Polarized fragmentation functions from ｅ + e -

1. Polarized fragmentation functions from ｅ+e- INT Workshop on orbital angular momentum, Seattle, February 10 Ralf Seidl (RIKEN)

2. Transverse quark polarization q(x),G(x) Unpolarized distribution function q(x) Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton (known from fixed target (SI)DIS experiments) Dq(x), DG(x) Helicity distribution function Dq(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) dq(x) Transversity distribution function dq(x) polarized fragmentation functions from Belle Sum of quarks with parallel and antiparallel polarization relative to proton spin (well known from Collider DIS experiments)

3. Helicity flip amplitude Chiral odd Since all interactions conserve chirality one needs another chiral odd object Does not couple to gluons adifferent QCD evolution than Dq(x) Valence dominateda Comparable to Lattice calculations, especially tensor charge No sumrule, but somehow more intuitive quantity: PDFs evolve into OAM, not other contributions Transversity properties Positivity bound: Soffer bound: polarized fragmentation functions from Belle

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 polarized fragmentation functions from Belle

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

6. KEKB: L>2.1x1034cm-2s-1 !! Belle detector KEKB Main research at Belle: CP violation and determination of Cabibbo Kobayashi Maskawa (CKM) matrix • Asymmetric collider • 8GeV e- + 3.5GeV e+ • √s = 10.58GeV (U(4S)) • e+e-U(4S)BB • Continuum production: 10.52 GeV • e+e-qq (u,d,s,c) • Integrated Luminosity: >1000 fb-1 • >70fb-1 => continuum polarized fragmentation functions from Belle

7. Belle Detector Aerogel Cherenkov cnt. n=1.015~1.030 SC solenoid 1.5T 3.5 GeVe+ CsI(Tl) 16X0 TOF counter 8 GeVe- Central Drift Chamber small cell +He/C2H6 Good tracking and particle identification! e(K)~85%, e(pK)<10% m / KL detection 14/15 lyr. RPC+Fe Si vtx. det. 3/4 lyr. DSSD polarized fragmentation functions from Belle

8. polarized fragmentation functions from Belle

9. Fragmentation functions in e+e- annihilation e- h e+ • Process: e+ e-hX • At leading order sum of unpolarized fragmentation functions from quark and anti-quark side polarized fragmentation functions from Belle

10. Collins fragmentation in e+e-: Angles and Cross section cos(f1+f2) method e+e- CMS frame: j2-p e- Q j1 j2 j1 [D.Boer: PhD thesis(1998)] e+ 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins polarized fragmentation functions from Belle

11. Final Collins results First direct measurement of the Collins effect: (PRL96: 232002) Red points : cos(f1 + f2) moment of Unlike sign pion pairs over like sign pion pair ratio : AUL Green points : cos(f1 + f2) moment of Unlike sign pion pairs over any charged pion pair ratio : AUC Nonzero asymmetries seen Factor 19 increase in statistics in second, long paper: 547 fb-1 data set (PRD78:032011) polarized fragmentation functions from Belle

12. polarized fragmentation functions from Belle

13. The Collins effect in the Artru fragmentation model A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: 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. In Artru Model: favored (ie up+) and disfavored (ie up-) Collins function naturally of opposite sign polarized fragmentation functions from Belle

14. 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 Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.1 91:98-107,2009 polarized fragmentation functions from Belle

15. Interference Fragmentation– thrust method j2-p p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)] • e+e-(p+p-)jet1(p+p-)jet2X • Look in the mass region around r-mass (largest interference expected) • Find pion pairs in opposite hemispheres • Observe angles j1+j2between 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)] polarized fragmentation functions from Belle

16. Asymmetry extraction Amplitude a12 directly measures ( IFF ) x ( -IFF ) (no double ratios) • Build normalized yields: • Fit with: or polarized fragmentation functions from Belle 16

17. Zero tests: Mixed Events False Asymmetries consistent with zero polarized fragmentation functions from Belle (Red/blue points: Thrust axis last or current event)

18. Weighted MC asymmetries Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed 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 polarized fragmentation functions from Belle

19. 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 polarized fragmentation functions from Belle

20. Published results: (z1x z2) Binning PRL107:072004(2011) Magnitude increasing with z polarized fragmentation functions from Belle

21. m1x m2 binning Magnitude increasing with mass, then leveling off polarized fragmentation functions from Belle

22. (z1x m1) Binning 2 d distributions of one hemisphere polarized fragmentation functions from Belle

23. (m1x z1) Binning polarized fragmentation functions from Belle

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

25. Unpolarized Fragmentation functions e- h e+ • Process: e+ e-hX • At leading order sum of unpolarized fragmentation functions from quark and anti-quark side polarized fragmentation functions from Belle

26. Current knowledge on fragmentation functions – DSS, HKNS,AKK 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 polarized fragmentation functions from Belle

27. Martin Leitgab polarized fragmentation functions from Belle

28. Martin Leitgab polarized fragmentation functions from Belle

29. polarized fragmentation functions from Belle

30. Expected uncertinties Projected relative statistical and systematic uncertainties e+e- -> h+- X data In the future: include k_t dependence and measure di-hadron FFs needed for transversity extraction from di-hadron correlations • Measurement will give precision data set for low Q2andhigh z:

31. Event Structure for hadron pairs in e+e- annihilation e+e- CMS frame: e- <Nh+,-> = 6.4 Q e+ Spin averaged cross section: Jet axis: Thrust polarized fragmentation functions from Belle

32. Unpolarized 2-hadron fragmentation 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p+,dp-,cc. Unfavored = dp+,up-,cc. Detect two hadrons simultaneously: e+e-hhX If two hadrons in opposite hemispheres one obtains sensitivity to favored/ disfavored fragmentation: polarized fragmentation functions from Belle • Difficulty: contribution from one quark fragmentation qhhX measure all three: • (hh)jet1 X • (h) jet1(h) jet2X • hhX, ( ) requires thrust cut

33. Sample MC (udsc) distributions - pp • 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 polarized fragmentation functions from Belle

34. Sample MC (udsc): p+p+/p+p-ratio • Yield ratios will be almost directly sensitive to disfavored/favored FF ratio • Acceptance effects cancel polarized fragmentation functions from Belle

35. Summary and outlook • First direct measurement of the interference fragmentation function • Large asymmetries seen, rising with z and invariant mass • No sign change at r 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 spindependent fragmentation functions at Belle • kT dependence of Collins function, • p0 ,h, K Collins, • pK, KK IFF • Measure other interesting QCD-related quantities at Belle: • Chiral-odd L-fragmentation function • L single spin asymmetry polarized fragmentation functions from Belle

36. Belle Fragmentation activity Black: about to start Green:ongoing Grey: finished polarized fragmentation functions from Belle

37. Backup Slides polarized fragmentation functions from Belle

38. 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 polarized fragmentation functions from Belle

39. Collins fragmentation in e+e- : Angles and Cross section cos(2f0) method e+e- CMS frame: • Independent of thrust-axis • Convolution integralI over transverse momenta involved e- Q2 j0 [Boer,Jakob,Mulders: NPB504(1997)345] e+ 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins polarized fragmentation functions from Belle

40. Similar to previous method Observe angles j1R+j2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation – “f0“ method jR2 p-jR1 polarized fragmentation functions from Belle

41. Subprocess contributions (MC) 8x8 m1 m2 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) polarized fragmentation functions from Belle

42. Subprocess contributions (MC) 9x9 z1 z2 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) polarized fragmentation functions from Belle

43. Zero tests: MC No opening cut Opening cut>0.7 Opening cut >0.8 Ph 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 43 polarized fragmentation functions from Belle

44. 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 polarized fragmentation functions from Belle

45. Sample MC (udsc) distributions - pp • opposite hemispheres • Yields very similar • Naturally dominating at higher z polarized fragmentation functions from Belle

46. Sample MC (udsc) distributions - pp • same hemisphere: • Distributions falling off rapidly • Naturally as z1+z2<1 • For same hemisphere also interesting: • zPair ,mPair distribution • Corresponding resonances’ FF (r , K*, F) • Also unpol Baseline for IFF polarized fragmentation functions from Belle

47. 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 polarized fragmentation functions from Belle

48. Rho Collins – similar plans for p0,h • Measure Collins effect for e+e-p±r0X • According to Artru model sign change expected wrt. pion Collins: sgn a12(p±r0) = - sgn a12(p±p± ) • Instead of double ratios to eliminate acceptance/radiative effects use combinatoric BG • Normally: polarized fragmentation functions from Belle

49. MC (uds) Rho Collins example • Acceptance effect visible in all three mass ranges • Magnitude similar, but need more statistics to confirm method polarized fragmentation functions from Belle

50. Collins amplitudes I M. Diefenthaler @ DIS07, hep-ex 0707.0222 and HERMES, PRL. 94 (2005) 012002 Large, nonzero asymmetries seen Transversity and Collins effect nonzero Large p- asymmetries require disfavored Collins function of opposite sign polarized fragmentation functions from Belle