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 Rencentres de Moriond March 19 th, La Thuile (see hep-ex/0507063 for details, submitted to PRL)

2. Spin dependent fragmentation functions at BELLE2 Moriond, March 19 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:

3. Spin dependent fragmentation functions at BELLE3 Moriond, March 19 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 Moriond, March 19 th SIDIS experiments (HERMES and COMPASS) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function Motivation: 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 proven in LO by Collins and Metz: [PRL93:( 2004)252001 ]

5. Spin dependent fragmentation functions at BELLE5 Moriond, March 19 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)]

6. Spin dependent fragmentation functions at BELLE6 Moriond, March 19 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]

7. Spin dependent fragmentation functions at BELLE7 Moriond, March 19 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 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 = Diagonal bins

8. Spin dependent fragmentation functions at BELLE8 Moriond, March 19 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 (even though double ratios will contain them) Cosine modulations clearly visible 22     )

9. Spin dependent fragmentation functions at BELLE9 Moriond, March 19 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

10. Spin dependent fragmentation functions at BELLE10 Moriond, March 19 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 (  pairs ) charm MC  pairs  Data (         )

11. Spin dependent fragmentation functions at BELLE11 Moriond, March 19 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±0.65±0.55)% –cos(2     ) method (4.26±0.78±0.68)% z1z1 z2z2 Systematic error A0A0 A 12

12. Spin dependent fragmentation functions at BELLE12 Moriond, March 19 th Systematic errors Contributions to systematic errors Double ratio method Higher moments Charge sign ratio MC double ratio Other uncertainties: smearing (reweighted MC) PID (variation of PID cuts) charm contribution (corrected by D * data sample)  content (evaluated in e + e -      enhanced sample)

13. Spin dependent fragmentation functions at BELLE13 Moriond, March 19 th Take unpolarized parameterizations (Kretzer at Q 2 =2.5GeV 2 ) Assume (PDF-like behavior) Assume Little sensitivity to to favored/disfavored Collins ratio An experimentalist’s interpretation: fitting parameterizations of the Collins function(s)

14. Spin dependent fragmentation functions at BELLE14 Moriond, March 19 th Other Favored/Unfavored Combinations    Unlike-sign pion pairs: (favored x favored +unfavored x unfavored) Like-sign pion pairs: (favored x unfavored +unfavored x favored)  ±   pairs (favored + unfavored) x (favored + unfavored) P.Schweitzer([hep-ph/0603054]): charged  pairs are similar (and are easier to handle): (favored + unfavored) x (favored + unfavored) Problem: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.

15. Spin dependent fragmentation functions at BELLE15 Moriond, March 19 th Why is it possible to include on_resonance data? Different Thrust distributions e + e -  q  q (q in uds) MC  (4S)  B + B - MC  (4S)  B 0  B 0 MC

16. Spin dependent fragmentation functions at BELLE16 Moriond, March 19 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 Interference Fragmentation – thrust method  2   1

17. Spin dependent fragmentation functions at BELLE17 Moriond, March 19 th Summary and outlook Double ratios: double ratios from data most systematic errors cancel Analysis procedure passes all null tests Main systematic uncertainties understood  Significant nonzero asymmetry with double ratios are observed Naive LO analysis shows significant Collins effect Data can be used for more sophisticated analysis Paper (hep-ex/0507063) is submitted On resonance  10 x statistics Include   and all charged  pairs into analysis:  Better distinction between favored and disfavored Collins function Interference fragmentation function analysis started Include Vector Mesons into analysis:  Possibility to test string fragmentation models used to describe Collins effect Summary: Outlook:

18. Spin dependent fragmentation functions at BELLE18 Moriond, March 19 th

19. Spin dependent fragmentation functions at BELLE19 Moriond, March 19 th Outline Motivation –Study transverse spin effects in fragmentation –Global transversity analysis –Feasibility  LEP analysis [hep-ph/9901216] The BELLE detector Collins analysis –Angular definitions and cross sections –Double Ratios to eliminate radiative/momentum correlation effects –An experimentalist’s interpretation Summary

20. Spin dependent fragmentation functions at BELLE20 Moriond, March 19 th

21. Spin dependent fragmentation functions at BELLE21 Moriond, March 19 th Typical hadronic events at Belle

22. Spin dependent fragmentation functions at BELLE22 Moriond, March 19 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 Moriond, March 19 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 Moriond, March 19 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 Moriond, March 19 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 Moriond, March 19 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 Moriond, March 19 th Preliminary Systematic errors Double Ratio vs Subtraction Method: R – S < 0.002  The difference was assigned as a systematic error.

28. Spin dependent fragmentation functions at BELLE28 Moriond, March 19 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 Preliminary

29. Spin dependent fragmentation functions at BELLE29 Moriond, March 19 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)

30. Spin dependent fragmentation functions at BELLE30 Moriond, March 19 th Take simple parameterization to test sensitivity on favored to disfavored Ratio Favored/Disfavored contribution  Sensitivity c b

31. Spin dependent fragmentation functions at BELLE31 Moriond, March 19 th Different charge combinations  additional information Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side: Like sign pairs contain one favored and one unfavored fragmentation function each: Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.

32. Spin dependent fragmentation functions at BELLE32 Moriond, March 19 th Example: Left-Right Asymmetry in Pion Rates sqsq π q q π sqsq = 0 ! AT =AT = N L - N R N L + N R Collins Effect N L : pions to the left N R : pions to the right

33. Spin dependent fragmentation functions at BELLE33 Moriond, March 19 th General Fragmentation Functions Number density for finding a spin-less hadron h from a transversely polarized quark, q: unpolarized FF Collins FF

34. Spin dependent fragmentation functions at BELLE34 Moriond, March 19 th Raw asymmetries vs transverse photon momentum Q T      Already MC contains large asymmetries Strong dependence against transverse photon Momentum Q T Expected to be due to radiative effects Difference of DATA and MC is signal  not so easy to determine DATA (  ) fiducial cut DATA (KK) fiducial cut UDS-MC fiducial cut CHARM-MC fiducial cut Unlike sign pairs Like sign pairs