1. Measurements of fragmentation functions at Belle: results and prospects 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) for the Belle Collaboration (see hep-ex/0607014 and Phys.Rev. Lett.96:232002,2006 for Collins results) Outline: The KEKB rings and the Belle Experiment Transverse Spin Physics Motivations Collins analysis and parameterizations Interference Fragmentation functions Unpolarized fragmentation functions

2. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 2 BNL, July 21 th KEKB: L>1.6x10 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 >60fb -1 => off-resonance Belle detector KEKB

3. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 3 BNL, July 21 th Good tracking and particle identification!

4. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 4 BNL, July 21 th SIDIS experiments (HERMES and COMPASS, EIC) 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. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 5 BNL, July 21 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:

6. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 6 BNL, July 21 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)]

7. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 7 BNL, July 21 th Applied cuts, binning Off-resonance data –60 MeV below  (4S) 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 z1z1 z2z2

8. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 8 BNL, July 21 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 (         )

9. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 9 BNL, July 21 th Other Favored/Unfavored Combinations  charged pions or   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) 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

10. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 10 BNL, July 21 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

11. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 11 BNL, July 21 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

12. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 12 BNL, July 21 th Fits to the HERMES data by the Torino Group A. Prokudin fitted the HERMES (Sivers and) Collins Data Either Soffer bound for transversity: 2  q(x) = | q +  q | Or  q(x) =  q(x) GRV1998 for unpolarized PDFs Kretzer FF Gaussian k T Assumption HERMES 02-04 Data COMPASS 02 Data

13. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 13 BNL, July 21 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?

14. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 14 BNL, July 21 th What about the data under the resonance? More than 540 fb -1 of on_resonance data  (4S) is just small resonance More than 75% of hadronic cross section from open quark-antiquark production

15. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 15 BNL, July 21 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

16. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 16 BNL, July 21 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

17. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 17 BNL, July 21 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

18. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 18 BNL, July 21 th Unpolarized FFs MC simulation, ~1.4 fb -1 2. Performed Systematic studies: –Smearing –Tracking efficiency –Acceptance –Energy scale Particle ID study not yet finished AKK: Try flavor tagged/enhanced analysis?

19. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 19 BNL, July 21 th Summary and outlook Collins analysis: –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 is published Important input for Transversity measurements now and in the future Leading order fits ongoing On resonance  >10 x statistics  long paper on Collins results Interference fragmentation function analysis started Unpolarized FF analysis almost complete but lacks manpower Many more QCD/Spin related studies possible (VM Collins, timelike DVCS,  Polarimetry, k T -dependent FFs, “ Sivers ” FF, Event Shapes ) Results: Prospects:

20. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 20 BNL, July 21 th

21. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 21 BNL, July 21 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 …

22. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 22 BNL, July 21 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

23. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 23 BNL, July 21 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:

24. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 24 BNL, July 21 th Typical hadronic events at Belle

25. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 25 BNL, July 21 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     )

26. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 26 BNL, July 21 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

27. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 27 BNL, July 21 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

28. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 28 BNL, July 21 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

29. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 29 BNL, July 21 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:

30. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 30 BNL, July 21 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. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 31 BNL, July 21 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. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 32 BNL, July 21 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. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 33 BNL, July 21 th Take simple parameterization to test sensitivity on favored to disfavored Ratio Favored/Disfavored contribution  Sensitivity c b

34. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 34 BNL, July 21 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

35. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 35 BNL, July 21 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 ”

36. R.Seidl: Measurements of fragmentation functions at Belle: results and prospects 36 BNL, July 21 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 …