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Measurements of chiral-odd fragmentation functions at Belle

Measurements of chiral-odd fragmentation functions at Belle. (see hep-ex/0507063 for details, submitted to PRL). DIS 2006 April 20 th , Tsukuba. D. Gabbert (University of Illinois and RBRC) M. Grosse Perdekamp (University of Illinois and RBRC) K. Hasuko (RIKEN/RBRC)

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Measurements of chiral-odd fragmentation functions at Belle

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  1. Measurements of chiral-odd fragmentation functions at Belle (see hep-ex/0507063 for details, submitted to PRL) DIS 2006 April 20th, Tsukuba 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) V. Siegle (RBRC) for the Belle Collaboration

  2. Collins effect in quark fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentationof a quark qwith spin sqinto a spinless hadron h carries an azimuthal dependence: Spin dependent fragmentation functions at BELLE

  3. 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. Spin dependent fragmentation functions at BELLE

  4. Motivation: Global Transversity Analysisdq(x) SIDIS experiments (HERMES and COMPASS) 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) Universality appears to be proven in LO by Collins and Metz: [PRL93:(2004)252001 ] The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function ! Spin dependent fragmentation functions at BELLE

  5. KEKB: L>1.5x1034cm-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: >500 fb-1 • >45fb-1 => off-resonance Spin dependent fragmentation functions at BELLE

  6. Belle Detector Aerogel Cherenkov cnt. n=1.015~1.030 SC solenoid 1.5T 3.5 GeVe+ CsI(Tl) 16X0 TOF conter 8 GeVe- Central Drift Chamber small cell +He/C2H6 Si vtx. det. 3/4 lyr. DSSD m / KL detection 14/15 lyr. RPC+Fe Good tracking and particle identification! Spin dependent fragmentation functions at BELLE

  7. 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 Spin dependent fragmentation functions at BELLE

  8. 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- Q j0 [Boer,Jakob,Mulders: NPB504(1997)345] e+ 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins Spin dependent fragmentation functions at BELLE

  9. Off-resonance data 60 MeV below U(4S) resonance 29.1 fb-1 Pions selected by PID cut Track selection: pT > 0.1GeV vertex cut:dr<2cm, |dz|<4cm Acceptance cut -0.6 < cosqh< 0.9 Event selection: Ntrack  3 Thrust > 0.8 Z1, Z2>0.2 Applied cuts, binning • Hemisphere cut • QT < 3.5 GeV 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 0.2 0.3 0.5 0.7 1.0 z1 = Diagonal bins z1 Spin dependent fragmentation functions at BELLE

  10. 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 Spin dependent fragmentation functions at BELLE

  11. 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 Spin dependent fragmentation functions at BELLE

  12. Other Favored/Unfavored Combinations charged pairs Improvement: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: • Unlike-sign pion pairs (UL): (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/L UL/C • Build new double ratios: • Unlike-sign/ charged pp pairs (UL/C) Favored = up+,dp-,cc. Unfavored = dp+,up-,cc. Spin dependent fragmentation functions at BELLE

  13. Testing the double ratios with MC • Asymmetries do cancel out for MC • Double ratios of p+p+/p-p- compatible with zero • Mixed events 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-) Spin dependent fragmentation functions at BELLE

  14. Systematic errors • Tau contributions • PID systematics* • MC double ratios • Charged ratios (p+p+ /p-p- )* • Higher order terms • Double ratio-subtraction method * - taken from UL/L analysis Further studies: Reweighting asymmetries: underestimation of cos(f1+f2) asymmetries Correlation studies: statistical errors rescaled by 14% Beam polarization studies consistent with zero Spin dependent fragmentation functions at BELLE

  15. Final charm corrected results for e+ e-p p X (29fb-1 of continuum data) Submitted to PRL Preliminary • Significant non-zero asymmetries • Rising behavior vs. z • cos(f1+f2) double ratios only marginally larger • UL/C asymmetries about 40-50% of UL/L asymmetries • First direct measurements of the Collins function Spin dependent fragmentation functions at BELLE

  16. Why is it possible to include on_resonance data?Different Thrust distributions • 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 Spin dependent fragmentation functions at BELLE

  17. 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 [Phys.Rev.D67:094003,2003] and Artru, Collins [Z.Phys.C69:277-286,1996 ] Interference Fragmentation – thrust method j2-p p-j1 Spin dependent fragmentation functions at BELLE

  18. Summary and outlook Outlook: Summary: • Double ratios: double ratios from data most systematic errors cancel • Analysis procedure passes all null tests • Systematic uncertainties understood •  Significant nonzero asymmetry with double ratios are observed • UL/C about half as large as UL/L double ratios • Data can be used for more sophisticatedanalysis • Paper with UL/L double ratios (hep-ex/0507063) is submitted • Leading order fits ongoing • On resonance 10 x statistics detailed final analysis on Collins results • Interference fragmentation function analysis started • Include Vector Mesons into Collins analysis: • Possibility to test string fragmentation models used to describe Collins effect • Many more QCD/Spin related studies possible (unpol FFs, timelike DVCS, L Polarimetry) Spin dependent fragmentation functions at BELLE

  19. Spin dependent fragmentation functions at BELLE

  20. Small double ratios in low thrust data sample A0 • Low thrust contains radiative effects • Collins effect vanishes Strong experimental indication that double ratio method works A12 Spin dependent fragmentation functions at BELLE

  21. Typical hadronic events at Belle Spin dependent fragmentation functions at BELLE

  22. Belle is well suited for FF measurements: • 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 (Q2 ~ 110 GeV2) - can apply pQCD Not too high energy (Q2 << MZ2) -avoids additional complication from Z interference • Sensitivity = A2sqrt(N)~ x19 (60) compared to LEP ABelle / ALEP ~ x2 (A scales as ln Q2) LBelle / LLEP~x23 (230) Spin dependent fragmentation functions at BELLE

  23. 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 Spin dependent fragmentation functions at BELLE

  24. What is the transverse momentum QT of the virtual photon? Ph1 Lepton-CMS • In the lepton CMS frame e-=-e+ and the virtual photon is only time-like: qm=(e-m+p+m)=(Q,0,0,0) • Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame where Ph1+Ph2=0 qm’=(q’0,q’) • Inclusive Cross section for radiative events (acc. to D.Boer): Ph2 e- e+ q’ Hadron-CMS e+’ e-’ P’h1 P’h2 qT Spin dependent fragmentation functions at BELLE

  25. Raw asymmetries vs QT Q j0 • QT describes transverse momentum of virtual photon in pp CMS system • Significant nonzero Asymmetries visible in MC (w/o Collins) • Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs j2 Q • uds MC (pp) Unlike sign pairs • uds MC (pp) Like sign pairs j1 Spin dependent fragmentation functions at BELLE

  26. Experimental issues • Cos2f 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(2fLab) asymmetries for jets or gg • False asymmetries from weak decays  Study effect in t decays, constrain through D tagging • False asymmetries from misidentified hemispheres  QT 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 Spin dependent fragmentation functions at BELLE

  27. Systematics: charm contribution? • Weak (parity violating) decays could also create asymmetries (seen in ttppnn, overall t dilution 5%) • Especially low dilution in combined z-bins with large pion asymmetry • Double ratios from charm MC compatible to zero • Charm decays cannot explain large double ratios seen in the data  Charm enhanced D* Data sample used to calculate and correct the charm contribution to the double ratios (see hep-ex/0507063 for details) Charm fraction N(charm)/N(all) Spin dependent fragmentation functions at BELLE

  28. Favored/Disfavored contribution Sensitivity Take simple parameterization to test sensitivity on favored to disfavored Ratio c b Spin dependent fragmentation functions at BELLE

  29. 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 Spin dependent fragmentation functions at BELLE

  30. Different model predictions for IFF • Jaffe at 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 Spin dependent fragmentation functions at BELLE

  31. Different model predictions for IFF PRELIMINARY f1, h1 from spectator model f1, h1=g1 from GRV98 & GRSV96 • Radici et al. [Phys. Rev. D65 (2002)] : Spectator model in the s-p channelano sign change observed (updated model has Breit-Wigner like asymmetry) Spin dependent fragmentation functions at BELLE

  32. What would we see? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m2pp m2pp m1pp m1pp “Jaffe” “Radici” Spin dependent fragmentation functions at BELLE

  33. What do we see? I: events • Animation of an event • lepton tracks, thrust axis and all particle momenta in the CMS frame • Ph1=P1+P2 • Ph2=P3+P4 • Plane defined by leptons and thrust • Planes defined by hadron pairs Spin dependent fragmentation functions at BELLE

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