1. Precision fragmentation function measurements at Belle Freiburg, June 6 2007 R. Seidl (University of Illinois and RBRC) Outline: Why QCD and spin physics? Transversity and the Collins function Transversity as thirsd leading twist distribution function Access to transversity over Collins fragmentation function Collins function measurements at Belle The Belle detector Improved statistics with on_resonance data First global analysis from SIDIS and Belle data Interference fragmentation function measurements unpolarized fragmentation function measurements

2. R.Seidl: Fragmentation function measurements at Belle2 Freiburg, June 6 th Why QCD and spin physics? QCD as the right theory of quarks and gluons, Perturbative part well understood Nucleon as simplest bound state of QCD poorly understood (though building block of most matter in universe) Significant surprises when including spin:  Spin crisis: Quarks contribute only ~30% to nucleon spin  Large transverse single spin asymmetries which are forbidden by perturbative QCD observed “You think you understand something? Now add spin...” – R. Jaffe

3. R.Seidl: Fragmentation function measurements at Belle3 Freiburg, June 6 th The (spin) structure of the Nucleon Longitudinal Spin Sum Rule: Transverse Spin (BLT) Sum Rule? Double Spin Asymmetries (pp,SIDIS) W-production (pp) Exclusive processes (DVCS,etc) Chiral-odd Fragmentation functions (Collins,IFF  Sivers effect?? Color Glass condensate ??

4. R.Seidl: Fragmentation function measurements at Belle4 Freiburg, June 6 th  q(x),  G(x) Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton (known from fixed target (SI)DIS experiments) q(x),G(x) Sum of quarks with parallel and antiparallel polarization relative to proton spin (well known from Collider DIS experiments)  q(x) Quark distributions Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton (first results from HERMES and COMPASS – with the help of Belle) Unpolarized distribution function q(x) Helicity distribution function  q(x) Transversity distribution function  q(x)

5. R.Seidl: Fragmentation function measurements at Belle5 Freiburg, June 6 th Cross sections in (semi)inclusive pp and DIS, factorization f q (x 1 )  f q (x 2 )  ̃̃  D h (z) f q (x 1 )   ̃̃  D h (z) Hard scales P T and Q 2 Convolution integrals over all involved momenta Factorization of involved distribution and fragmentation functions (k T )-dependent distribution and fragmentation functions k k’ Q

6. R.Seidl: Fragmentation function measurements at Belle6 Freiburg, June 6 th Transversity properties Helicity flip amplitude Chiral odd Since all interactions conserve chirality one needs another chiral odd object Does not couple to gluons  different QCD evolution than  q(x) Valence dominated  Comparable to Lattice calculations, especially tensor charge Positivity bound: Soffer bound:

7. R.Seidl: Fragmentation function measurements at Belle7 Freiburg, June 6 th Finding another chiral odd object in SIDIS  Collins fragmentation function Cross section factorizes:  ep  ehX =  q q p  q (x)   QED D q  h (z) Transverse momentum dependent Distribution functionsTransverse momentum dependent Fragmentation functions Both Sivers and Collins Effect create azimuthal asymmetries

8. R.Seidl: Fragmentation function measurements at Belle8 Freiburg, June 6 th Azimuthal asymmetries in SIDIS Sivers and Collins effect are not distiguishable with longitudinally polarized target Higher Twist effects are kinematically favored in longitudinal case With transversely polarized target a 2 nd angle allows to distinguish effects U: unpolarized beam T: transversely polarized target

9. R.Seidl: Fragmentation function measurements at Belle9 Freiburg, June 6 th J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation with of a quark q with spin s q into a spinless hadron h carries an azimuthal dependence: Collins effect in quark fragmentation

10. R.Seidl: Fragmentation function measurements at Belle10 Freiburg, June 6 th The Collins effect in the Artru fragmentation model 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. A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: In Artru Model: favored (ie u    ) and disfavored (ie u    ) Collins function naturally of opposite sign

11. R.Seidl: Fragmentation function measurements at Belle11 Freiburg, June 6 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 ! Universality appears to be proven in LO by Collins and Metz: [PRL93:( 2004)252001 ] +most recent work from Amsterdam Group

12. R.Seidl: Fragmentation function measurements at Belle12 Freiburg, June 6 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

13. R.Seidl: Fragmentation function measurements at Belle13 Freiburg, June 6 th Good tracking and particle identification!

14. R.Seidl: Fragmentation function measurements at Belle14 Freiburg, June 6 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:

15. R.Seidl: Fragmentation function measurements at Belle15 Freiburg, June 6 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)]

16. R.Seidl: Fragmentation function measurements at Belle16 Freiburg, June 6 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]

17. R.Seidl: Fragmentation function measurements at Belle17 Freiburg, June 6 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

18. R.Seidl: Fragmentation function measurements at Belle18 Freiburg, June 6 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2     )

19. R.Seidl: Fragmentation function measurements at Belle19 Freiburg, June 6 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

20. R.Seidl: Fragmentation function measurements at Belle20 Freiburg, June 6 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 (         )

21. R.Seidl: Fragmentation function measurements at Belle21 Freiburg, June 6 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

22. R.Seidl: Fragmentation function measurements at Belle22 Freiburg, June 6 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

23. R.Seidl: Fragmentation function measurements at Belle23 Freiburg, June 6 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

24. R.Seidl: Fragmentation function measurements at Belle24 Freiburg, June 6 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  rescalied with 1.21 Correlation studies:  statististical error rescaled by1.02 (UL) and 0.55 (UC) – after rigorous errorcalculation correct Beampolarization studies  consistent with zero Correction ofcharm events A 0 (cos(2   )) moments A 12 (cos(       )) moments

25. R.Seidl: Fragmentation function measurements at Belle25 Freiburg, June 6 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

26. R.Seidl: Fragmentation function measurements at Belle26 Freiburg, June 6 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

27. R.Seidl: Fragmentation function measurements at Belle27 Freiburg, June 6 th Global Analysis - SIDIS measurements I: HERMES (proton) Nonzero Asymmetries  Collins function and Transversity nonzero Same magnitude, opposite sign for    and   Asymmetries  Hint for a large and negative disfavored Collins function PRL 94, 012002 (2005) and hep-ex/0612010 Taken at  QSM value of  r = -0.30 of Schweitzer and Wakamatsu HH

28. R.Seidl: Fragmentation function measurements at Belle28 Freiburg, June 6 th Global Analysis - SIDIS measurements II: COMPASS (deuteron) Smaller asymmetries than in proton case  Hint of cancellation of transversity in isoscalar target PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007 -A Coll First fits to HERMES and COMPASS data using assumptions on Transversity show results consistent with each other Kaon asymmetries shown last year (both experiments)

29. R.Seidl: Fragmentation function measurements at Belle29 Freiburg, June 6 th Global Analysis- Belle Collins function: asymmetries for double ratios of  unlikesign  likesign for 29 fb -1 Direct measurement of the Collins effect Collins function large Consistent with large, negative disfavored Collins function RS et al., PRL 96, 232002 (2006) +inclusion of  (4S) data:  >500 fb -1 (not yet included in global fit by Anselmino et al: hep-ex 0701006) PRELIMINARY

30. R.Seidl: Fragmentation function measurements at Belle30 Freiburg, June 6 th First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data HERMES A UT p data COMPASS A UT d data Belle e + e - Collins data Kretzer FF  First extraction of transversity (up to a sign) Anselmino et al: hep-ex 0701006

31. R.Seidl: Fragmentation function measurements at Belle31 Freiburg, June 6 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 and Artru,Collins Early work by Collins, Heppelman, Ladinski Interference fragmentation function  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

32. R.Seidl: Fragmentation function measurements at Belle32 Freiburg, June 6 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

33. R.Seidl: Fragmentation function measurements at Belle33 Freiburg, June 6 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)?

34. R.Seidl: Fragmentation function measurements at Belle34 Freiburg, June 6 th Future measurements I: EIC, transverse spin Transversity at higher x already measured by HERMES, COMPASS and JLAB12, first DY transversity from JPARC or FAIR?  Lower x will be interesting for tensor charge

35. R.Seidl: Fragmentation function measurements at Belle35 Freiburg, June 6 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

36. R.Seidl: Fragmentation function measurements at Belle36 Freiburg, June 6 th Backup Slides Belle

37. R.Seidl: Fragmentation function measurements at Belle37 Freiburg, June 6 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

38. R.Seidl: Fragmentation function measurements at Belle38 Freiburg, June 6 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 ”

39. R.Seidl:The W physics program at PHENIX 39 PVSA, BNL April 27 th Sivers interpretation Taken from H. Tanaka in Trento’04 Attractive rescattering of hit quark by gluon creates transverse momentum M.Burkardt [hep-ph0309269] – impact parameter formalism Orbital angular momentum at finite impact parameter observed and true x differ Observable left/right asymmetry >