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## Fragmentation Functions at Belle

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**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 Example: COMPASS results for Collins Asymmetries on proton target (see talk by H. Wollny) 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**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:**General Form of Fragmentation Functions**Number density for finding hadron h from a transversely polarized quark, q: unpolarized FF Collins FF**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!**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**Belle detector**KEKB KEKB: L>1.7x1034cm-2s-1 !! • Asymmetric collider • 8GeV e- + 3.5GeV e+ • √s = 10.58GeV (U(4S)) • e+e-U(4S)BB • Continuum production: 10.52 GeV • e+e-qq (u,d,s,c) • Integrated Luminosity: >700 fb-1 • >60fb-1 => continuum**Large acceptance, good tracking and particle identification!**Collins Asymmetries in Belle**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**Collins Fragmentation: Angles and Cross Sectioncos(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**Examples of fits toazimuthal 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 No change in cosine moments when including sine and higher harmonics**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**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 • Charm-tagged Data sample also increases 0.5 0.8 1.0**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 Applied Cuts, Binning • 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**Final Collins results**Belle 547 fb-1 data set (Phys.Rev.D78:032011,2008.)**Combined Analysis: Extract Transversity**Distributions Factorization + Universality ?! 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**Extraction of Quark Transversity Distributions**and Collins Fragmentation Functions SIDIS + e+e- Fit includes: Soffer Bound HERMES SIDIS New fit + COMPASS SIDIS Old fit + 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**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!**Why di-hadron SSA in SIDIS & p+p**• Di-hadron vs single hadron • Collinear factorization • No model uncertainties due to kT 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**j2-p • 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+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) • Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] • Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] p-j1 • Model predictions by: • Jaffe et al. [PRL 80,(1998)] • Radici et al. [PRD 65,(2002)]**Expected sensitivities for 60 fb-1**• (p+p-) (p+p-) pairs as a function of the invariant mass mpp,1 x mpp,2 • Similar distributions to be shown as a function of zpp,1 x zpp,2 • Other hadron combinations**Courtesy**Ruizhe Yang 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-**Definition of Vectors and Angles**Bacchetta and Radici, PRD70, 094032 (2004)**vs invariant mass of the pair**Ruizhe Yang, U of I, PKU RBRC Workshop 2008 Consistent with 0, despite the second bin of p0h- pairs and the last bin of h+h- pairs are 2s from 0.**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