First Measurement of the Collins fragmentation function at Belle

1. First Measurement of the Collinsfragmentation function at Belle (see hep-ex/0507063 for details, accepted by PRL) QCDN06 June 14th, Frascati, Italy 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) for the Belle Collaboration

2. Collins effect in quark fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation with of a quark qwith spin sqinto a spinless hadron h carries an azimuthal dependence: Measurement of the Collins fragmentation function 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. Measurement of the Collins fragmentation function at BELLE

4. Important input for global Transversity Analysis 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 provenin LO by Collins and Metz: [PRL93:(2004)252001 ] +most recent work from Amsterdam Group The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function ! Measurement of the Collins fragmentation function 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: >600 fb-1 • >45fb-1 => off-resonance Measurement of the Collins fragmentation function at BELLE

6. Good tracking and particle identification! Measurement of the Collins fragmentation function at BELLE

7. 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 Measurement of the Collins fragmentation function at BELLE

8. 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 Measurement of the Collins fragmentation function at BELLE

9. 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 Measurement of the Collins fragmentation function at BELLE

10. Off-resonance data 60 MeV below U(S) resonance 29.1 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 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 = Diagonal bins • Hemisphere cut • QT < 3.5 GeV z1 Measurement of the Collins fragmentation function at BELLE

11. 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 Measurement of the Collins fragmentation function at BELLE

12. 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 Measurement of the Collins fragmentation function 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-) Measurement of the Collins fragmentation function at BELLE

14. Small double ratios in low thrust data sample A0 • Low thrust contains radiative effects • Collins effect at least smeared for low thrust Strong experimental indication that double ratio method works A12 Measurement of the Collins fragmentation function at BELLE

15. Results for e+ e-p p X for 29fb-1 A0 Final results • Significant non-zero asymmetries • Rising behavior vs. z • cos(f1+f2) double ratios only marginally larger • First direct measurement of the Collins function • Integrated results: • cos(2f0) method (3.06±0.57±0.55)% • cos(2f1+f2) method (4.26±0.68±0.68)% A12 Systematic error z1 z2 Measurement of the Collins fragmentation function at BELLE

16. 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 (UL): (fav x fav + unf x unf) • Like-sign pion pairs (L): (fav x unf + unf x fav) • p±p0 pairs (fav + unf) x (fav + unf) • charged pp pairs are similar (C): (P.Schweitzer([hep-ph/0603054]): (fav + unf) x (fav + unf) ~ fav2 + unf2- 2 fav x unf UL/L UL/C ~ -2 fav x unf (oversimplified) • Build new double ratios: • Unlike-sign/ charged pp pairs (UL/C) Favored = up+,dp-,cc. Unfavored = dp+,up+,cc. Measurement of the Collins fragmentation function at BELLE

17. 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 errrors rescaled by 14% Beam polarization studies consistent with zero Measurement of the Collins fragmentation function at BELLE

18. 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 • UL/C asymmetries about 40-50% of UL/L asymmetries • First direct measurements of the Collins function Measurement of the Collins fragmentation function at BELLE

19. What about the data under the resonance? • Almost 600 fb-1 of on_resonance data • U(4S) is just small resonance • More than 75% of hadronic cross section Measurement of the Collins fragmentation function at BELLE

20. 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 Measurement of the Collins fragmentation function at BELLE

21. 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 and Artru,Collins Early work by Collins, Heppelman, Ladinski Interference Fragmentation – thrust method j2-p p-j1 Measurement of the Collins fragmentation function at BELLE

22. 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) Measurement of the Collins fragmentation function at BELLE

23. 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” Measurement of the Collins fragmentation function at BELLE

24. 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 UL/L double ratios • Data can be used for more sophisticatedanalysis • Paper with UL/L double ratios (hep-ex/0507063) is accepted • Leading order fits ongoing • On resonance >10 x statistics long paper 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) Measurement of the Collins fragmentation function at BELLE

25. Measurement of the Collins fragmentation function at BELLE

26. QCD: the right theory, but many surprisesespecially in spin … • Spin composition of the nucleon: • Contribution of quark spin small • Contribution of gluon spin also small? • Orbital angular momentum? Sivers effect? • Single spin asymmetries small in pQCD • …but large and nonzero! • Understandable by gauge link contributions • Sivers effect: • Unpolarized quarks in transversely polarized nucleon • Non-centered quark distribution in impact parameter space • Rescattering creates left-right asymmetry • Boer-Mulders effect: • Transversely polarized quarks in unpolarized nucleon • Vacuum polarization effect? • Collins effect: • Fragmentation of transversly polarized quark into unpolarized hadron • Connects microscopic quantitiy (transverse spin) to macroscopic quantity (azimuthal asymmetries) Measurement of the Collins fragmentation function at BELLE

27. Fits to our UL/L data: Efremov, Goeke, Schweitzer: [hep-ph/0603054]: • Taking reasonable transversity from cQSM • Gaussian intrinsic transverse momentum dependence • HERMES, COMPASS and Belle results are consistent with each other • However: Fit errors on Collins function still large • Probably improvement by UL/C data (not yet included) • Can we do better? Measurement of the Collins fragmentation function at BELLE

28. 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 Measurement of the Collins fragmentation function at BELLE

29. Typical hadronic events at Belle Measurement of the Collins fragmentation function at BELLE

30. 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 Measurement of the Collins fragmentation function at BELLE

31. 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 Measurement of the Collins fragmentation function at BELLE

32. 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 Measurement of the Collins fragmentation function at BELLE

33. Favored/Disfavored contribution Sensitivity Take simple parameterization to test sensitivity on favored to disfavored Ratio c b Measurement of the Collins fragmentation function at BELLE

34. 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 Measurement of the Collins fragmentation function at BELLE