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Transverse Spin-dependent Fragmentation Functions at Belle Experiment

This outline discusses the extraction of transversity using Collins Fragmentation Functions at Belle, including experimental techniques and recent results from pp and SIDIS. The text explores the Collins Effect in quark fragmentation, emphasizing azimuthal asymmetries and di-hadron correlations in e+e- annihilation. It delves into the challenges of measuring the Collins function due to unknown quark spin directions. Various methods to eliminate gluon contributions, like double ratios and subtraction, are detailed, along with applied cuts and binning strategies for data analysis.

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Transverse Spin-dependent Fragmentation Functions at Belle Experiment

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  1. Transverse Spin dependent Fragmentation Functions at Anselm Vossen (University of Illinois) Matthias Grosse Perdekamp (University of Illinois) Martin Leitgab (University of Illinois) Akio Ogawa (BNL/RBRC) Ralf Seidl (RBRC) Kieran Boyle (RBRC)

  2. Outline • Motivation • Collins FF for transversity extraction in global QCD Analysis of single transverse spin asymmetries in pp and SIDIS • Measuring Fragmentation Functions at Belle • Experimental techniques • Collins FF results • Interference Fragmentation Functions • Planned measurements of IFF at Belle • Recent results from pp and SIDIS • Summary & Outlook

  3. Transverse Spin Asymmetries at RHIC PHENIX, forward p0at s = 62 GeV, nucl-ex/0701031 Transversity • QCD: : very small • Single transverse spin asymmetries pick up: • Sivers Effect: kT in quark distribution • Quark transverse polarization x Collins fragmentation function: kT in fragmentation function δq x CFF 3

  4. Transversity Quark Distributions δq(x)from Transverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS) Example: New COMPASS results for Collins Asymmetries on proton target (consistent with previous HERMES results) Collins- and IFF- asymmetries in semi-inclusive deep inelastic scattering (SIDIS) and pp measure ~ δq(x) x CFF(z)  combined analysis with CFF from e+e- annihilation

  5. Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence:

  6. General Form of Fragmentation Functions Number density for finding hadron h from a transversely polarized quark, q: unpolarized FF Collins FF 6

  7. Collins FF in e+e- : Need Correlation between Hemispheres ! • Quark spin direction unknown: measurement of • Collins function in one hemisphere is not possible • sin φ modulation will average out. • Correlation between two hemispheres with • sin φi Collins single spin asymmetries results in • cos(φ1+φ2) modulation of the observed di-hadron • yield. • Measurement of azimuthal correlations for pion pairs • around the jet axis in two-jet events!

  8. Collins Effect in di-Hadron Correlations In e+e- Annihilation into Quarks! • Collins effect in e+e- • quark fragmentation • will lead to azimuthal • asymmetries in di-hadron • correlation measurements! • Experimental requirements: • Small asymmetries  • very large data sample! • Good particle ID to high • momenta. • Hermetic detector electron q1 z2 z1 q2 quark-1 spin quark-2 spin z1,2 relative pion momenta positron 8

  9. KEKB: L>1.96 x 1034cm-2s-1 !! Belle detector KEKB • Asymmetric collider • 8GeV e- + 3.5GeV e+ • √s = 10.58GeV (U(4S)) • e+e-U(4S)BB • Continuum production: 10.52 GeV • e+e-qq (u,d,s,c) • Integrated Luminosity: >700 fb-1 • >60fb-1 => continuum 9

  10. Large acceptance, good tracking and particle identification! Collins Asymmetries in Belle 10 May 28th

  11. Measuring Light Quark Fragmentation Functions on the ϒ(4S) Resonance e+e-qq̅, q∈uds 4s “off” e+e-cc̅ • small B contribution (<1%) in high thrust sample • >75% of X-section continuum under • ϒ(4S) resonance • 29 fb-1 547 fb-1 • several systematic errors reduce with more • statistics 0.5 0.8 1.0 11

  12. Collins Fragmentation: Angles and CrossSection: cos(f1+f2) Method (e+e- CMS frame) Observable: yield, N12 ( φ1+φ2 )of π+π- pairs j2-p e- Q j1 j2 j1 e+ 2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins 12

  13. Collins Fragmentation: Angles and Cross Section cos(2f0) Method (CMS Frame) Observable: yield, N0 ( 2φ0 ) of π+π- pairs e- Q Independent of thrust-axis Convolution integralI over transverse momenta [Boer,Jakob,Mulders: NPB504(1997)345] j0 e+ 2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins 13

  14. Examples of fits to azimuthal asymmetries Cosine modulations clearly visible P1 contains information on Collins function N(f)/N0 2f0 (f1+f2) D1 : spin averaged fragmentation function, H1: Collins fragmentation function 14

  15. 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 15

  16. Applied Cuts, Binning Two data sets: off-resonance data ( 29.1 fb-1 ) 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 • Hemisphere cut • QT < 3.5 GeV • Pion PID selection (z1, z2)-binning z2 1.0 3 6 8 9 0.7 2 5 7 8 0.5 1 4 5 6 0.3 1 2 3 0 0.2 0.2 0.3 0.5 0.7 1.0 z1 16

  17. Final Collins results Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.) 17

  18. Combined Analysis: Extract Transversity Distributions Factorization + Evolution e+e- ~ CFF(z1) x CFF(z2) ~ IFF(z1) x IFF(z2) SIDIS ~ δq(x) x CFF(z) ~ δq(x) x IFF(z) pp  jets ~ G(x1) x δq(x2) x CFF(z) pp  h+ + h- + X ~ G(x1) x δq(x2) x IFF(z) pp  l+ + l- + X ~ δq(x1) x δq(x2) Transversity, δq(x) Tensor Charge Theory Lattice QCD: Tensor Charge

  19. Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e+e- Fit includes: Soffer Bound HERMES SIDIS (p) + COMPASS SIDIS (d) + Belle e+e- Old fit New fit transversity dist. + Collins FF Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk and Melis at Transversity 2008, Ferrara. Previously: Phys. Rev. D75:05032,2007 19

  20. Collins Extraction of Transversity:unknown Transverse Momentum Dependences! Collins FF transversity hadron FF quark pdf k┴transverse quark momentum in nucleon p┴ transverse hadron momentum in fragmentation Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 The transverse momentum dependencies are unknown and very Difficult to obtain experimentally! 20

  21. Interference Fragmentation–thrust method j2-p p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)] • e+e-(p+p-)jet1(p-p+)jet2X • Find pion pairs in opposite hemispheres • Observe angles j1+j2between 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) collinear factorization • Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] • Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] • Independent Measurement • Favourable in pp: no Sivers 21

  22. Expected sensitivities for ~580 fb-1 (p+p-) (p+p-) A A A Minv<0.4 GeV 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV A A 0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

  23. (p+p0) (p+p0) A A A 0.4 GeV<Minv<0.55 GeV 0.55 GeV<Minv<0.77 GeV Minv<0.4 GeV A A 0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

  24. (p+K-) (K+p-) A A Minv<0.7 GeV 0.7 GeV<Minv<0.85 GeV A A A 0.85 GeV<Minv<1.0 GeV 1.0 GeV<Minv

  25. Measurements of quark transversity 1991 2005 Underway Future p+p RHIC Collins asym. STAR, PHENIX, BRAHMS, 2004~2005 Inclusive AN E704, 1991 Large forward SSA RHIC IFF asym. JParc, RHIC, FAIR Drell-Yan HERMES 2005, COMPASS 2006 AUT SIDIS COMPASS p target JLab 3He and 12 GeV BELLE 2006 Collins FF BELLE IFF e++e- BELLE kT dep. Pol. & upol FF, pol. Lambda FF 25

  26. Definition of Vectors and Angles Bacchetta and Radici, PRD70, 094032 (2004) 26

  27. Models • Main contribution: interference of hadron pairs produced in relative s and p wave • P wave from Vector meson decay • S wave from non-resonant background • Signal around vector meson mass • Two different theoretical models gave different prediction of mass dependence • Sign change is not observed in HERMES/COMPASS results Jaffe, Jin and Tang, PRL 80 (1998) 1166 Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006)

  28. SSA from di-hadron production See Talk R. Yang

  29. IFF in SIDIS • R defined by: • R = (z1p2 – z2p1)/(z1+z2) • (X. Artru, hep-ph/0207309) R

  30. Di-Hadron SSA in SIDIS

  31. Summary & Outlook Gluon contribution is Small (Phenix, Compass results) Proposed Transverse Spin Sum rule Bakker, Leader, Trueman Phys.Rev.D70:114001,2004 • Collins FF at Belle final ->global analysis • 2H Interference FF Analysis underway • Plans for kT dependent Pol. & Upol. FFs • Necessary for global analysis w/o model assumptions • Polarized Lambda FF • 2H Interference FF Measurements at Phenix, HERMES and COMPASS • Non vanishing effect at HERMES and COMPASS • Together with Belle results -> Independent extraction of transversity

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