Measurements of fragmentation functions at Belle: results and prospects

1. Measurements of fragmentation functions at Belle: results and prospects (see hep-ex/0607014 and Phys.Rev. Lett.96:232002,2006 for Collins results) • Outline: • The KEKB rings and the Belle Experiment • Transverse Spin Physics • Motivations • Collins analysis and parameterizations • Interference Fragmentation functions • Unpolarized fragmentation functions 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) for the Belle Collaboration

2. 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: >600 fb-1 • >60fb-1 => off-resonance R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

3. Good tracking and particle identification! R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

4. Important input for global Transversity Analysis SIDIS experiments (HERMES and COMPASS, EIC) 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 ! R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

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:Measurements of fragmentation functions at Belle: results and prospects

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:Measurements of fragmentation functions at Belle: results and prospects

7. Off-resonance data 60 MeV below U(4S) 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 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:Measurements of fragmentation functions at Belle: results and prospects

8. 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-) R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

9. 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): (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. R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

10. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

11. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

12. Fits to the HERMES data by the Torino Group • A. Prokudin fitted the HERMES (Sivers and) Collins Data • Either Soffer bound for transversity: 2dq(x) = | q + Dq | • Or dq(x) = Dq(x) • GRV1998 for unpolarized PDFs • Kretzer FF • Gaussian kT Assumption HERMES 02-04 Data COMPASS 02 Data R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

13. 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? R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

14. 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:Measurements of fragmentation functions at Belle: results and prospects

15. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

16. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

17. 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:Measurements of fragmentation functions at Belle: results and prospects

18. Unpolarized FFs MC simulation, ~1.4 fb-1 • Performed Systematic studies: • Smearing • Tracking efficiency • Acceptance • Energy scale • Particle ID study not yet finished • AKK: Try flavor tagged/enhanced analysis? 2. R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

19. Summary and outlook Prospects: Results: • Collins analysis: • 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 sophisticated analysis • Paper is published • Important input for Transversity measurements now and in the future • Leading order fits ongoing • On resonance >10 x statistics long paper on Collins results • Interference fragmentation function analysis started • Unpolarized FF analysis almost complete but lacks manpower • Many more QCD/Spin related studies possible (VM Collins, timelike DVCS, L Polarimetry, kT-dependent FFs, “Sivers”FF, Event Shapes ) R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

20. R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

21. 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) R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

22. 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: R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

23. 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. R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

24. Typical hadronic events at Belle R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

25. 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:Measurements of fragmentation functions at Belle: results and prospects

26. 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:Measurements of fragmentation functions at Belle: results and prospects

27. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

28. 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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

29. 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) R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

33. Favored/Disfavored contribution Sensitivity Take simple parameterization to test sensitivity on favored to disfavored Ratio c b R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

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 R.Seidl:Measurements of fragmentation functions at Belle: results and prospects

35. 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:Measurements of fragmentation functions at Belle: results and prospects

36. 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) R.Seidl:Measurements of fragmentation functions at Belle: results and prospects