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Measurement of Collins Asymmetries in e+e- Annihilation at Belle Workshop on Exclusive Reactions at <a href="talks/ High Momentum Transfer Sandorfi.pdf"> May 24th , Thomas Jefferson Laboratory D. Gabbert Illinois and RBRC M. G.Perdekamp Illinois and RBRC K. Hasuko RIKEN and RBRC S. Lange Frankfurt M. Leitgab Illinois D. Mertens Illinois A. Ogawa BNL and RBRC R. Seidl Illinois and RBRC V. Siegle RBRC for the Belle Collaboration ----------- Outline ------------ o Motivation Collins FF for global QCD analysis of single transverse asymmetries in pp and SIDIS o Collins Asymmetries from e+e- LEP first work on Delphi data in the 90s: Efremov, Smirnova, Tkatchev and Bonivento, Matteuzzi, Kotzinian Experimental technique Results May 24th Measurement of Collins Asymmetries at Belle 2 Motivation Transversity Quark Distributions from Collins- and Interference-Fragmentation New HERMES results for Collins Asymmetries M. Diefenthaler, DIS 2007, Munich Collins- and IFF- asymmetries in SIDIS and pp are of the form ~ Transversity (x) x CFF(z) ~ Transversity (x) x IFF(z) Collins- and IFF- asymmetries in e+e- are of the form ~ CFF(z1) x CFF(z2) ~ IFF(z1) x IFF(z2) global QCD analysis May 24th Measurement of Collins Asymmetries at Belle 3 Global Analysis: RBRC Transversity Workshop 2000 Extract Transversity Distributions SIDIS ⇒ Factorization e + e - ⇒ Collins x Collins transversity × Collins + Universality ?! Interference FF transversity × IFF HERMES, COMPASS, x Interference FF JLAB, EIC Belle RHIC / GSI pp ⇒ Transversity A N for inclusive hadrons, Jets Tensor Charge Theory A T in Jets : transversity × Collins transversity × IFF GSI A TT Drell Yan : Lattice QCD: Tensor Charge transversity × transversity May 24th Measurement of Collins Asymmetries at Belle 4 First QCD Analysis Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk of SIDIS + e+e- ! Phys. Rev. D75:05032,2007 Fit includes: HERMES SIDIS + COMPASS SIDIS + Belle e+e- transversity dist. + Collins FF May 24th Measurement of Collins Asymmetries at Belle 5 Measurement of Collins Asymmetries In e+e- at KEK B with the Belle Phys.Rev.Lett.96:232002,2006 and update at Spin 2006 in Kyoto Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) v sq v h, p h φ v v ph ⊥ q k r k : quark momentum Collins Effect: v Fragmentation of a sq : quark spin v transversely polarized ph : hadron momentum quark q into spin-less v ph ⊥ : transverse hadron momentum hadron h carries an z h = Eh Eq azimuthal dependence: ( ) v v v ∝ k × ph ⊥ ⋅ sq = 2 Eh s : relative hadron momentum ∝ sin φ May 24th Measurement of Collins Asymmetries at Belle 7 General Form of Fragmentation Functions Number density for finding hadron h from a transversely polarized quark, q: Dq ↑ ( z , ph ⊥ ) = D1q ,h ( z ) + H1⊥ q ,h ( z , ph ⊥ h v 2 ) ( kˆ × p )⋅ sv v h⊥ q zM h unpolarized FF Collins FF May 24th Measurement of Collins Asymmetries at Belle 8 Collins FF in e+e- : Need Correlation between Hemispheres ! 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 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! May 24th Measurement of Collins Asymmetries at Belle 9 Event Structure at Belle e+e- CMS frame: 2Eh z= , s = 10.52 GeV Near-side Hemisphere: s hi , i=1,Nn with zi e- Θ <Nh+,-> = 6.4 e+ Jet axis: Thrust Spin averaged cross section: Far-side: dσ (e + e − → h1h2 X ) 3α 2 hj , j=1,Nf with zj = 2 A( y )∑ ea D1 (z1 )D1 (z2 ) 2 dΩdz1dz2 Q a ,a 1 ( cm ) 1 A( y ) = ⎛ − y + y 2 ⎞ = (1 + cos 2 Θ) ⎜ ⎟ ⎝2 ⎠ 4 May 24th Measurement of Collins Asymmetries at Belle 10 Collins Fragmentation: Angles and Cross Section cos(φ1+φ2) Method e+e- CMS frame: ϕ2−π e- Observables: N12(φ1+φ2), A12(z1,z2) Θ r ϕ1 Ph 2 r Ph1 ϕ2 ϕ1 e+ 2-hadron inclusive transverse momentum dependent cross section: dσ (e + e − → h1h 2 X ) = L B(y )cos (ϕ1 + ϕ 2 )H1 [1] (z1 )H1 [1] (z 2 ) ⊥ ⊥ dΩdz1dz 2d qT2 Net anti-alignment of cm 1 B(y ) = y(1 − y ) = sin 2 Θ transverse quark spins 4 May 24th Measurement of Collins Asymmetries at Belle 11 Collins Fragmentation: Angles and Cross Section cos(2φ0) Method Observables: N0(φ0), A12(z1,z2) e+e- CMS frame: r Θ e- •Independent of thrust-axis Ph 2 A0 r •Convolution integral I Ph1 over transverse momenta involved ϕ0 [Boer,Jakob,Mulders: NPB504(1997)345] e+ 2-hadron inclusive transverse momentum dependent cross section: dσ (e + e − → h1h 2 X ) (⎡ ) ˆ ⋅ kT h ⋅ pT − kT ⋅ pT H1 H1 ⎤ ⊥ ⊥ = L B(y )cos (2ϕ 0 )I ⎢ 2h ˆ dΩdz1dz 2d 2qT ⎣ M1M 2 ⎥ ⎦ Net anti-alignment of 1 cm B(y ) = y(1 − y ) = sin 2 Θ transverse quark spins 4 May 24th Measurement of Collins Asymmetries at Belle 12 Hadronic Events observed with Belle 1.5 x 109 hadronic events in analysis v ∑ ˆ pi ⋅ n On resonance: 547fb-1 ,i =√s=10.52 GeV (published) ~1 thrust = particles v ~ 0.5 Off resonance: 29fb -1 , √s=10.58 GeV (preliminary) ∑ pi i May 24th Measurement of Collins Asymmetries at Belle 13 Gluon Emission dN ⎡ qT 2 ⎤ ∝ ∑⎢ 2 sin θ cos(2φ0 ) D1 ( z1 )D1 ( z 2 )⎥ 2 dΩdz1dz 2 dqT ⎣ Q + QT 2 ⎦ e- QT e+ Frame: v v z2 z1 p1 = − p2 May 24th Measurement of Collins Asymmetries at Belle 14 Examples of Fits to Azimuthal Asymmetries N(φ)/N0 2φ0 (φ1+φ2) D1 : spin averaged fragmentation function, H1: Collins fragmentation function May 24th Measurement of Collins Asymmetries at Belle 15 Method to eliminate gluon contributions: Double ratios for unlike- and like sign pions Double ratio method: ⎡ e 2 ( H Fav ⋅ H + H Unf ⋅ H ) ⎤ sin (θ ) ⎢ ∑q Fav Unf 2 F~ ⎥ cos(φ ) 1 + cos (θ ) ⎢ ∑ e 2 ( D Fav ⋅ D + DUnf ⋅ D ) ⎥ 2 Fav Unf 0 ⎣ q ⎦ A0(z1,z2) May 24th Measurement of Collins Asymmetries at Belle 16 Two Double Ratios Double ratios unlike/like-sign not very sensitive in separating favored and disfavored Collins functions look at unlike-sign/charge-sum • Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) • Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) • π±π0 pairs UL (favored + unfavored) x (favored + unfavored) • A. Efremov et al. ([hep-ph/0603054]): charged ππ pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) UC Observables: A12(UL), A12(UC) published and input to A0(UL) , A0(UC) fit by Anselmino et al. May 24th Measurement of Collins Asymmetries at Belle 17 Final Charm Corrected Results for e+ e- π π X (29fb-1, off-resonance Data) Phys.Rev.Lett.96:232002,2006 • Significant non-zero asymmetries • Rising behavior vs. z • UL/C asymmetries about 40- 50% of UL/L asymmetries • First direct measurements of the Collins function • UL/L data published A0(UL/L) (3.06 ± 0.57 ± 0.55)% A12(UL/L) (4.26 ± 0.68 ± 0.68)% A0(UL/C) (1.27 ± 0.49 ± 0.35)% A12(UL/C) (1.75 ± 0.59 ± 0.41)% May 24th Measurement of Collins Asymmetries at Belle 18 Preliminary Charm Corrected Results for e+ e- π π X (547 fb-1 ,on-resonance) • Significance largely Preliminary increased • Behavior unchanged • Reduced systematics • Precise measurements of the Collins function Integrated results: A0(UL/L) (2.67 ± 0.10 ± 0.26)% A12(UL/L) (3.55 ± 0.08 ± 0.15)% A0(UL/C) (1.11 ± 0.11 ± 0.22)% A12(UL/C) (1.46 ± 0.09 ± 0.13)% May 24th Measurement of Collins Asymmetries at Belle 19 Summary and Outlook Summary: Outlook: • Observation of large azimuthal • Future spin dependent FFs: asymmetries in light quark frag- update Collins FF mentation. Updated statistics: measure pT dependence interference fragmentation ∫Ldt = 29 fb-1 547 fb-1 Collins FF for VMs • Double ratios reliably cancel Lambdas contributions from detector acceptance and gluon radiation. • Precision measurement of spin averaged fragmentation func- important input for the tions as input to RHIC program transverse spin physics with inclusive hadrons and future programs at RHIC, HERMES, precision measurements in COMPASS and JLab SIDIS. May 24th Measurement of Collins Asymmetries at Belle 20 Input also for precision Belle Impact on the Knowledge of FFs measurements of quark helicity distributions in Compilation of at SIDIS, in particulardata Belle: Charged h+/-, pions, kaons, protons available for electron- a possible futurethe char- ged hadron collider. polarized protonFF FF h+,- Belle MC pions FF kaons protons <1% of data sample work in progress precision at high z! Eh Eh z= z= s /2 s /2 May 24th Measurement of Collins Asymmetries at Belle 21 What is Known Experimentally ? Hirai, Kumano, Nagai, Sudo hep-ph/0612009 (including errors!) Earlier work: Kretzer Binnewies, Potter, Albino Kniehl, Kramer, Potter Albino, Kniehl, Kramer May 24th Measurement of Collins Asymmetries at Belle 22 Motivation I ∆G from QCD Analysis of ALL for inclusive hadrons: π0,+,-, η, K+,- PHENIX π0 cross section a |η|<0.35 Idea: QCD analysis of Phys.Rev.Lett.91:241803,2003 LEP and Belle data will fix uncertainty in know- ledge of FFs (gluon FF, flavor separation) Deviation connected to uncertainties in FFs gluon FF! May 24th Measurement of Collins Asymmetries at Belle 23 Why is the Collins Fragmentation Function Interesting? o Very basic QCD process: Fundamental test case for any approach to solve QCD at soft scales. o Tests of universality and factorization between e+e-, DIS and p-p collisions o Symmetry properties o Evolution is fundamental QCD prediction o Connection between microscopic and macroscopic observables: Probe/analyzer for transverse quark spin critical input for transverse proton spin program at DESY, CERN, JLab and RHIC May 24th Measurement of Collins Asymmetries at Belle 24 May 24th Measurement of Collins Asymmetries at Belle 25 KEKB: L>1.6 x 1034cm-2s-1 !! 1.5 x 109 hadronic events in analysis • KEKB •Average Trigger rates: – Asymmetric collider Υ(4S) BB 11.5Hz – 8GeV e- + 3.5GeV e+ q⎯q 28 Hz – √s = 10.58GeV (Υ(4S)) μμ + ττ 16 Hz e+e- Υ(4S) Β⎯Β Bhabha 4.4 Hz – Off-resonance: 10.52 GeV 2γ 35 Hz e+e- q⎯q (u,d,s,c) – Integrated Luminosity: > 600 fb-1 > 60fb-1 => off-resonance KEKB Belle detector May 24th Measurement of Collins Asymmetries at Belle 26 Good tracking and particle identification! May 24th Measurement of Collins Asymmetries at Belle 27 Belle is Well Suited for FF Measurements: • Good detector performance (acceptance, momentum resolution, pid) • Jet production from light quarks 25 σ(e+e- → hadrons)(nb) off-resonance (60 MeV below resonance) (~10% of all data) 20 • Intermediate Energy 15 Sufficiently high scale (Q2 ~ 110 GeV2) - can apply pQCD 10 Not too high energy (Q2 << MZ2) -avoids complication from Z interference 5 • Sensitivity = A2sqrt(N) ~ x 25 (100) compared to LEP ϒ(2S) ϒ(3S) ϒ(1S) ϒ(4S) 0 9.44 9.46 10.00 10.02 10.34 10.37 10.54 10.58 10.62 ABelle / ALEP ~ x 2 (A scales as ln Q2) e+e- Center-of-Mass Energy (GeV) ∫LBelle dt / ∫LLEP dt ~ x 46 (600) Total number of hadronic events ~ 1.5 x 109 May 24th Measurement of Collins Asymmetries at Belle 28 Applied Cuts, Binning • Originally off_resonance • Hemisphere cut data, now also (Ph 2 ⋅ n ) n ⋅ (Ph1 ⋅ n ) n < 0 ˆ ˆ ˆ ˆ on_resonance data (29.1 • QT < 3.5 GeV 547 fb-1) • Pion PID selection • Track selection: – pT > 0.1GeV – vertex cut: dr<2cm, |dz|<4cm z2 1.0 • Acceptance cut – -0.6 < cosθi < 0.9 3 6 8 9 • Event selection: 0.7 – Ntrack ≥ 3 2 5 7 8 0.5 – Thrust > 0.8 1 4 5 6 – Z1, Z2>0.2 0.3 0 1 2 3 0.2 0.2 0.3 0.5 0.7 1.0 z1 May 24th Measurement of Collins Asymmetries at Belle 29 Experimental Issues • Cos2φ moments have two contributions: – Collins Can be isolated either by subtraction or double ratio method – Radiative effects Cancels exactly in subtraction method, and in LO of double ratios • Beam Polarization zero? cos(2φ) asymmetries for jets or γγ • False asymmetries from weak decays Study effect in τ decays, constrain through D tagging • False asymmetries from misidentified hemispheres QT or polar angle cut • False asymmetries from acceptance Cancels in double ratios, can be estimated in charge ratios, fiducial cuts • Decaying particles lower z cut May 24th Measurement of Collins Asymmetries at Belle 30 Why is it Possible to Include Data on Resonance? Different Thrust Distributions 25 σ(e+e- → hadrons)(nb) 20 e+ e- qq̅, q∈uds 15 10 e+e- cc̅ 5 ϒ(1S) ϒ(2S) ϒ(3S) ϒ(4S) B+ B− 0 9.44 9.46 10.00 10.02 10.34 10.37 10.54 10.58 10.62 e+e- Center-of-Mass Energy (GeV) B0 B0 • small B contribution (<1%) in high thrust sample •>75% of X-section continuum under Υ (4S) resonance •29 fb-1 547 fb-1 ∑ p ⋅ˆn i •many systematic errors reduce with more thrust = i statistics ∑p i i • Charm-tagged Data sample also increases May 24th Measurement of Collins Asymmetries at Belle 31 Collins Asymmetries I: 4x4 z1, z2 binning A0 (cos(2φ0)) moments A12 (cos(φ1 + φ2)) moments PRELIMINAR PRELIMINAR Y Y • 547 fb-1 charm corrected data sample, • UL and UC double ratios May 24th Measurement of Collins Asymmetries at Belle 32 Collins Asymmetries II: sin2 θ/(1+cos2 θ) Binning (UL) • Nonzero quark PRELIMINARY polarization ~ sin2 θ • Unpolarized de- nominator ~ 1+cos2 θ • Clear linear behavior seen when using either thrustz or 2nd hadron as thrustz polar angle θ2 • Better agreement for thrust axis (~approximate quark axis) • UC plots similar May 24th Measurement of Collins Asymmetries at Belle 33 Collins Asymmetries III: QT Binning (UL) PRELIMINARY • Reduced asymmetries in low thrust sample • At low thrust significant B contribution (for t<0.8 ~20 % B for t>0.8 < 1 % B) • A12 thrust axis dependent • High QT (>3.5 GeV) asymmetries from beam related BG • UC plots similar Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) May 24th Measurement of Collins Asymmetries at Belle 34 Improved Systematic Errors (UC) • Tau contributions • PID systematics∗ A0 (cos(2φ0)) moments • MC double ratios • Charged ratios (π+π+ /π−π− ) • Higher order terms • Double ratio-subtraction method A12 (cos(φ1 + φ2)) moments Reweighting asymmetries: underestimation of cos(φ1+φ2) asymmetries rescaled by 1.21 Correlation studies: statistical errrors rescaled by 1.02 (UL) and 0.55 (UC) Beam polarization studies consistent with zero May 24th Measurement of Collins Asymmetries at Belle 35 Collins Asymmetry Collins FF QCD analysis: (I) Efremov, Goeke, Schweitzer (Phys.Rev.D73:094025,2006): consistency between Belle, HERMES and COMPASS asymmetries. (II) Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin and Tuerk (hep-ph/0701006 ) extract transversity distributions and the Collins FF (see tomorrow). (III) UIUC fit to Belle data (work in progress): May 24th Measurement of Collins Asymmetries at Belle 36 Spin Averaged FF + Collins Asymmetry Kretzer FFs (also KKP) Experimental double ratio: May 24th Measurement of Collins Asymmetries at Belle 37 Fits of the Belle Collins Asymmetries A0 with∫Ldt = 29 fb-1 May 24th Measurement of Collins Asymmetries at Belle 38 Fits of the Belle Collins Asymmetries A12 with∫Ldt = 29 fb-1 May 24th Measurement of Collins Asymmetries at Belle 39 Results for the Collins FF A0 A12 H fav H fav D fav D fav H fav H fav D fav D fav H dis H dis D dis D dis H fav D fav 0<z<1 May 24th Measurement of Collins Asymmetries at Belle 40

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