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 QCD: : very small Single transverse spin asymmetries pick up: –Sivers Effect: k T in quark distribution –Quark transverse polarization x Collins fragmentation function: k T in fragmentation function δq x CFF 3 Transversity PHENIX, forward    at s = 62 GeV, nucl-ex/0701031

4. Transversity Quark Distributions δq(x) from Transverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS) 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 Example: New COMPASS results for Collins Asymmetries on proton target (consistent with previous HERMES results)

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

7. o Quark spin direction unknown: measurement of Collins function in one hemisphere is not possible sin φ modulation will average out. o Correlation between two hemispheres with sin φ i Collins single spin asymmetries results in cos(φ 1 +φ 2 ) modulation of the observed di-hadron yield. Measurement of azimuthal correlations for pion pairs around the jet axis in two-jet events! Collins FF in e + e - : Need Correlation between Hemispheres !

8. 8 q1q1 quark-1 spin 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 Collins Effect in di-Hadron Correlations In e + e - Annihilation into Quarks! electron positron q2q2 quark-2 spin z2z2 z1z1 z 1,2 relative pion momenta

9. KEKB: L>1.96 x 10 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 9 Belle detector KEKB

10. Collins Asymmetries in Belle10 May 28 th Large acceptance, good tracking and particle identification!

11. 11 Measuring Light Quark Fragmentation Functions on the ϒ (4S) Resonance 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 e + e -  qq̅, q ∈ uds e + e -  cc̅ 0.5 0.8 1.0 4s “off”

12. 12 Collins Fragmentation: Angles and Cross Section: cos(     ) Method (e+e- CMS frame)       2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins  e-e- e+e+ Observable: yield, N 12 ( φ 1 +φ 2 ) of π + π - pairs

13. 13 Collins Fragmentation: Angles and Cross Section cos(2   ) Method (CMS Frame)  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 [Boer,Jakob,Mulders: NPB504(1997)345] e-e- e+e+ Observable: yield, N 0 ( 2φ 0 ) of π + π - pairs

14. Examples of fits to azimuthal asymmetries 14 D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0 22     ) Cosine modulations clearly visible P1 contains information on Collins function

15. 15 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. 16 Applied Cuts, Binning Two data sets: off-resonance data ( 29.1 fb -1 ) on-resonance data ( 547 fb -1 ) Track selection: –p T > 0.1GeV –vertex cut: dr < 2cm, |dz| <4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –N track  3 –Thrust > 0.8 –z 1, z 2 > 0.2 Hemisphere cut Q T < 3.5 GeV Pion PID selection z2z2 0 123 456 78 9 0.2 0.3 0.5 0.7 1.0 0.20.30.50.71.0 5 86 1 2 3 z1z1 (z 1, z 2 )-binning

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

18. Combined Analysis: Extract Transversity Distributions Transversity, δq(x) Tensor Charge Lattice QCD: Tensor Charge Factorization + Evolution Theory SIDIS ~ δq(x) x CFF(z) ~ δq(x) x IFF(z) e + e - ~ CFF(z 1 ) x CFF(z 2 ) ~ IFF(z 1 ) x IFF(z 2 ) pp  jets ~ G(x 1 ) x δq(x 2 ) x CFF(z) pp  h + + h - + X ~ G(x 1 ) x δq(x 2 ) x IFF(z) pp  l + + l - + X ~ δq(x 1 ) x δq(x 2 )

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

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

21. Interference Fragmentation–thrust method e + e -  (  +  - ) jet1 (     ) jet2 X 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) 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  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

22. Expected sensitivities for ~580 fb -1 (     ) (     ) M inv <0.4 GeV0.4 GeV<M inv <0.55 GeV0.55 GeV<M inv <0.77 GeV 0.77 GeV <M inv < 1.2 GeV 1.2 GeV M inv < 2.0 GeV A AA A A

23. (     ) (     ) A A A AA M inv <0.4 GeV 0.4 GeV<M inv <0.55 GeV 0.55 GeV<M inv <0.77 GeV 0.77 GeV <M inv < 1.2 GeV 1.2 GeV M inv < 2.0 GeV

24. (     ) (K    ) M inv <0.7 GeV0.7 GeV<M inv <0.85 GeV 0.85 GeV<M inv <1.0 GeV 1.0 GeV<M inv A A A A A

25. 25 Measurements of quark transversity p+p SIDIS e + +e - E704, 1991 Large forward SSA STAR, PHENIX, BRAHMS, 2004~2005 Inclusive A N HERMES 2005, COMPASS 2006 A UT BELLE 2006 Collins FF BELLE IFF RHIC IFF asym. RHIC Collins asym. JParc, RHIC, FAIR Drell-Yan COMPASS p target JLab 3 He and 12 GeV Underway Future 19912005 BELLE k T dep. Pol. & upol FF, pol. Lambda FF

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

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 Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006) Two different theoretical models gave different prediction of mass dependence Sign change is not observed in HERMES/COMPASS results

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

29. IFF in SIDIS  R defined by: R = (z 1 p 2 – z 2 p 1 )/(z 1 +z 2 ) (X. Artru, hep-ph/0207309) R

30. Di-Hadron SSA in SIDIS

31. Summary & Outlook Collins FF at Belle final ->global analysis 2H Interference FF Analysis underway Plans for k T 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 Proposed Transverse Spin Sum rule Bakker, Leader, Trueman Phys.Rev.D70:114001,2004 Gluon contribution is Small (Phenix, Compass results)