1. Outline: The Belle detector unpolarized fragmentation function measurements Understanding the systematics for precision measurements at high z Expected precision The Collins function measurements Access to transversity over Collins fragmentation function Collins function measurements at Belle Interference fragmentation function measurements Light quark and spin dependent fragmentation function measurements at Belle  G workshop, UIUC, June 17, 2008 M. Grosse Perdekamp (University of Illinois) M. Leitgab (University of Illinois) A. Ogawa (BNL/RBRC) R. Seidl (RBRC) representing the Belle collaboration

2. Fragmentation workshop, Trento, February 26 th KEKB: L>1.7x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e - + 3.5GeV e + √s = 10.58GeV (  (4S)) e + e -   (4S)  B  B Continuum production: 10.52 GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: >700 fb -1 >60fb -1 => continuum 2 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle D G workshop, UIUC, June 16-17 Belle detector KEKB

3.  / K L detection 14/15 lyr. RPC+Fe C entral D rift C hamber small cell +He/C 2 H 6 CsI(Tl) 16X 0 Aerogel Cherenkov cnt. n=1.015~1.030 Si vtx. det. 3/4 lyr. DSSD TOF conter SC solenoid 1.5T 8 GeV e  3.5 GeV e  Belle Detector Good tracking and particle identification!  (K)~85%,  (   K)<10%  G workshop, UIUC, June 16-17 3

4. Fragmentation workshop, Trento, February 26 th Single hadron cross section 4 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Process: e + e -  hX At leading order sum of unpolarized fragmentation functions from quark and anti-quark side e-e- e+e+ h

5. Fragmentation workshop, Trento, February 26 th World data and motivation for precise FFs Most data obtained at LEP energies, At lower CMS energies very little data available 3-jet fragmentation to access gluon FF theoretically difficult  Gluon fragmentation from evolution not yet well constrained  Higher z FFs (>0.7) hardly available 5 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle

6. Fragmentation workshop, Trento, February 26 th Systematic studies: Particle identification Particle identification: create PID efficiency matrix for K, ,p,e,  PID responses from MC not reliable, use well identified decays from data: –Use D *   slow  D 0   slow  fast K for K,  identification –Use    p for p,  identification  Unfolding 6 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle REAL Particles Reconstructed particles  Kp  e  K p  e =

7. Fragmentation workshop, Trento, February 26 th D * analysis Measure signal N i and yield contributions in Fit of  m(D * -m(K,  fast )) distribution to obtain real K,  yields Repeat Fits for particular particle likelihood selection to obtain N i  j Ratio of signals gives efficiency 7 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle

8. Fragmentation workshop, Trento, February 26 th  analysis, leptons Similarly calculate efficiencies from m(P  distribution Most kinematic regions well covered So far: lepton efficiencies from MC, in the future: extract efficiencies form J/  decays Perform inversion of efficiency matrix, keep stable inverse matrices 8 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle

9. Fragmentation workshop, Trento, February 26 th Acceptance correction, status Correction from MC for missing acceptance in forward/backward regions and empty PID matrix elements in (q Lab,p Lab ) Status: –  and K FFs in intermediate z-region close to being able to be released –P and higher z (>0.75) data need more studies (PID efficiency matrix) 9 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle ++ K+K+

10. Fragmentation workshop, Trento, February 26 th Further FF measurements Additional FF measurements planned: –    cross check with completely different systematics) –  (PHENIX A LL measurement available, higher strange content??) –Other decaying particles (K S,f 0,…?) –k t dependent FFs 10 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle

11. Fragmentation workshop, Trento, February 26 th Event Structure for Hadron pairs 11 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle = 6.4 Far-side: h j, j=1,N f with z j e + e - CMS frame: e-e- e+e+  Spin averaged cross section: Jet axis: Thrust Near-side Hemisphere: h i, i=1,N n with z i

12. Unpolarized 2-hadron fragmentation Detect two hadrons simultaneously If two hadrons in opposite hemispheres one obtains sensitivity to favored/disfavored fragmentation: Problems: –Either need to ensure two- jet topology (thrust cut) –Or contribution from one quark fragmentation q  hhX R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle12 Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored)  ±   or any charge hadron pairs (C): (favored + unfavored) x (favored + unfavored) Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.

13. Fragmentation workshop, Trento, February 26 th Collins fragmentation in e + e - : Angles and Cross section cos(  1 +  2 ) method 13 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle       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)]

14. Fragmentation workshop, Trento, February 26 th Examples of fits to azimuthal asymmetries 14 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle 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 22     ) Cosine modulations clearly visible P1 contains information on Collins function

15. 15D G workshop, UIUC, June 16-17R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle 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

16. 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 What about the data under the resonance? D G workshop, UIUC, June 16-1716R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle

17. Fragmentation workshop, Trento, February 26 th Why is it possible to include on_resonance data? Different Thrust distributions 17 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle e + e -  q  q (u d s) MC  (4S)  B + B - MC  (4S)  B 0  B 0 MC Charm-tagged Data sample (used for charm correction) also increases with statistics Largest systematic errors reduce with more statistics e + e -  qq ̅, q∈uds e + e -  cc ̅

18. Fragmentation workshop, Trento, February 26 th Improved systematic errors (UC) Tau contribution (not shown) Quark axis correction PID systematics MC uncertainties Charged ratios (  +  + /  -  - ) higher moments in Fit (not shown) difference double ratio-subtraction method 18 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Beam polarization studies  consistent with zero Correction for charm events

19. Final Collins results Belle 547 fb -1 data set (submitted to PRD arXiv:0805.2975) EIC workshop, May 21thR.Sei dl: Trans versit y meas urem ents at EIC 19

20. 20D G workshop, UIUC, June 16-17R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Towards a global transversity analysis SIDIS experiments (HERMES and COMPASS, eRHIC) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function 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 ! Universality understood Evolution ?

21. Fragmentation workshop, Trento, February 26 th Interference Fragmentation – thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Stay in the mass region around r-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)] 21 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

22. Fragmentation workshop, Trento, February 26 th Interference Fragmentation – “  0 “ method 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 22 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle  R2  R1

23. Fragmentation workshop, Trento, February 26 th Summary and outlook Continue to measure precise spin dependent fragmentation functions at Belle –kT dependence of Collins function –Artru model test with Vector meson Collins –Interference Fragmentation function measurements (started) Measure other interesting QCD- related quantities at Belle: –Chiral-odd  -fragmentation function –  single spin asymmetry –Event shapes –R-ratio with ISR 23 R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Measure precise unpolarized fragmentation functions of many final states  Important input for general QCD physics and helicity structure measurements Analysis progressing: PID studies Acceptance correction Belle Collins data largely improved from 29  547 fb -1 Significant, nonzero asymmetries  Collins function is large Long Collins paper submitted

24. 24D G workshop, UIUC, June 16-17R.Seidl: Light quark and spin dependent fragmentation function measurements at Belle Backup Slides

25. Fragmentation workshop, Trento, February 26 th R.Sei dl: Light quark and spin depen dent fragm entati on functi on meas urem ents at Belle 25 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]

26. Fragmentation workshop, Trento, February 26 th R.Sei dl: Light quark and spin depen dent fragm entati on functi on meas urem ents at Belle 26 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

27. Fragmentation workshop, Trento, February 26 th R.Sei dl: Light quark and spin depen dent fragm entati on functi on meas urem ents at Belle 27 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

28. Fragmentation workshop, Trento, February 26 th R.Sei dl: Light quark and spin depen dent fragm entati on functi on meas urem ents at Belle 28 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

29. Fragmentation workshop, Trento, February 26 th R.Sei dl: Light quark and spin depen dent fragm entati on functi on meas urem ents at Belle 29 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 ”