance: 29fb -1, √s=10.52 GeV (published) On resonance: 547fb -1, √s=10.58 GeV (preliminary)

17. Collins Asymmetries in Belle17 September 6 th Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance small B contribution (<1%) in high thrust sample >75% of X-section continuum under ϒ  (4S) resonance 29 fb -1  547 fb -1 several systematic errors reduce with more statistics Charm-tagged Data sample also increases e + e -  qq ̅, q∈uds e + e -  cc ̅ 0.5 0.8 1.0

18. Collins Asymmetries in Belle18 September 6 th Applied Cuts, Binning Originally off-resonance data, now also on-resonance data (29.1  547 fb -1 ) Track selection: –p T > 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 Pion PID selection 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 z1z1

19. Collins Asymmetries in Belle19 September 6 th e-e- e+e+ Jet axis: Thrust = 6.4 Near-side Hemisphere: h i, i=1,N n with z i far-side hemisphere: h j, j=1,N f with z j  Event Structure at Belle e + e - CMS frame: Spin averaged cross section:

20. Collins Asymmetries in Belle20 September 6 th Collins Fragmentation: Angles and Cross Section: cos(     ) Method (e+e- CMS frame)       2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins  e-e- e+e+ Observable: yield, N 12 (φ 1 +φ 2 ) of π + π - pairs

21. Collins Asymmetries in Belle21 September 6 th Collins Fragmentation: Angles and Cross Section cos(2   ) Method (CMS Frame)  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 [Boer,Jakob,Mulders: NPB504(1997)345] e-e- e+e+ Observable: yield, N 0 (2φ 0 ) of π + π - pairs

22. Collins Asymmetries in Belle22 September 6 th z2z2 QTQT e- e+ z1z1 Frame: Complication: Radiative Contribution to the Di-Hadron Cross Section same cos(2Φ 0 ) dependence as Collins effect …

23. Collins Asymmetries in Belle23 September 6 th Examples of Fits to Azimuthal Asymmetries D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N 0 (   )/ 22     ) 2a 0 R0R0 R 12 2a 12 N 12 ( Φ 1 +Φ 2 )/ a 0 and a 12 contain Collins + radiative effects + acceptance effects

24. Collins Asymmetries in Belle24 September 6 th Large Radiative and Acceptance Effects ! Example: a 0 for unlike-sign pion pairs: a 0 U generated uds-MC vs reconstructed uds-MC vs data (Difference MC-data: charm contribution) a 0 for like-sign pion pairs: a 0 L generated uds-MC vs reconstructed uds-MC vs data (Difference MC-data: charm contribution) generated uds-MC reconstructed uds-MC data reconstructed uds-MC generated uds-MC

25. Collins Asymmetries in Belle25 September 6 th Method to eliminate gluon contributions: Double ratios for unlike- and like sign pions (I) radiative effects are charge independent and cancel. (II) Acceptance effects cancel. (III) R UL and R L depend depend on H fav and H dis differently.  A 12 retains sensitivity for the Collins effect! Cross checked against subtraction RUL-RL with identical results. Form double ratios for unlike and like-sign pion pairs:

26. Collins Asymmetries in Belle26 September 6 th Two Double Ratios Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored)  ±   pairs (favored + unfavored) x (favored + unfavored) A. Efremov et al. ([hep-ph/0603054]): charged  pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) Double ratios unlike/like-sign not very sensitive in separating favored and disfavored Collins functions  look at unlike-sign/charge-sum UL UC Observables: A 12 (UL), A 12 (UC) A 0 (UL), A 0 (UC) published and input to fit by Anselmino et al.

27. Collins Asymmetries in Belle27 September 6 th Consistency Checks for Double Ratio (0) Check that Monte Carlo Double asymmetries are 0. (1) Calibrate with “known” physics asymmetry: Weak decays produce azimuthal asymmetries. Showed that double ratio method give correct asymmetry for tau-sample. (2) Comparison of Double Ratio with Subtraction Method leads to identical results. (3) Observe polar angle dependence (4) Smaller asymmetry for lower thrust sample (5) Null tests: (a) mixed events give 0 asymmetry (b) single side asymmetries average to 0

28. Collins Asymmetries in Belle28 September 6 th Double Ratios From Monte Carlo Monte Carlo knows Radiative and accep- tance effects! Do they cancel in the final double ratio? Assign largest observed average MC double ratio + statistical error as systematic error =0.0013∓0.0009  0.0022

29. Collins Asymmetries in Belle29 September 6 th Collins Asymmetries: sin 2  /(1+cos 2  ) Binning (UL) Nonzero quark polarization ~ sin 2  Unpolarized de- nominator ~ 1+cos 2  Clear linear behavior seen when using either thrustz or 2 nd hadron as polar angle Better agreement for thrust axis (~approximate quark axis) UC plots similar thrustz   PRELIMINARY

30. Collins Asymmetries in Belle30 September 6 th Other Experimental Issues Beam Polarization zero?  cos(2  ) asymmetries for jets or  False asymmetries from weak decays  estimate charm contribution 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 from data, fiducial cuts Correlations from decays  lower z cut

31. Collins Asymmetries in Belle31 September 6 th Final Charm Corrected Results for e + e -   X (29fb -1, off-resonance Data) Significant non-zero asymmetries Rising behavior vs. z UL/C asymmetries about 40- 50% of UL/L asymmetries First direct measurements of the Collins function UL/L data published Phys.Rev.Lett.96:232002,2006

32. Collins Asymmetries in Belle32 September 6 th Preliminary Charm Corrected Results for e + e -   X (547 fb -1,on-resonance) Significance largely increased Behavior unchanged Reduced systematics Precise measurements of the Collins function Preliminary

33. Collins Asymmetries in Belle33 September 6 th Improved Systematic Errors (UC) Tau contributions PID systematics  MC double ratios Charged ratios (          Higher order terms Double ratio-subtraction method Reweighting asymmetries:  underestimation of cos      asymmetries  rescaled by 1.21 Correlation studies:  statistical errrors rescaled by 1.02 (UL) and 0.55 (UC) A 0 (cos(2   )) moments A 12 (cos(       )) moments

34. Collins Asymmetries in Belle34 September 6 th Collins Asymmetries I: 4x4 z 1, z 2 binning 547 fb -1 charm corrected data sample, UL and UC double ratios PRELIMINARY A 0 (cos(2   )) momentsA 12 (cos(       )) moments

35. Collins Asymmetries in Belle35 September 6 th First QCD Analysis of SIDIS + e + e - ! Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 HERMES SIDIS + COMPASS SIDIS + Belle e + e -  transversity dist. + Collins FF Fit includes:

36. Collins Asymmetries in Belle36 September 6 th Summary & Outlook  Observation of large azimuthal asymmetries in light quark frag- mentation. Updated statistics: ∫Ldt = 29 fb -1  547 fb -1  Double ratios reliably cancel contributions from detector acceptance and gluon radiation.  Important input for the transverse spin physics programs at RHIC, HERMES, COMPASS and JLab.  Fundamental test case for QCD at soft scales!  Future spin dependent FFs:  update Collins FF  measure p T dependence  interference fragmentation  Collins FF for VMs  Lambdas  Precision measurement of spin averaged fragmentation func- tions as input to RHIC program with inclusive hadrons and future precision measurements in SIDIS.

37. Collins Asymmetries in Belle37 September 6 th Motivation ∆G from QCD Analysis of A LL for inclusive hadrons: π 0,+,-, η, K +,- PHENIX π 0 cross section a |η|<0.35 Phys.Rev.Lett.91:241803,2003 Deviation connected to uncertainties in FFs  gluon FF! Idea: QCD analysis of LEP and Belle data will fix uncertainty in know- ledge of FFs (gluon FF, flavor separation)

38. Collins Asymmetries in Belle38 September 6 th What is Known Experimentally in e + e - ? Hirai, Kumano, Nagai, Sudo hep-ph/0612009 (including errors!) Earlier work: Kretzer Binnewies, Potter, Albino Kniehl, Kramer, Potter Albino, Kniehl, Kramer Most recent work: De Florian, Sassot, Stratmann

39. Collins Asymmetries in Belle39 September 6 th Belle MC <1% of data sample  work in progress Belle Impact on the Knowledge of FFs FF Compilation of data available for the char- ged hadron FF Belle: Charged h +/-, pions, kaons, protons precision at high z!  h+,-  pions  kaons  protons Input also for precision measurements of quark helicity distributions in SIDIS, in particular at a possible future electron- polarized proton collider.

40. Collins Asymmetries in Belle40 September 6 th Collins Asymmetries III: Q T Binning (UL) Reduced asymmetries in low thrust sample At low thrust significant B contribution (for t<0.8 ~20 % B for t>0.8 < 1 % B) A 12 thrust axis dependent High Q T (>3.5 GeV) asymmetries from beam related BG UC plots similar Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) PRELIMINARY