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Transverse Spin Dependent Di-Hadron Fragmentation Functions at

Transverse Spin Dependent Di-Hadron 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). Outline. Motivation

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Transverse Spin Dependent Di-Hadron Fragmentation Functions at

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  1. Transverse Spin DependentDi-Hadron 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 • Analysis of Transverse Spin Effects in SIDIS, proton-proton • Recent experimental results • Transversity extraction • Measuring Fragmentation Functions at Belle • Experimental techniques • Interference Fragmentation Function Measurement • Comparison with theory • Summary & Outlook

  3. Transverse Spin Asymmetries • Experimental results in SIDIS and pp

  4. Transverse Spin Asymmetries- Single Hadrons PHENIX, forward p0at s = 62 GeV, nucl-ex/0701031 • Large transverse single spin effects persist at large scale • Convolution of different effects Transversity 4

  5. Transverse Spin Asymmetries • Experimental results in SIDIS and pp • Access to fundamental aspects of QCD and nucleon structure: • TMDs, orbital angular momentum • Initial, final state interactions • Gauge invariance of correlators • Prominent effects: • Transversity * Collins • Sivers Effect • Separation of different effects requires measurements at multiple experiments, channels -> pp, SIDIS, e+e-

  6.    ↑ ↓ ↓ ↑ ↑ ↑ ↑ ↑ Measuring Transversity in SIDIS • Transversity base:   _ _ + = _ + Difference in densities for ↑, ↓ quarks in ↑ nucleon • Helicity base: • Need chiral odd partner => Fragmentation function

  7. _ Chiral odd FFs Collins effect + * * _ + q N _ + : Collins FF

  8. Collins Fragmentation at Belle • First extraction of transversity quark distribution Together with HERMES, COMPASS First, still model dependent transversity Extraction : • Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex 0701006 Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)

  9. Collins Extraction of Transversity: model dependence from 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 difficult to obtain experimentally!

  10. Lz Lz-1 _ Chiral odd FFs Interference Fragmentation Function + * * _ + q N _ +

  11. Advantages of IFF • Independent Measurement • Favourable in pp: no Sivers • Transverse momentum is integrated • Collinear factorization • No assumption about kt in evolution • Universal function • evolution known, collinear scheme can be used • directly applicable to semi-inclusive DIS and pp • First experimental results from HERMES, COMPASS, PHENIX

  12. Interference FF in Quark Fragmentation q Interference Fragmentation Function: Fragmentation of a transversely polarized quark q into two spin-less hadron h1, h2 carries an azimuthal dependence:

  13. Di-Hadron SSA in SIDIS (both on proton target, sign convention different)

  14. SSA from di-hadron production Extended kinematic regime compared with SIDIS Hard scale As expected: No significant asymmetries seen at central-rapidity. Added statistics from 2008 running

  15. General Form of Fragmentation Functions Number density for finding Hadron pairwith invariant mass MPair from a transversely polarized quark, q: unpolarized FF Interference FF 15

  16. Spin Dependent FF in e+e- : Need Correlation between Hemispheres ! • Quark spin direction unknown: measurement of • Interference Fragmentation function in one hemisphere is not possible • sin φ modulation will average out. • Correlation between two hemispheres with • sin φRi single spin asymmetries results in • cos(φR1+φR2) modulation of the observed di-hadron • yield. • Measurement of azimuthal correlations for di-pion pairs • around the jet axis in two-jet events!

  17. Measuring di-Hadron Correlations In e+e- Annihilation into Quarks • Interference 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 q2 z1 quark-1 spin quark-2 spin z1,2 relative pion pair momenta positron 17

  18. KEKB: L>2.11 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: ~ 950 fb-1 • >70 fb-1 => continuum 18

  19. He/C2H6 Large acceptance, good tracking and particle identification! Collins Asymmetries in Belle 19 May 28th

  20. Interference Fragmentation–thrust method j2-p p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)] Amplitude of modulationdirectly measures IFF! (squared) e+e-(p+p-)jet1(p-p+)jet2X Find pion pairs in opposite hemispheres Measure azimuthal correlations of Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 20 (Here: z1, (z2)relative momenta of first (second) pair)

  21. 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 • 73 fb-1 662 fb-1 0.5 0.8 1.0 21

  22. Asymmetry extraction • Build normalized yields: • Fit with: or 22 Amplitude a12 directly measures IFF! (squared)

  23. Zero tests: MC No opening cut Opening cut>0.7 Opening cut >0.8 Ph A small asymmetry seen due to acceptance effect Mostly appearing at boundary of acceptance Opening cut in CMS of 0.8 (~37 degrees) reduces acceptance effect to the sub-per-mille level 23

  24. Zero tests: Mixed Events False Asymmetries consistent with zero (Red/blue points: Thrust axis last or current event)

  25. Weighted MC asymmetries Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed Inject asymmetries in Monte Carlo Reconstruction smears thrust axis, ~94% of input asymmetry is reconstructed (Integrated over thrust axis: 98%) Effect is understood, can be reproduced in Toy MC Asymmetries corrected 25

  26. Cuts and Binning Similar to Collins analysis, full off-resonance and on-resonance data (7-55): ~73 fb-1 + 588 fb-1 Visible energy >7GeV PID: Purities in Pion/Pion Sample > 90% Same Hemisphere cut within pair (p+p-), opposite hemisphere between pairs All 4 hadrons in barrel region: -0.6 < cos (q) <0.9 Thrust axis in central area: abs(thrustz)<0.75 Thrust > 0.8 zhad1,had2>0.1 z1 = zhad1+zhad2 and z2 in 9x9 bins mpp1 and mpp2 in 8x8 bins: [0.25 - 2.0] GeV 26

  27. First observation of IFF asymmetries in in e+e- coming up…

  28. Results including systematic errors Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary 28 8x8 m1 m2 binning

  29. Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary Preliminary 9x9 z1 z2 binning

  30. Comparison with Collins FF extraction • a12 Asymmetries directly measure IFF squared • IFF asymmetries can be integrated over kt • No double ratios necessary to cancel gluon radiation effects

  31. Subprocess contributions (MC) 9x9 z1 z2 binning tau contribution (only significant at high z) charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution)

  32. Subprocess contributions (MC) Data not corrected for Charm contributions 8x8 m1 m2 binning charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at highest masses) uds (main contribution) Charm Asymmetries in simulated data consistent with zero! To be checked with charm enhanced sample 32

  33. Systematic Errors • Dominant: • MC asymmetry + its statistical error (up to % level) • Smaller contributions: • mixed asymmetries: per mille level • higher moments: sub per mille level • axis smearing, • tau contribution • Charm contributions • Possible Gluon radiation not accounted for

  34. Model predictions for e+e- Invariant mass1 dependence for increasing z1 z1 dependence for increasing z2 Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009. 34

  35. Comparison to theory predictions Leading order, experimental results might contain effects from gluon radiation not contained in the model Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm ) Z dependence : Rising behavior steeper However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well 35

  36. Projections for (p+p0) (p+p0) for 580 fb-1 a12 0.55 GeV<Minv<0.77 GeV a12 a12 0.4 GeV<Minv<0.55 GeV Minv<0.4 GeV a12 a12 0.77 GeV <Minv< 1.2 GeV 1.2 GeV Minv< 2.0 GeV

  37. Projections for (p+K-) (K+p-) for 580 fb-1 A a12 a12 Minv<0.7 GeV 0.7 GeV<Minv<0.85 GeV a12 a12 0.85 GeV<Minv<1.0 GeV 1.0 GeV<Minv

  38. 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

  39. 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 39

  40. Summary • First measurement of Interference Fragmentation Function! • Asymmetry significant • Combined Analysis of Di-hadron and single hadron measurements possible • Systematic effects to be finalized • Future goal: Combined analysis of SIDIS, pp, e+e- data • Extract transversity • Disentangle contributions to AN

  41. Backup

  42. Charm asymmetries Interference fragmentation functions Charm meeting, June 4th 42

  43. Charm Studies • Look at Events with D0 decay in Pi,K pair • Asymmetries with and without Pi from D0 decay • Way to separate between QCD effects and weak decays? K- c /c D0 p+ /u p+ u

  44. 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 44

  45. 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

  46. 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 46

  47. Final Collins results Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.) 47

  48. 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 48

  49. 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! 49

  50. 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 50

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