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Precision fragmentation function measurements at Belle

Precision fragmentation function measurements at Belle. 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

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Precision fragmentation function measurements at Belle

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  1. Precision fragmentation function measurements at Belle • 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 Freiburg, June 6 2007 R. Seidl (University of Illinois and RBRC)

  2. Why QCD and spin physics? “You think you understand something? Now add spin ...” – R. Jaffe • 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 R.Seidl: Fragmentation function measurements at Belle

  3. The (spin) structure of the Nucleon Longitudinal Spin Sum Rule: W-production (pp) Exclusive processes (DVCS,etc) Double Spin Asymmetries (pp,SIDIS) Transverse Spin (BLT) Sum Rule? ColorGlasscondensate ?? Chiral-odd Fragmentation functions (Collins,IFF,L) Sivers effect?? R.Seidl: Fragmentation function measurements at Belle

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

  5. Cross sections in (semi)inclusive pp and DIS, factorization k’ fq(x1) fq(x2)  s̃̃ Dh(z) k Q fq(x1) s̃̃ Dh(z) • Hard scales PT and Q2 • Convolution integrals over all involved momenta • Factorization of involved distribution and fragmentation functions • (kT)-dependent distribution and fragmentation functions R.Seidl: Fragmentation function measurements at Belle

  6. Transversity properties • Helicity flip amplitude • Chiral odd • Since all interactions conserve chirality one needs another chiral odd object • Does not couple to gluons adifferent QCD evolution than Dq(x) • Valence dominateda Comparable to Lattice calculations, especially tensor charge Positivity bound: Soffer bound: R.Seidl: Fragmentation function measurements at Belle

  7. Finding another chiral odd object in SIDIS a Collins fragmentation function Cross section factorizes: sepgehX = Sqqpgq(x)sQED Dqgh(z) Transverse momentum dependent Distribution functions Transverse momentum dependent Fragmentation functions Both Sivers and Collins Effect create azimuthal asymmetries R.Seidl: Fragmentation function measurements at Belle

  8. 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 2nd angle allows to distinguish effects U: unpolarized beam T: transversely polarized target R.Seidl: Fragmentation function measurements at Belle

  9. Collins effect in quark fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation with of a quark qwith spin sqinto a spinless hadron h carries an azimuthal dependence: R.Seidl: Fragmentation function measurements at Belle

  10. 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. In Artru Model: favored (ie up+) and disfavored (ie up-) Collins function naturally of opposite sign R.Seidl: Fragmentation function measurements at Belle

  11. Towards a global transversity analysis SIDIS experiments (HERMES and COMPASS, eRHIC) 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 ] +most recent work from Amsterdam Group Spin dependent Fragmentation function analysis in e+e- Annihilation yields information on the Collins and the Interference Fragmentation function ! R.Seidl: Fragmentation function measurements at Belle

  12. KEKB: L>1.6x1034cm-2s-1 !! Belle detector 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: >700 fb-1 • >60fb-1 => off-resonance R.Seidl: Fragmentation function measurements at Belle

  13. Good tracking and particle identification! R.Seidl: Fragmentation function measurements at Belle

  14. 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 R.Seidl: Fragmentation function measurements at Belle

  15. 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 R.Seidl: Fragmentation function measurements at Belle

  16. 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- Q2 j0 [Boer,Jakob,Mulders: NPB504(1997)345] e+ 2-hadron inclusive transverse momentum dependent cross section: Net (anti-)alignment of transverse quark spins R.Seidl: Fragmentation function measurements at Belle

  17. Off-resonance data 60 MeV below U(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 < cosqi< 0.9 Event selection: Ntrack  3 Thrust > 0.8 Z1, Z2>0.2 Applied cuts, binning z2 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 z1 R.Seidl: Fragmentation function measurements at Belle

  18. Examples of fits to azimuthal asymmetries Cosine modulations clearly visible N(f)/N0 2f0 (f1+f2) D1 : spin averaged fragmentation function, H1: Collins fragmentation function No change in cosine moments when including sine and higher harmonics R.Seidl: Fragmentation function measurements at Belle

  19. 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 R.Seidl: Fragmentation function measurements at Belle

  20. Testing the double ratios with MC • Asymmetries do cancel out for MC • Double ratios of p+p+/p-p- compatible with zero • Mixed event pion pairs 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 (UL/L double ratios) • uds MC (UL/C double ratios) • Data (p+p+/p-p-) R.Seidl: Fragmentation function measurements at Belle

  21. Other Favored/Unfavored Combinations charged pions or p0 Challenge: current double ratios not very sensitive to favored to disfavored Collins function ratio  Examine other combinations: • Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) • Like-sign pion pairs (L): (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 easier to handle) (C): (favored + unfavored) x (favored + unfavored) UL UC • Build new double ratios: • Unlike-sign/ charged pp pairs (UC) Favored = up+,dp-,cc. Unfavored = dp+,up-,cc. R.Seidl: Fragmentation function measurements at Belle

  22. What about the data under the resonance? • More than 540 fb-1 of on_resonance data • U(4S) is just small resonance • More than 75% of hadronic cross section from open quark-antiquark production R.Seidl: Fragmentation function measurements at Belle

  23. Why is it possible to include on_resonance data?Different Thrust distributions • e+ e- q q (u d s) MC • U(4S)B+B- MC • U(4S)B0B0 MC • Largest systematic errors reduce with • more statistics • Charm-tagged Data sample also • increases with statistics R.Seidl: Fragmentation function measurements at Belle

  24. Improved systematic errors (UC) • Tau contribution • PID error • MC double ratios • Charged ratios (p+p+ /p-p- ) • higher moments in Fit • difference double ratio-subtraction method A0 (cos(2f0)) moments A12 (cos(f1 +f2)) moments • reweighted MC-asymmetries: cos(f1+f2) 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 R.Seidl: Fragmentation function measurements at Belle

  25. Final charm corrected results for e+ e-p p X (29fb-1 of continuum data) Final results Preliminary results • Significant non-zero asymmetries • Rising behavior vs. z • cos(f1+f2) double ratios only marginally larger • UC asymmetries about 40-50% of UL asymmetries • First direct measurements of the Collins function R.Seidl: Fragmentation function measurements at Belle

  26. Charm corrected results for e+ e-p p X (547 fb-1) PRELIMINARY • Significance largely increased • Behavior unchanged • Reduced systematic errors due to statistics • Precise measurements of the Collins function R.Seidl: Fragmentation function measurements at Belle

  27. Global Analysis - SIDIS measurements I: HERMES (proton) • Nonzero Asymmetries • Collins function and Transversity nonzero • Same magnitude, opposite sign for p+and p- Asymmetries • Hint for a large and negative disfavored Collins function hH PRL 94, 012002 (2005) and hep-ex/0612010 Taken at cQSM value of dr = -0.30 of Schweitzer and Wakamatsu R.Seidl: Fragmentation function measurements at Belle

  28. Global Analysis - SIDIS measurements II: COMPASS (deuteron) -AColl • 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 • First fits to HERMES and COMPASS data using assumptions on Transversity show results consistent with each other • Kaon asymmetries shown last year (both experiments) R.Seidl: Fragmentation function measurements at Belle

  29. Global Analysis- Belle Collins function: asymmetries for double ratios of ppunlikesign / pplikesign for 29 fb-1 PRELIMINARY • Direct measurement of the Collins effect • Collins function large • Consistent with large, negative disfavored Collins function + inclusion of U(4S) data:  >500 fb-1 (not yet included in global fit by Anselmino et al: hep-ex 0701006) RS et al., PRL 96, 232002 (2006) R.Seidl: Fragmentation function measurements at Belle

  30. First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data • HERMES AUTp data • COMPASS AUT d data • Belle e+ e- Collins data • Kretzer FF  First extraction of transversity (up to a sign) Anselmino et al: hep-ex 0701006 R.Seidl: Fragmentation function measurements at Belle

  31. 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 Early work by Collins, Heppelman, Ladinski Interference fragmentation function j2-p p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)] R.Seidl: Fragmentation function measurements at Belle

  32. Different model predictions for IFF PRELIMINARY f1, h1 from spectator model f1, h1=g1 from GRV98 & GRSV96 • Jaffe et al. [Phys. Rev. Lett. 80 (1998)] : inv. mass behavior out of pp-phaseshift analysisasign change at r-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 channelano sign change observed (updated model has Breit-Wigner like asymmetry) R.Seidl: Fragmentation function measurements at Belle

  33. Unpolarized FF as important input for allprecise QCD measurements MC simulation, ~1.4 fb-1 • No low-Q2 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)? 2. R.Seidl: Fragmentation function measurements at Belle

  34. 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 R.Seidl: Fragmentation function measurements at Belle

  35. 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 spindependent fragmentation functions at Belle • kT 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 L-fragmentation function • Event shapes • R-ratio with ISR R.Seidl: Fragmentation function measurements at Belle

  36. Backup Slides Belle R.Seidl: Fragmentation function measurements at Belle

  37. Similar to previous method Observe angles j1R+j2R between the event-plane (beam, two-pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation – “f0“ method jR2 p-jR1 R.Seidl: Fragmentation function measurements at Belle

  38. What would we see in e+e-? Simply modeled the shapes of these predictions in an equidistant Mass1 x Mass2 binning m2pp m2pp m1pp m1pp “Jaffe” “Radici” R.Seidl: Fragmentation function measurements at Belle

  39. Sivers interpretation • 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 Taken from H. Tanaka in Trento’04 > R.Seidl:The W physics program at PHENIX

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