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Unpolarized and Polarized Fragmentation Functions at Belle

This paper presents the latest developments in the study of unpolarized and polarized fragmentation functions at the Belle experiment. The authors discuss the measurement techniques, data analysis, and comparison to theoretical predictions.

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Unpolarized and Polarized Fragmentation Functions at Belle

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  1. Unpolarized and polarized fragmentation functionsＢｅｌｌｅの破砕関数 核子構造研究の新展開 2011, 1月7日 Ralf Seidl (RIKEN) Anselm Vossen (University of Indiana) Matthias Grosse Perdekamp (University of Illinois) Martin Leitgab (University of Illinois) Akio Ogawa (BNL/RBRC) Kobayashi Noriaki (Titech) Shibata Toshiaki (Titech) Miyachi Yoshiyuki (Yamagata)€

  2. KEKB: L>2.1x1034cm-2s-1 !! Belle detector KEKB Main research at Belle: CP violation and determination of Cabbibo Kobayashi Masukawa (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 Unpolarized and polarized fragmentation functions

  3. 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 Unpolarized and polarized fragmentation functions

  4. 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 Unpolarized and polarized fragmentation functions

  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 Unpolarized and polarized fragmentation functions

  6. 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 Unpolarized and polarized fragmentation functions

  7. Final Collins results First direct measurement of the Collins effect: (PRL96: 232002) Nonzero asymmetries Belle 547 fb-1 data set (PRD78:032011) Unpolarized and polarized fragmentation functions

  8. 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 Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.1 91:98-107,2009 Unpolarized and polarized fragmentation functions

  9. 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 • Stay in the mass region around r-mass • 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 easy  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)] Unpolarized and polarized fragmentation functions

  10. Asymmetry extraction Amplitude a12 directly measures ( IFF ) x ( -IFF ) (no double ratios) • Build normalized yields: • Fit with: or Unpolarized and polarized fragmentation functions 10

  11. Results including systematic errors Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary 8x8 m1 m2 binning Unpolarized and polarized fragmentation functions 11

  12. Results for 9x9 z1 z2 binning Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Unpolarized and polarized fragmentation functions

  13. Comparison to theory predictions Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm ) Z dependence : Rising behavior steeper However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well Unpolarized and polarized fragmentation functions

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

  15. 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 R.Seidl: fragmentation functions from Belle

  16. 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 Unpolarized and polarized fragmentation functions

  17. 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 Unpolarized and polarized fragmentation functions

  18. Systematic studies: Particle identification = • Particle identification: create PID efficiency matrix for K,p,p,e,m • PID responses from MC not reliable, use well identified decays from data: • Use D*pslowD0pslowpfastK for K,p identification • Use L pp for p,p identification • J/y m+m-, e+ e- for leptons (if needed also U(1S))  Unfolding Unpolarized and polarized fragmentation functions

  19. Martin Leitgab’s Spin 2010 talk Unpolarized and polarized fragmentation functions

  20. D* Extraction final extraction: large acceptance region covered CosqLab K- • Status of FF analysis: • PID study finished • Smearing correction finished • Acceptance correction + nonQCD contribution removal ongoing • Plan: have results soon PLab K+ Unpolarized and polarized fragmentation functions

  21. 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 Unpolarized and polarized fragmentation functions

  22. 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: Unpolarized and polarized fragmentation functions • Difficulty: contribution from one quark fragmentation qhhX measure all three: • (hh)jet1 X • (h) jet1(h) jet2X • hhX, ( ) requires thrust cut

  23. 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 Unpolarized and polarized fragmentation functions

  24. Sample MC (udsc) distributions - pp • opposite hemispheres • Yields very similar • Naturally dominating at higher z Unpolarized and polarized fragmentation functions

  25. 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 Unpolarized and polarized fragmentation functions

  26. Sample MC (udsc): p+p+/p+p-ratio • Yield ratios will be almost directly sensitive to disfavored/favored FF ratio • Acceptance effects cancel Ｂｅｌｌｅハドロンの今後

  27. 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 Unpolarized and polarized fragmentation functions

  28. 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: Unpolarized and polarized fragmentation functions

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

  30. 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 • Significant, nonzero Collins asymmetries, long paper published • 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 Unpolarized and polarized fragmentation functions

  31. Belle Fragmentation activity Black: about to start Green: ongoing Grey: finished

  32. Backup Slides Unpolarized and polarized fragmentation functions

  33. 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 Unpolarized and polarized fragmentation functions

  34. 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 Unpolarized and polarized fragmentation functions

  35. 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 Unpolarized and polarized fragmentation functions

  36. 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) Unpolarized and polarized fragmentation functions

  37. Subprocess contributions (MC) Data not corrected for Charm contributions 8x8 m1 m2 binning charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at highest masses) uds (main contribution) Charm Asymmetries in simulated data consistent with zero! To be checked with charm enhanced sample Unpolarized and polarized fragmentation functions 37

  38. 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 38 Unpolarized and polarized fragmentation functions

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

  40. 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 Unpolarized and polarized fragmentation functions 40

  41. Model predictions for e+e- Invariant mass1 dependence for increasing z1 z1 dependence for increasing z2 Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009. Unpolarized and polarized fragmentation functions 41

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