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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

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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

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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)

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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:

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

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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 !

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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

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KEKB: L>1.7x10 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 8 Belle detector KEKB

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

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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

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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

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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 22 ) Cosine modulations clearly visible P1 contains information on Collins function

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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

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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 0.5 0.8 1.0 4s “off”

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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 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

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

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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 )

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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

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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!

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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

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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)]

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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

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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 19912005 Courtesy Ruizhe Yang

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

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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

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

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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

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