1. 8 th Circum Pan Pacific Symposium on High Energy Spin Physics Cairns, June 21, 2011 Ralf Seidl (RIKEN) for the Belle Collaboration

2. Transverse quark polarization Pac Spin, June 21, 2011 polarized fragmentation functions from Belle2  q(x),  G(x) Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton (known from fixed target (SI)DIS experiments) q(x),G(x)  q(x) Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton (first results from HERMES and COMPASS – with the help of Belle) Unpolarized distribution function q(x) Helicity distribution function  q(x) Transversity distribution function  q(x) Sum of quarks with parallel and antiparallel polarization relative to proton spin (well known from Collider DIS experiments)

3. Transversity properties Pac Spin, June 21, 2011 polarized fragmentation functions from Belle3 Helicity flip amplitude Chiral odd Since all interactions conserve chirality one needs another chiral odd object Does not couple to gluons  different QCD evolution than  q(x) Valence dominated  Comparable to Lattice calculations, especially tensor charge Positivity bound: Soffer bound:

4. How to access Transversity: another chiral-odd function Drell Yan: Combine two Transversity distributions with each other SIDIS/pp: Combine Transversity distributions with chiral- odd fragmentation function (FF) Total process is chiral-even: OK Possible Partners: Collins FF Interference FF Transverse L FF Most require single spin asymmetries in the fragmentation Pac Spin, June 21, 2011 polarized fragmentation functions from Belle4

5. Towards a global transversity analysis: Chiral –odd Fragmentation functions Pac Spin, June 21, 2011 polarized fragmentation functions from Belle5 RHIC and SIDIS experiments measure: Transversity  q(x) X Collins Fragmentation function or Interference Fragmentation function (IFF) 2 Unknown Functions measured together Universality understood Evolution ? Belle measures: Collins X Collins - finished for charged pion pairs or IFF X IFF – charged pions about to be published Transversity

6. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle6 KEKB: L>2.1x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e - + 3.5GeV e + √s = 10.58GeV (  (4S)) e + e -   (4S)  B  B Continuum production: 10.52 GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: >1000 fb -1 >70fb -1 => continuum Belle detector KEKB Main research at Belle: CP violation and determination of Cabibbo Kobayashi Maskawa (CKM) matrix

7.  / 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 counter SC solenoid 1.5T 8 GeV e  3.5 GeV e  Belle Detector Good tracking and particle identification!  (K)~85%,  (   K)<10% Pac Spin, June 21, 2011 polarized fragmentation functions from Belle7

8. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle8 Fragmentation functions in e + e - annihilation Process: e + e -  hX At leading order sum of unpolarized fragmentation functions from quark and anti- quark side e-e- e+e+ h

9. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle9 Collins fragmentation in e + e - : Angles and Cross section cos(  1 +  2 ) 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)]

10. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle10 Final Collins results First direct measurement of the Collins effect: (PRL96: 232002) Red points : cos(  1 +  2 ) moment of Unlike sign pion pairs over like sign pion pair ratio : A UL Green points : cos(  1 +  2 ) moment of Unlike sign pion pairs over any charged pion pair ratio : A UC Nonzero asymmetries seen Factor 19 increase in statistics in second, long paper: 547 fb -1 data set (PRD78:032011)

11. Transverse single spin asymmetries in SIDIS Measure azimuthal asymmetries for (at least) two angular modulations simultaneously Pac Spin, June 21, 2011 polarized fragmentation functions from Belle11 U: unpolarized beam T: transversely polarized target

12. Collins amplitudes I Pac Spin, June 21, 2011 polarized fragmentation functions from Belle12 Large, nonzero asymmetries seen Transversity and Collins effect nonzero Large  - asymmetries require disfavored Collins function of opposite sign and HERMES, PRL. 94 (2005) 012002 M. Diefenthaler @ DIS07, hep-ex 0707.0222

13. COMPASS, hep-ex/0802.2160 deuteron Collins amplitudes II Compatible with zero due to cancellation Pac Spin, June 21, 2011 polarized fragmentation functions from Belle13 Asymmetries nonzero, consistent with HERMES

14. SIDIS: Most recent Collins moments Not completely used in fit, yet Pac Spin, June 21, 2011 polarized fragmentation functions from Belle14 final HERMES data-set h−h− h+h+ h+h+ h−h− Proton Deuteron Compass

15. First global analysis from Collins Hermes, Compass d and Belle data First results available, still open questions from evolution of Collins FF and transverse momentum dependence More data available now Cross check using interference fragmentation functions needed Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 15 Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.1 91:98-107,2009

16. Interference Fragmentation – thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Look in the mass region around  - mass (largest interference expected) 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 known  directly applicable to semi-inclusive DIS and pp) Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 16 polarized fragmentation functions from Belle  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)] Pac Spin, June 21, 2011

17. Asymmetry extraction Build normalized yields: Fit with: or 17 Amplitude a 12 directly measures ( IFF ) x ( -IFF ) (no double ratios) Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

18. Zero tests: Mixed Events False Asymmetries consistent with zero (Red/blue points: Thrust axis last or current event) Pac Spin, June 21, 2011 18polarized fragmentation functions from Belle

19. Inject asymmetries in Monte Carlo Reconstruction smears thrust axis, ~94% of input asymmetry is reconstructed (Integrated over thrust axis: 98%) Effect is understood, can be reproduced in Toy MC Asymmetries corrected Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed Weighted MC asymmetries Pac Spin, June 21, 2011 19polarized fragmentation functions from Belle

20. 20 Systematic Errors Dominant: MC asymmetry + its statistical error (up to % level) Smaller contributions: PID: per mille level higher moments: sub per mille level Uncertainty on axis smearing correction mixed asymmetries: per mille level Tau asymmetries Note: asymmetries contain events from u,d,s and c events arXiv:1104.2425 Submitted to PRL Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

21. 21 Results incl. sys. errors: (z 1 x z 2 ) Binning Magnitude increasing with z Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

22. m 1 x m 2 binning Magnitude increasing with mass, then leveling off Pac Spin, June 21, 2011 22polarized fragmentation functions from Belle

23. (z 1 x m 1 ) Binning 23 2 d distributions of one hemisphere Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

24. (m 1 x z 1 ) Binning Pac Spin, June 21, 2011 24polarized fragmentation functions from Belle

25. First transversity extraction from HERMES and Belle IFF data Pac Spin, June 21, 2011 polarized fragmentation functions from Belle25 Early studies indicate little effect of evolution in Collins function, both results comparable Prelimnary data by Compass and PHENIX not used Alessandro Bacchetta at RHIC DY workshop May 2011: Bacchetta, Radici, Courtoy, arXiv:1104.3855

26. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle26 Unpolarized Fragmentation functions Process: e + e -  hX At leading order sum of unpolarized fragmentation functions from quark and anti- quark side e-e- e+e+ h

27. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle27 World data and motivation for precise FFs Most data obtained at LEP energies, At lower CMS energies very little data available 3-jet fragmentation to access gluon FF theoretically difficult  Gluon fragmentation from evolution not yet well constrained  Higher z FFs (>0.7) hardly available

28. Current knowledge on fragmentation functions – DSS, HKNS,AKK Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 28 DeFlorian, Sassot, Stratmann, Phys.Rev.D75:114010,2007. Differences between different global fits still large for high-z gluon contributions, kaons and disfavored fragmentation Hirai, Kumano, Nagai, Sudoh, Phys.Rev.D75: 094009,2007

29. Systematic studies: Particle identification Particle identification: create PID efficiency matrix for K, ,p,e,  PID responses from MC not reliable, use well identified decays from data: Use D *   slow D 0   slow  fast K for K,  identification Use    p for p,  identification J/    +  -, e + e - for leptons (if needed also  (1S))  Unfolding 29 polarized fragmentation functions from Belle REAL Particles Reconstructed particles  Kp  e  K p  e = Pac Spin, June 21, 2011

30. polarized fragmentation functions from Belle30 Martin Leitgab’s Spin 2010 talk

31. D* Extraction final extraction: large acceptance region covered K+K+ K-K- P Lab Cos  Lab Pac Spin, June 21, 2011 31polarized fragmentation functions from Belle Status of FF analysis: PID study finished Smearing correction finished Acceptance correction + nonQCD contribution removal ongoing Plan: have results soon

32. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle32 Event Structure for hadron pairs in e + e - annihilation = 6.4 e + e - CMS frame: e-e- e+e+  Spin averaged cross section: Jet axis: Thrust

33. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle33 Unpolarized 2-hadron fragmentation Detect two hadrons simultaneously: e + e -  hhX If two hadrons in opposite hemispheres one obtains sensitivity to favored/ disfavored fragmentation: Difficulty: contribution from one quark fragmentation q  hhX  measure all three: (hh) jet1 X (h) jet1 (h) jet2 X hhX, ( ) requires thrust cut Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) any charge hadron pairs (C): (favored + unfavored) x (favored + unfavored) Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.

34. Sample MC (udsc) distributions -  45 fb -1 sampled (~50% of off resonance data) PID corrected using Martin’s Matrices Smearing not yet corrected (but small) Acceptance not yet corrected  Statistic reasonable out to high z Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 34

35. Sample MC (udsc):         ratio Yield ratios will be almost directly sensitive to disfavored/favored FF ratio Acceptance effects cancel Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 35

36. Summary and outlook First direct measurement of the interference fragmentation function Large asymmetries seen, rising with z and invariant mass No sign change at  mass No double ratios make interpretation simple Submitted to PRL Significant, nonzero Collins asymmetries, Data used already in Global analysis Measure precise unpolarized fragmentation functions of many final states  Important input for general QCD physics and helicity structure measurements Analysis progressing: PID studies finished smearing correction finished Acceptance correction ongoing New di-hadron fragmentation function analysis started Information of favored/disfavored FF Vector meson FFs VM Collins analysis started Artru Model test Continue to measure precise spin dependent fragmentation functions at Belle kT dependence of Collins function,   , K Collins, pK, KK IFF Measure other interesting QCD- related quantities at Belle: Chiral-odd  -fragmentation function  single spin asymmetry Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 36

37. Belle Fragmentation activity RIKEN/RBRCIllinoisIndianaTitech Unpol FFs e + e -  hX: e + e -  (hh)X, (h)(h)X,hhX: Unpol k T dependence: Neutral hadrons: (     ) John Koster Charged di- hadrons: Ralf Seidl Charged hadrons ( ,K,P): Martin Leitgab Collins FFs e + e -  (h)(h)X: k T dependence:  0 : John Koster   : Ralf Seidl  : Ralf Seidl  0 : John Koster  K,KK: Francesca Giordano Francesca Giordano  ± : ? Interference FF: e + e -  (hh)(hh)X Charged  Ralf Seidl Charged  : Anselm Vossen  0 : Anselm Vossen Charged  K, KK: Nori-aki Kobayashi Local P :  (polFF,SSA) : Jet-jet asy: Anselm Vossen 37 Black: about to start Green: ongoing Grey: finished Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

38. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle38 Backup Slides

39. polarized fragmentation functions from Belle 39 Pac Spin, June 21, 2011 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: In Artru Model: favored (ie u    ) and disfavored (ie u    ) Collins function naturally of opposite sign

40. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle40 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]

41. Pac Spin, June 21, 2011 polarized fragmentation functions from Belle41 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

42. 42 Subprocess contributions (MC) 8x8 m 1 m 2 binning tau contribution (only significant at high z) charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution) Pac Spin, June 21, 2011 polarized fragmentation functions from Belle

43. Subprocess contributions (MC) tau contribution (only significant at high z) charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution) Pac Spin, June 21, 2011 43polarized fragmentation functions from Belle 9x9 z 1 z 2 binning

44. Zero tests: MC A small asymmetry seen due to acceptance effect Mostly appearing at boundary of acceptance Opening cut in CMS of 0.8 (~37 degrees) reduces acceptance effect to the sub-per-mille level 44 PhPh No opening cut Opening cut>0.7 Opening cut >0.8 Pac Spin, June 21, 2011 44polarized fragmentation functions from Belle

45. Heavy flavor fragmentation Rolf Seuster: Phys.Rev.D73:032002,2006, 103 fb -1 Charmed hadron fragmentation much harder than light hadron fragmentation heavy quark more likely to stay in heavy hadron Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 45

46. Sample MC (udsc) distributions -  opposite hemispheres Yields very similar  Naturally dominating at higher z Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 46

47. Sample MC (udsc) distributions -  same hemisphere: Distributions falling off rapidly Naturally as z 1 +z 2 <1 For same hemisphere also interesting: z Pair,m Pair distribution Corresponding resonances’ FF ( , K *,  ) Also unpol Baseline for IFF Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 47

48. Higher statistics available at high z B decays almost at rest  no hadrons above 0.5 Instead of about 90 pb -1 almost 1000 fb -1 available Useful at high z, where statistics is low Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 48

49. Measure Collins effect for e + e -   ±    X According to Artru model sign change expected wrt. pion Collins: sgn a 12 (  ±   ) = - sgn a 12 (  ±  ± ) Instead of double ratios to eliminate acceptance/radiative effects use combinatoric BG Rho Collins – similar plans for  ,  Normally: Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 49

50. MC (uds) Rho Collins example Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 50 Acceptance effect visible in all three mass ranges Magnitude similar, but need more statistics to confirm method