Measurements of chiral-odd fragmentation functions at Belle

1. Measurements of chiral-odd fragmentation functions at Belle (see hep-ex/0507063 for details, submitted to PRL) Rencentres de Moriond March 19th, La Thuile 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: Fragmentation of a transversely polarized quark q into spin-less 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 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 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. 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

6. 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

7. 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 z1 0.2 0.3 0.5 0.7 1.0 = Diagonal bins • Hemisphere cut • QT < 3.5 GeV Spin dependent fragmentation functions at BELLE

8. Examples of fits to azimuthal asymmetries Cosine modulations clearly visible N(f)/N0 2f0 (f1+f2) No change in cosine moments when including sine and higher harmonics (even though double ratios will contain them) D1 : spin averaged fragmentation function, H1: Collins fragmentation function Spin dependent fragmentation functions at BELLE

9. 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

10. 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 (pp-pairs) • charm MC (pp-pairs) • Data (p+p+/p-p-) Spin dependent fragmentation functions at BELLE

11. Results for e+ e-p p X for 29fb-1 A0 • 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±0.65±0.55)% • cos(2f1+f2) method (4.26±0.78±0.68)% A12 Systematic error z1 z2 Spin dependent fragmentation functions at BELLE

12. MC double ratio Charge sign ratio Higher moments Double ratio method Contributions to systematic errors • Other uncertainties: • smearing (reweighted MC) • PID (variation of PID cuts) • charm contribution (corrected by • D* data sample) • t content (evaluated in • e+ e- t+ t-enhanced sample) Systematic errors Spin dependent fragmentation functions at BELLE

13. An experimentalist’s interpretation: fitting parameterizations of the Collins function(s) • Take unpolarized parameterizations (Kretzer at Q2=2.5GeV2) • Assume (PDF-like behavior) • Assume • Little sensitivity to to favored/disfavored Collins ratio Spin dependent fragmentation functions at BELLE

14. Other Favored/Unfavored Combinations p0 Problem: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: • Unlike-sign pion pairs: (favored x favored +unfavored x unfavored) • Like-sign pion pairs: (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 are easier to handle): (favored + unfavored) x (favored + unfavored) Favored = up+,dp-,cc. Unfavored = dp+,up+,cc. Spin dependent fragmentation functions at BELLE

15. Why is it possible to include on_resonance data?Different Thrust distributions • e+ e- q q • (q in uds) MC • U(4S)B+B- MC • U(4S)B0B0 MC Spin dependent fragmentation functions at BELLE

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 Interference Fragmentation – thrust method j2-p p-j1 Spin dependent fragmentation functions at BELLE

17. Summary and outlook Outlook: Summary: • Double ratios: double ratios from data most systematic errors cancel • Analysis procedure passes all null tests • Main systematic uncertainties understood •  Significant nonzero asymmetry with double ratios are observed • Naive LO analysis shows significant Collins effect • Data can be used for more sophisticatedanalysis • Paper (hep-ex/0507063) is submitted • On resonance 10 x statistics • Include p0 and all charged pp pairs into analysis: • Better distinction between favored and disfavored Collins function • Interference fragmentation function analysis started • Include Vector Mesons into analysis:  Possibility to test string fragmentation models used to describe Collins effect Spin dependent fragmentation functions at BELLE

18. Spin dependent fragmentation functions at BELLE

19. Outline • Motivation • Study transverse spin effects in fragmentation • Global transversity analysis • Feasibility  LEP analysis [hep-ph/9901216] • The BELLE detector • Collins analysis • Angular definitions and cross sections • Double Ratios to eliminate radiative/momentum correlation effects • An experimentalist’s interpretation • Summary Spin dependent fragmentation functions at BELLE

20. 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. Double Ratio vs Subtraction Method: Preliminary Systematic errors R – S < 0.002 • The difference was assigned as a systematic error. Spin dependent fragmentation functions at BELLE

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

29. 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

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

31. Different charge combinations additional information Favored = up+,dp-,cc. Unfavored = dp+,up+,cc. • Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side: • Like sign pairs contain one favored and one unfavored fragmentation function each: Spin dependent fragmentation functions at BELLE

32. NL- NR AT= = 0! NL+ NR π sq sq q q π Example: Left-Right Asymmetry in Pion Rates Collins Effect NL : pions to the left NR : pions to the right Spin dependent fragmentation functions at BELLE

33. General Fragmentation Functions Number density for finding a spin-less hadron h from a transversely polarized quark, q: unpolarized FF Collins FF Spin dependent fragmentation functions at BELLE

34. Raw asymmetries vs transverse photon momentum QT Unlike sign pairs Like sign pairs • Already MC contains large asymmetries • Strong dependence against transverse photon Momentum QT • Expected to be due to radiative effects • Difference of DATA and MC is signal • not so easy to determine • DATA (pp) fiducial cut • DATA (KK) fiducial cut • UDS-MC fiducial cut • CHARM-MC fiducial cut j2 Q Q j1 j0 Spin dependent fragmentation functions at BELLE