1. Measurements of chiral-odd fragmentation functions at Belle D. Gabbert (University of Illinois and RBRC) 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) V. Siegle (RBRC) for the Belle Collaboration DIS 2006 April 20 th, Tsukuba (see hep-ex/0507063 for details, submitted to PRL)

2. Spin dependent fragmentation functions at BELLE2 DIS2006, April 20 th J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation of a quark q with spin s q into a spinless hadron h carries an azimuthal dependence: Collins effect in quark fragmentation

3. Spin dependent fragmentation functions at BELLE3 DIS2006, April 20 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. Spin dependent fragmentation functions at BELLE4 DIS2006, April 20 th SIDIS experiments (HERMES and COMPASS) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function Motivation: Global Transversity Analysis  q(x) 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 proven in LO by Collins and Metz: [PRL93:( 2004)252001 ]

5. Spin dependent fragmentation functions at BELLE5 DIS2006, April 20 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: >500 fb -1 >45fb -1 => off-resonance Belle detector KEKB

6. Spin dependent fragmentation functions at BELLE6 DIS2006, April 20 th Good tracking and particle identification!  / K L detection 14/15 lyr. RPC+Fe C entral D rift C hamber small cell +He/C 2 H 6 CsI(Tl) 16X 0 Aerogel Cherenkov cnt. n=1.015~1.030 Si vtx. det. 3/4 lyr. DSSD TOF conter SC solenoid 1.5T 8 GeV e  3.5 GeV e  Belle Detector

7. Spin dependent fragmentation functions at BELLE7 DIS2006, April 20 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)]

8. Spin dependent fragmentation functions at BELLE8 DIS2006, April 20 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]

9. Spin dependent fragmentation functions at BELLE9 DIS2006, April 20 th Applied cuts, binning Off-resonance data –60 MeV below  (4S) resonance –29.1 fb -1 Pions selected by PID cut Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos  h < 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 z1z1

10. Spin dependent fragmentation functions at BELLE10 DIS2006, April 20 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     )

11. Spin dependent fragmentation functions at BELLE11 DIS2006, April 20 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

12. Spin dependent fragmentation functions at BELLE12 DIS2006, April 20 th Other Favored/Unfavored Combinations  charged pairs Unlike-sign pion pairs (UL): (favored x favored+unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored +unfavored x favored)  ±   pairs (favored + unfavored) x (favored + unfavored) P.Schweitzer( [hep-ph/0603054] ): charged  pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) Improvement: 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

13. Spin dependent fragmentation functions at BELLE13 DIS2006, April 20 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. Spin dependent fragmentation functions at BELLE14 DIS2006, April 20 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 errors rescaled by 14% Beam polarization studies  consistent with zero

15. Spin dependent fragmentation functions at BELLE15 DIS2006, April 20 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 Submitted to PRL Preliminary

16. Spin dependent fragmentation functions at BELLE16 DIS2006, April 20 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

17. Spin dependent fragmentation functions at BELLE17 DIS2006, April 20 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 [Phys.Rev.D67:094003,2003] and Artru, Collins [Z.Phys.C69:277-286,1996 ] Interference Fragmentation – thrust method  2   1

18. Spin dependent fragmentation functions at BELLE18 DIS2006, April 20 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 as UL/L double ratios Data can be used for more sophisticated analysis Paper with UL/L double ratios (hep-ex/0507063) is submitted Leading order fits ongoing On resonance  10 x statistics  detailed final analysis 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:

19. Spin dependent fragmentation functions at BELLE19 DIS2006, April 20 th

20. Spin dependent fragmentation functions at BELLE20 DIS2006, April 20 th Small double ratios in low thrust data sample Low thrust contains radiative effects Collins effect vanishes  Strong experimental indication that double ratio method works A0A0 A 12

21. Spin dependent fragmentation functions at BELLE21 DIS2006, April 20 th Typical hadronic events at Belle

22. Spin dependent fragmentation functions at BELLE22 DIS2006, April 20 th Good detector performance (acceptance, momentum resolution, pid) Jet production from light quarks  off-resonance (60 MeV below resonance) (~10% of all data) Intermediate Energy  Sufficiently high scale (Q 2 ~ 110 GeV 2 ) - can apply pQCD  Not too high energy (Q 2 << M Z 2 ) -avoids additional complication from Z interference Sensitivity = A 2 sqrt(N) ~ x19 (60) compared to LEP A Belle / A LEP ~ x2 (A scales as ln Q 2 ) L Belle / L LEP ~ x23 (230) Belle is well suited for FF measurements:

23. Spin dependent fragmentation functions at BELLE23 DIS2006, April 20 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:

24. Spin dependent fragmentation functions at BELLE24 DIS2006, April 20 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

25. Spin dependent fragmentation functions at BELLE25 DIS2006, April 20 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

26. Spin dependent fragmentation functions at BELLE26 DIS2006, April 20 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

27. Spin dependent fragmentation functions at BELLE27 DIS2006, April 20 th Systematics: charm contribution? Weak (parity violating) decays could also create asymmetries (seen in    overall  dilution 5%) Especially low dilution in combined z-bins with large pion asymmetry Double ratios from charm MC compatible to zero  Charm decays cannot explain large double ratios seen in the data  Charm enhanced D * Data sample used to calculate and correct the charm contribution to the double ratios (see hep-ex/0507063 for details) Charm fraction N(charm)/N(all)

28. Spin dependent fragmentation functions at BELLE28 DIS2006, April 20 th Take simple parameterization to test sensitivity on favored to disfavored Ratio Favored/Disfavored contribution  Sensitivity c b

29. Spin dependent fragmentation functions at BELLE29 DIS2006, April 20 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

30. Spin dependent fragmentation functions at BELLE30 DIS2006, April 20 th Different model predictions for IFF Jaffe at 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

31. Spin dependent fragmentation functions at BELLE31 DIS2006, April 20 th PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96 Different model predictions for IFF 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)

32. Spin dependent fragmentation functions at BELLE32 DIS2006, April 20 th What would we see? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m1  m2  “ Jaffe ”“ Radici ”

33. Spin dependent fragmentation functions at BELLE33 DIS2006, April 20 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