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Precision fragmentation function measurements at Belle

Precision fragmentation function measurements at Belle. Outline: The Collins function measurements Access to transversity over Collins fragmentation function Collins function measurements at Belle The Belle detector Improved statistics with on_resonance data

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Precision fragmentation function measurements at Belle

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  1. Precision fragmentation function measurements at Belle • Outline: • The Collins function measurements • Access to transversity over Collins fragmentation function • Collins function measurements at Belle • The Belle detector • Improved statistics with on_resonance data • Interference fragmentation function measurements • unpolarized fragmentation function measurements Trento, June 14 2007 M. Grosse Perdekamp (University of Illinois and RBRC) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC)

  2. Towards a global transversity analysis SIDIS experiments (HERMES and COMPASS, eRHIC) measure dq(x) together with either Collins Fragmentation function or Interference Fragmentation function There are always 2 unknown functions involved which cannot be measured independently RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x) Comlpex universality? Spin dependent Fragmentation function analysis in e+e- Annihilation yields information on the Collins and the Interference Fragmentation function ! R.Seidl: Fragmentation function measurements at Belle

  3. KEKB: L>1.6x1034cm-2s-1 !! Belle detector KEKB • Asymmetric collider • 8GeV e- + 3.5GeV e+ • Ös = 10.58GeV (U(4S)) • e+e-U(4S)BB • Off-resonance: 10.52 GeV • e+e-qq (u,d,s,c) • Integrated Luminosity: >700 fb-1 • >60fb-1 => off-resonance R.Seidl: Fragmentation function measurements at Belle

  4. Good tracking and particle identification! R.Seidl: Fragmentation function measurements at Belle

  5. Event Structure at Belle e+e- CMS frame: Near-side Hemisphere: hi , i=1,Nn with zi e- <Nh+,-> = 6.4 Q e+ Jet axis: Thrust Spin averaged cross section: Far-side: hj , j=1,Nf with zj R.Seidl: Fragmentation function measurements at Belle

  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 R.Seidl: Fragmentation function measurements at Belle

  7. 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 R.Seidl: Fragmentation function measurements at Belle

  8. Off-resonance data 60 MeV below U(4S) resonance 29.1 fb-1  Later also on-resonance data: 547 fb-1 Track selection: pT > 0.1GeV vertex cut:dr<2cm, |dz|<4cm Acceptance cut -0.6 < cosqi< 0.9 Event selection: Ntrack  3 Thrust > 0.8 Z1, Z2>0.2 Applied cuts, binning z2 z2 1.0 3 6 8 9 0.7 2 5 7 8 0.5 1 5 4 6 0.3 0 1 2 3 0.2 z1 0.2 0.3 0.5 0.7 1.0 = Diagonal bins • Hemisphere cut • QT < 3.5 GeV z1 R.Seidl: Fragmentation function measurements at Belle

  9. Examples of fits to azimuthal asymmetries Cosine modulations clearly visible N(f)/N0 2f0 (f1+f2) D1 : spin averaged fragmentation function, H1: Collins fragmentation function No change in cosine moments when including sine and higher harmonics R.Seidl: Fragmentation function measurements at Belle

  10. Methods to eliminate gluon contributions: Double ratios and subtractions Double ratio 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 Subtraction method: 2 methods give very small difference in the result R.Seidl: Fragmentation function measurements at Belle

  11. Testing the double ratios with MC • Asymmetries do cancel out for MC • Double ratios of p+p+/p-p- compatible with zero • Mixed event pion pairs also show zero result • Asymmetry reconstruction works well for t 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 (p+p+/p-p-) R.Seidl: Fragmentation function measurements at Belle

  12. Other Favored/Unfavored Combinations charged pions or p0 Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: • Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) • Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) • p±p0 pairs (favored + unfavored) x (favored + unfavored) • P.Schweitzer([hep-ph/0603054]): charged pp pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) UL UC • Build new double ratios: • Unlike-sign/ charged pp pairs (UC) Favored = up+,dp-,cc. Unfavored = dp+,up-,cc. R.Seidl: Fragmentation function measurements at Belle

  13. What about the data under the resonance? • More than 540 fb-1 of on_resonance data • U(4S) is just small resonance • More than 75% of hadronic cross section from open quark-antiquark production R.Seidl: Fragmentation function measurements at Belle

  14. Why is it possible to include on_resonance data?Different Thrust distributions e+e-qq̅, q∈uds e+e-cc̅ • e+ e- q q (u d s) MC • U(4S)B+B- MC • U(4S)B0B0 MC • Largest systematic errors reduce with • more statistics • Charm-tagged Data sample also • increases with statistics R.Seidl: Fragmentation function measurements at Belle

  15. Improved systematic errors (UC) • Tau contribution • PID error • MC double ratios • Charged ratios (p+p+ /p-p- ) • higher moments in Fit • difference double ratio-subtraction method A0 (cos(2f0)) moments A12 (cos(f1 +f2)) moments • reweighted MC-asymmetries: cos(f1+f2) asymmetries underestimated rescaled with 1.21 • Correlation studies: • statistical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous error calculation correct • Beam polarization studies • consistent with zero • Correction of charm events R.Seidl: Fragmentation function measurements at Belle

  16. Final charm corrected results for e+ e-p p X (29fb-1 of continuum data) Final results Preliminary results • Significant non-zero asymmetries • Rising behavior vs. z • cos(f1+f2) double ratios only marginally larger • UC asymmetries about 40-50% of UL asymmetries • First direct measurements of the Collins function R.Seidl: Fragmentation function measurements at Belle

  17. Charm corrected results for e+ e-p p X (547 fb-1) PRELIMINARY • Significance largely increased • Behavior unchanged • Reduced systematic errors due to statistics • Precise measurements of the Collins function R.Seidl: Fragmentation function measurements at Belle

  18. Collins asymmetries II: sin2q/(1+cos2q) binning (UL) • Nonzero quark polarization ~ sin2 q • Unpolarized de-nominator ~ 1+cos2q • Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle • Better agreement for thrust axis (~approximate quark axis) • UC plots similar PRELIMINARY thrustz q2 R.Seidl: Fragmentation function measurements at Belle

  19. 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+j2 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] Interference Fragmentation – thrust method j2-p p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)] R.Seidl: Fragmentation function measurements at Belle

  20. 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 R.Seidl: Fragmentation function measurements at Belle

  21. Different model predictions for IFF PRELIMINARY f1, h1 from spectator model f1, h1=g1 from GRV98 & GRSV96 • Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of pp-phaseshift analysisasign change at r-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 channelano sign change observed (updated model has Breit-Wigner like asymmetry) R.Seidl: Fragmentation function measurements at Belle

  22. Unpolarized FF as important input for allprecise QCD measurements MC simulation, ~1.4 fb-1 • No low-Q2 data available  important for evolution • No high-z data available • Huge amount of B-factory data can help • Favored/Disfavored disentangling by detecting hadron pairs (as in Collins analysis)? 2. R.Seidl: Fragmentation function measurements at Belle

  23. Summary and outlook • A first successful global analysis of transversity data using the HERMES,COMPASS and published Belle data • Belle Collins data largely improved from 29  547 fb-1 • Significant, nonzero asymmetries  Collins function is large • Long Collins paper is nearly finished • Continue to measure precise spindependent fragmentation functions at Belle • kT dependence of Collins function • Favored/disfavored disentanglement • Initerference Fragmentation function measurements (started) • Measure precise unpolarized fragmentation functions of many final states  Important input for general QCD physics and helicity structure measurements • Measure other interesting QCD-related quantities at Belle: • Chiral-odd L-fragmentation function • Event shapes • R-ratio with ISR R.Seidl: Fragmentation function measurements at Belle

  24. Backup Slides R.Seidl: Fragmentation function measurements at Belle

  25. B, charm and uds contributions in the data uds quarks charm quarks Charged B-mesons Neutral B-mesons Open symbols: charm enhanced data sample used for charm correction Full symbols: main data sample R.Seidl: Fragmentation function measurements at Belle

  26. Collins asymmetries IIa: sin2q/(1+cos2q) binning (UC) • Nozeron quark polarization ~ sin2 q • Unpolarized de-nominator ~ 1+cos2q • Clear linear behavior seen when using either thrustz or 2nd hadron as polar angle • Better agreement for thrust axis (~approximate quark axis) • Similar behavior, smaller magnitude as UL asymmetries PRELIMINARY thrustz q2 R.Seidl: Fragmentation function measurements at Belle

  27. Collins asymmetries III: QT binning (UL) PRELIMINARY • Reduced asymmetries in low thrust sample • At low thrust significant B contribution (for t<0.8 ~20 % B for t>0.8 < 1 % B) • A12 thrust axis dependent • High QT (>3.5 GeV) asymmetries from beam related BG • UC plots similar Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) R.Seidl: Fragmentation function measurements at Belle

  28. Collins asymmetries IIIa: QT binning (UC) PRELIMINARY • Reduced asymmetries in low thrust sample • At low thrust significant heavy quark contribution • High QT (>3.5 GeV) asymmetries from beam related BG • similar behavior, but smaller magnitude as UL asymmetries Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) R.Seidl: Fragmentation function measurements at Belle

  29. What would we see in e+e-? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m2pp m2pp m1pp m1pp “Jaffe” “Radici” R.Seidl: Fragmentation function measurements at Belle

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