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 Workshop on Hadron Structure and Spectroscopy August 1 st – August 3 rd, Prague

2. Measurements of chiral-odd fragmentation functions at Belle2 August 1st Outline oMotivation  Global transversity analysis  LEP  Re-analysis of Delphi data by Efremov, Smirnova and Tkatchev [hep-ph/9901216] oThe BELLE detector oCollins analysis  Angular definitions and cross sections  Double Ratios to eliminate radiative/momentum correlation effects  An experimentalist’s interpretation oSummary

3. Measurements of chiral-odd fragmentation functions at Belle3 August 1st Motivation: Global Transversity Analysis Transversity Tensor Charge BLT sum rule and Lattice QCD Factorization and Universality?Collins ? / IFF ok! RBRC workshop September 2000

4. Measurements of chiral-odd fragmentation functions at Belle4 August 1st KEKB –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: >400 fb -1 >30fb -1 => off-resonance Belle detector KEKB KEKB: L>1.5x10 34 cm -2 s -1 !!

5. Measurements of chiral-odd fragmentation functions at Belle5 August 1st

6. Measurements of chiral-odd fragmentation functions at Belle6 August 1st Good tracking and particle identification!

7. Measurements of chiral-odd fragmentation functions at Belle7 August 1st Typical hadronic events at Belle ~ 1 ~ 0.5

8. Measurements of chiral-odd fragmentation functions at Belle8 August 1st 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 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:

9. Measurements of chiral-odd fragmentation functions at Belle9 August 1st 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:

10. Measurements of chiral-odd fragmentation functions at Belle10 August 1st Collins fragmentation: 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+

11. Measurements of chiral-odd fragmentation functions at Belle11 August 1st Collins fragmentation: 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]

12. Measurements of chiral-odd fragmentation functions at Belle12 August 1st Applied cuts, binning Off-resonance data (in the future also resonance) 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 Light quark selection Hemisphere cut <0 Opening angle cuts: - cos(2   ) method:  - cos(     ) method:      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 z-binning: 0.2 0.3 0.5 0.7 1.0

13. Measurements of chiral-odd fragmentation functions at Belle13 August 1st 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

14. Measurements of chiral-odd fragmentation functions at Belle14 August 1st Q T vs z 1 and z 2

15. Measurements of chiral-odd fragmentation functions at Belle15 August 1st Examples of fitting the azimuthal asymmetries Cosine modulations clearly visible No change in cosine moments when including higher harmonics (even though double ratios will contain them) D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0

16. Measurements of chiral-odd fragmentation functions at Belle16 August 1st 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

17. Measurements of chiral-odd fragmentation functions at Belle17 August 1st Data vs MC for raw asymmetries data: pions data: kaons MC: uds MC: charm Unlike sign pairslike sign pairs

18. Measurements of chiral-odd fragmentation functions at Belle18 August 1st 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

19. Measurements of chiral-odd fragmentation functions at Belle19 August 1st 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  ) 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

20. Measurements of chiral-odd fragmentation functions at Belle20 August 1st Systematic errors Double Ratio vs Subtraction Method: R – S < 0.002  The difference was assigned as a systematic error.

21. Measurements of chiral-odd fragmentation functions at Belle21 August 1st Double ratio Tests Asymmetries do cancel out for MC Double ratios of         compatible to 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 (         )

22. Measurements of chiral-odd fragmentation functions at Belle22 August 1st Results for  -pairs for 30fb -1 Significant non- zero asymmetries Rising behaviour vs. z cos      double ratios only marginally larger First direct measurement of the Collins function z1z1 z2z2

23. Measurements of chiral-odd fragmentation functions at Belle23 August 1st Systematic errors Double ratio method Higher moments Charge sign ratio MC double ratio Other errors: smearing, pid, charm content

24. Measurements of chiral-odd fragmentation functions at Belle24 August 1st Systematics from 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  Systematic errors from charm are preliminary Charm fraction N(charm)/N(all)

25. Measurements of chiral-odd fragmentation functions at Belle25 August 1st Take unpolarized parameterizations (Kretzer at Q 2 =2.5GeV 2 ) Assume (PDF-like behaviour) Assume Sensitivity studies in progress An experimentalist’s interpretation: fitting parameterizations of the Collins function(s)

26. Measurements of chiral-odd fragmentation functions at Belle26 August 1st Summary and outlook Double ratios: –double ratios from data –most systematic errors cancel Analysis procedure passes zero tests Main systematic uncertainties understood Significant nonzero double ratios  Naïve LO analysis shows significant Collins effect Finalize analysis On resonance  10 x statistics Include    into analysis:  Better distinction between favored and disfavored Collins function Include VMs into analysis:  Possibility to test string fragmentation models used to describe Collins effect Expansion of analysis to Interference fragmentation function straightforward Summary:Outlook:

27. Measurements of chiral-odd fragmentation functions at Belle27 August 1st 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.