Measurements of chiral-odd fragmentation functions at Belle

1. Measurements of chiral-odd fragmentation functions at Belle SSA workshop June1st – 3rd, BNL, NY 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. Outline • Motivation • 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 measurements of chiral-odd fragmentation functions at Belle

3. 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 ! measurements of chiral-odd fragmentation functions at Belle

4. KEKB: L>1.5x1034cm-2s-1 !! Belle detector KEKB • 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: >400 fb-1 >30fb-1 => off-resonance measurements of chiral-odd fragmentation functions at Belle

5. Good tracking and particle identification! measurements of chiral-odd fragmentation functions at Belle

6. 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) measurements of chiral-odd fragmentation functions 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 measurements of chiral-odd fragmentation functions at Belle

8. Collins fragmentation: Angles and Cross section cos(f1+f2) method e+e- CMS frame: j2-p e- Q j1 j2 j1 e+ 2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins measurements of chiral-odd fragmentation functions at Belle

9. Collins fragmentation: 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 measurements of chiral-odd fragmentation functions at Belle

10. Off-resonance data (in the future also resonance) 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 • Light quark selection • Hemisphere cut • <0 • Opening angule cuts: • - cos(2f0) method: y>120 • - cos(f1+f2) method:y1<60,y2>120 z-binning: 0.2 0.3 0.5 0.7 1.0 measurements of chiral-odd fragmentation functions at Belle

11. Examples of fitting the azimuthal asymmetries • Cosine modulations clearly visible • No change in cosine moments when including higher harmonics (even though double ratios will contain them) N(f)/N0 D1 : spin averaged fragmentation function, H1: Collins fragmentation function measurements of chiral-odd fragmentation functions at Belle

12. 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 measurements of chiral-odd fragmentation functions at Belle

13. 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: measurements of chiral-odd fragmentation functions at Belle

14. Testing the double ratios with MC • Asymmetries do cancel out for MC • Double ratios of p+p+/p-p- compatible to 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-) measurements of chiral-odd fragmentation functions at Belle

15. Results for p-pairs for 30fb-1 • Significant non-zero asymmetries • Rising behaviour vs. z • cos(f1+f2) double ratios only marginally larger • First direct measurement of the Collins function z1 z2 measurements of chiral-odd fragmentation functions at Belle

16. 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  Systematic errors from charm are preliminary Charm fraction N(charm)/N(all) measurements of chiral-odd fragmentation functions at Belle

17. An experimentalist’s interpretation: fitting parameterizations of the Collins function(s) • Take unpolarized parameterizations (Kretzer at Q2=2.5GeV2) • Assume (PDF-like behaviour) • Assume • Sensitivity studies in progress measurements of chiral-odd fragmentation functions at Belle

18. Favored/Disfavored contribution Sensitivity Take simple parameterization to test sensitivity on favored to disfavored Ratio c b measurements of chiral-odd fragmentation functions at Belle

19. Summary and outlook • Double ratios: • double ratios from data • most systematic errors cancel • Analysis procedure passes zero tests • Main systematic uncertainties understood • Significant nonzero double ratios  Naïve LO analysis shows significant Collins effect Summary: Outlook: • Finalize analysis • On resonance 10 x statistics • Include p0into analysis: • Better distinction between favored and disfavored Collins function • Include VMs into analysis:  Possibility to test string fragmentation models used to describe Collins effect • Expansion of analysis to Interference fragmentation function straightforward measurements of chiral-odd fragmentation functions at Belle

20. 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 measurements of chiral-odd fragmentation functions at Belle

21. 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: measurements of chiral-odd fragmentation functions at Belle

22. 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 measurements of chiral-odd fragmentation functions at Belle