1. Precision fragmentation function measurements at Belle Trento, June 14 2007 M. Grosse Perdekamp (University of Illinois and RBRC) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC) Outline: The Collins function measurements Access to transversity over Collins fragmentation function Collins function measurements at Belle The Belle detector Improved statistics with on_resonance data Interference fragmentation function measurements unpolarized fragmentation function measurements

2. R.Seidl: Fragmentation function measurements at Belle2 Trento, June 14 th SIDIS experiments (HERMES and COMPASS, eRHIC) measure q(x) together with either Collins Fragmentation function or Interference Fragmentation function Towards a global transversity analysis RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x) There are always 2 unknown functions involved which cannot be measured independently Spin dependent Fragmentation function analysis in e + e - Annihilation yields information on the Collins and the Interference Fragmentation function ! Comlpex universality?

3. R.Seidl: Fragmentation function measurements at Belle3 Trento, June 14 th KEKB: L>1.6x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e - + 3.5GeV e + s = 10.58GeV ( (4S)) e + e - S Off-resonance: 10.52 GeV e + e - q q (u,d,s,c) Integrated Luminosity: >700 fb -1 >60fb -1 => off-resonance Belle detector KEKB

4. R.Seidl: Fragmentation function measurements at Belle4 Trento, June 14 th Good tracking and particle identification!

5. R.Seidl: Fragmentation function measurements at Belle5 Trento, June 14 th e-e- e+e+ Jet axis: Thrust = 6.4 Near-side Hemisphere: h i, i=1,N n with z i Far-side: h j, j=1,N f with z j Event Structure at Belle e + e - CMS frame: Spin averaged cross section:

6. R.Seidl: Fragmentation function measurements at Belle6 Trento, June 14 th Collins fragmentation in e + e - : Angles and Cross section cos( ) method 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins e + e - CMS frame: e-e- e+e+ [D.Boer: PhD thesis(1998)]

7. R.Seidl: Fragmentation function measurements at Belle7 Trento, June 14 th Collins fragmentation in e + e - : Angles and Cross section cos(2 ) method 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins Independent of thrust-axis Convolution integral I over transverse momenta involved e + e - CMS frame: e-e- e+e+ [Boer,Jakob,Mulders: NPB504(1997)345]

8. R.Seidl: Fragmentation function measurements at Belle8 Trento, June 14 th Applied cuts, binning Off-resonance data –60 MeV below (4S) resonance –29.1 fb -1 Later also on-resonance data: 547 fb -1 Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos i < 0.9 Event selection: –Ntrack 3 –Thrust > 0.8 –Z 1, Z 2 >0.2 Hemisphere cut Q T < 3.5 GeV z1z1 z2z2 0123 4 5 6 78 9 0.2 0.3 0.5 0.7 1.0 0.20.30.50.71.0 5 86 1 2 3 = Diagonal bins z1z1 z2z2

9. R.Seidl: Fragmentation function measurements at Belle9 Trento, June 14 th Examples of fits to azimuthal asymmetries D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N( )/N 0 No change in cosine moments when including sine and higher harmonics Cosine modulations clearly visible 2 )

10. R.Seidl: Fragmentation function measurements at Belle10 Trento, June 14 th Methods to eliminate gluon contributions: Double ratios and subtractions Double ratio method: Subtraction 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 2 methods give very small difference in the result

11. R.Seidl: Fragmentation function measurements at Belle11 Trento, June 14 th Testing the double ratios with MC Asymmetries do cancel out for MC Double ratios of compatible with zero Mixed event pion pairs also show zero result Asymmetry reconstruction works well for 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 ( )

12. R.Seidl: Fragmentation function measurements at Belle12 Trento, June 14 th Other Favored/Unfavored Combinations charged pions or Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) ± pairs (favored + unfavored) x (favored + unfavored) P.Schweitzer([hep-ph/0603054]): charged pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio Examine other combinations: Favored= u,d,cc. Unfavored= d,u,cc. Build new double ratios: Unlike-sign/ charged pairs (UC) UL UC

13. R.Seidl: Fragmentation function measurements at Belle13 Trento, June 14 th What about the data under the resonance? More than 540 fb -1 of on_resonance data (4S) is just small resonance More than 75% of hadronic cross section from open quark-antiquark production

14. R.Seidl: Fragmentation function measurements at Belle14 Trento, June 14 th Why is it possible to include on_resonance data? Different Thrust distributions e + e - q q (u d s) MC (4S) B + B - MC (4S) B 0 B 0 MC Largest systematic errors reduce with more statistics Charm-tagged Data sample also increases with statistics e + e - qq ̅, quds e + e - cc ̅

15. R.Seidl: Fragmentation function measurements at Belle15 Trento, June 14 th Improved systematic errors (UC) Tau contribution PID error MC double ratios Charged ratios ( higher moments in Fit difference double ratio-subtraction method reweighted MC-asymmetries: cos asymmetries underestimated rescaled with 1.21 Correlation studies: statistical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous error calculation correct Beam polarization studies consistent with zero Correction of charm events A 0 (cos(2 )) moments A 12 (cos( )) moments

16. R.Seidl: Fragmentation function measurements at Belle16 Trento, June 14 th Final charm corrected results for e + e - X (29fb -1 of continuum data) Significant non-zero asymmetries Rising behavior vs. z cos( + ) double ratios only marginally larger UC asymmetries about 40- 50% of UL asymmetries First direct measurements of the Collins function Final results Preliminary results

17. R.Seidl: Fragmentation function measurements at Belle17 Trento, June 14 th Charm corrected results for e + e - X (547 fb -1 ) Significance largely increased Behavior unchanged Reduced systematic errors due to statistics Precise measurements of the Collins function PRELIMINAR Y

18. R.Seidl: Fragmentation function measurements at Belle18 Trento, June 14 th Collins asymmetries II: sin 2 /(1+cos 2 ) binning (UL) Nonzero quark polarization ~ sin 2 Unpolarized de- nominator ~ 1+cos 2 Clear linear behavior seen when using either thrustz or 2 nd hadron as polar angle Better agreement for thrust axis (~approximate quark axis) UC plots similar thrustz PRELIMINARY

19. R.Seidl: Fragmentation function measurements at Belle19 Trento, June 14 th e + e - ( + - ) jet1 ( - + ) jet2 X Stay in the mass region around -mass Find pion pairs in opposite hemispheres Observe angles 1 2 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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996 )] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] Interference Fragmentation – thrust method 2 1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

20. R.Seidl: Fragmentation function measurements at Belle20 Trento, June 14 th Similar to previous method Observe angles 1R 2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation – method R2 R1

21. R.Seidl: Fragmentation function measurements at Belle21 Trento, June 14 th Different model predictions for IFF Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of - phaseshift analysis sign change at 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 channel no sign change observed (updated model has Breit-Wigner like asymmetry) PRELIMINARY f 1, h 1 from spectator model f 1, h 1 =g 1 from GRV98 & GRSV96

22. R.Seidl: Fragmentation function measurements at Belle22 Trento, June 14 th Unpolarized FF as important input for all precise QCD measurements MC simulation, ~1.4 fb -1 2. No low-Q 2 data available important for evolution No high-z data available Huge amount of B-factory data can help Favored/Disfavored disentangling by detecting hadron pairs (as in Collins analysis)?

23. R.Seidl: Fragmentation function measurements at Belle23 Trento, June 14 th Summary and outlook A first successful global analysis of transversity data using the HERMES,COMPASS and published Belle data Belle Collins data largely improved from 29 547 fb -1 Significant, nonzero asymmetries Collins function is large Long Collins paper is nearly finished Continue to measure precise spin dependent fragmentation functions at Belle –k T dependence of Collins function –Favored/disfavored disentanglement –Initerference Fragmentation function measurements (started) Measure precise unpolarized fragmentation functions of many final states Important input for general QCD physics and helicity structure measurements Measure other interesting QCD-related quantities at Belle: –Chiral-odd -fragmentation function –Event shapes –R-ratio with ISR

24. R.Seidl: Fragmentation function measurements at Belle24 Trento, June 14 th Backup Slides

25. R.Seidl: Fragmentation function measurements at Belle25 Trento, June 14 th B, charm and uds contributions in the data uds quarks charm quarks Charged B-mesons Neutral B-mesons Open symbols: charm enhanced data sample used for charm correction Full symbols: main data sample

26. R.Seidl: Fragmentation function measurements at Belle26 Trento, June 14 th Collins asymmetries IIa: sin 2 /(1+cos 2 ) binning (UC) Nozeron quark polarization ~ sin 2 Unpolarized de- nominator ~ 1+cos 2 Clear linear behavior seen when using either thrustz or 2 nd hadron as polar angle Better agreement for thrust axis (~approximate quark axis) Similar behavior, smaller magnitude as UL asymmetries thrustz PRELIMINARY

27. R.Seidl: Fragmentation function measurements at Belle27 Trento, June 14 th Collins asymmetries III: Q T binning (UL) Reduced asymmetries in low thrust sample At low thrust significant B contribution (for t<0.8 ~20 % B for t>0.8 < 1 % B) A 12 thrust axis dependent High Q T (>3.5 GeV) asymmetries from beam related BG UC plots similar Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) PRELIMINARY

28. R.Seidl: Fragmentation function measurements at Belle28 Trento, June 14 th Collins asymmetries IIIa: Q T binning (UC) Reduced asymmetries in low thrust sample At low thrust significant heavy quark contribution High Q T (>3.5 GeV) asymmetries from beam related BG similar behavior, but smaller magnitude as UL asymmetries Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) PRELIMINARY

29. R.Seidl: Fragmentation function measurements at Belle29 Trento, June 14 th What would we see in e + e - ? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m1 m2 Jaffe Radici