Fragmentation Functions at Belle 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) for the Belle collaboration SPIN2008, University of Virginia

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 PHENIX Summary & Outlook

Motivation: Transversity Quark Distributions δq(x) from Transverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering 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: COMPASS results for Collins Asymmetries on proton target (see talk by H. Wollny)

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:

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

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 !

7 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

KEKB: L>1.7x10 34 cm -2 s -1 !! Asymmetric collider 8GeV e GeV e + √s = 10.58GeV (  (4S)) e + e -   (4S)  B  B Continuum production: GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: >700 fb -1 >60fb -1 => continuum 8 Belle detector KEKB

Collins Asymmetries in Belle9 May 28 th Large acceptance, good tracking and particle identification!

10 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

11 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

Examples of fits to azimuthal asymmetries 12 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 22     ) Cosine modulations clearly visible P1 contains information on Collins function

13 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

14 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 Charm-tagged Data sample also increases e + e -  qq̅, q ∈ uds e + e -  cc̅ s “off”

15 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 z2z z1z1 (z 1, z 2 )-binning

Final Collins results Belle 547 fb -1 data set (Phys.Rev.D78:032011,2008.) 16

Combined Analysis: Extract Transversity Distributions Transversity, δq(x) Tensor Charge Lattice QCD: Tensor Charge Factorization + Universality ?! 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 )

18 Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk and Melis at Transversity 2008, Ferrara. Previously: Phys. Rev. D75:05032,2007 HERMES SIDIS + COMPASS SIDIS + 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 Old fit

19 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!

20 Why di-hadron SSA in SIDIS & p+p Di-hadron vs single hadron – Collinear factorization – No model uncertainties due to k T dependence of FF and PDF – Doesn’t need quark momentum – No need to separate effects like Sivers/Collins effects in single hadron measurement – Completely independent measurement Di-hadron measurement in fixed target vs collider – At higher scale sub-leading twist effects suppressed factorization assumption better justified

Interference Fragmentation – thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Stay in the mass region around r-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[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 21  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

Expected sensitivities for 60 fb -1 (     ) (     ) pairs as a function of the invariant mass m ,1 x m ,2 Similar distributions to be shown as a function of z ,1 x z ,2 Other hadron combinations 22

23 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 Courtesy Ruizhe Yang

24 Definition of Vectors and Angles Bacchetta and Radici, PRD70, (2004)

25 vs invariant mass of the pair Consistent with 0, despite the second bin of  0 h - pairs and the last bin of h + h - pairs are 2  from 0. Systematic errors Polarization 5% Relative lumi. 5x10 -4 No systematic effects detected from bunch shuffling Ruizhe Yang, U of I, PKU RBRC Workshop 2008

26 Future Prospects from future large transverse spin data sample from PHENIX Sub-percent sensitivity possible

Summary & Outlook Collins FF at Belle final ->global analysis 2H Interference FF Analysis underway Plans for k_T dependent Upol FFs – Necessary for global analysis w/o model assumptions 2H Interference FF at Phenix – First measurement of IFF at p-p collider – Analysis of 2008 data underway