Measurement of Collins Asymmetries in e + e - Annihilation at Belle

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1 Measurement of Collins Asymmetries in e + e - Annihilation at Belle Workshop on Exclusive Reactions at High Momentum Transfer, 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

2 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 Measurement of Collins Asymmetries at Belle

3 Motivation Transversity Quark Distributions from Collins- and Interference-Fragmentation New HERMES results for Collins Asymmetries M. Diefenthaler, DIS 007, 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(z ) x CFF(z ) ~ IFF(z ) x IFF(z ) global QCD analysis Measurement of Collins Asymmetries at Belle 3

4 Global Analysis: Extract Transversity Distributions RBRC Transversity Workshop 000 SIDIS transversity Collins transversity IFF HERMES, COMPASS, JLAB, EIC Factorization + Universality?! e + e - Belle Collins x Collins Interference FF x Interference FF Theory Transversity Tensor Charge Lattice QCD: Tensor Charge RHIC / GSI pp GSI A A T A N for inclusive hadrons, Jets in Jets : transversity Collins transversity IFF Drell Yan : transversity transversity TT Measurement of Collins Asymmetries at Belle 4

5 First QCD Analysis of SIDIS + e + e -! Anselmino, Boglione, D Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:0503,007 Fit includes: HERMES SIDIS + COMPASS SIDIS + Belle e + e - transversity dist. + Collins FF Measurement of Collins Asymmetries at Belle 5

6 Measurement of Collins Asymmetries In e + e - at KEK B with the Belle Phys.Rev.Lett.96:300,006 and update at Spin 006 in Kyoto

7 Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 6(993) s v q q k v h, p v h φ p v h r k v s v p v p z q h h h = = E h E h E q s : quark momentum : quark spin : hadron momentum : transverse hadron momentum : relative hadron momentum Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence: v v v ( k p h ) sq sinφ Measurement of Collins Asymmetries at Belle 7

8 Measurement of Collins Asymmetries at Belle 8 General Form of Fragmentation Functions ( ) h q h h h q h q h h q zm s p k p z H z D p z D v v v + = ˆ ), ( ) ( ), (,, Number density for finding hadron h from a transversely polarized quark, q: unpolarized FF Collins FF

9 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 φ i Collins single spin asymmetries results in cos(φ +φ ) modulation of the observed di-hadron yield. Measurement of azimuthal correlations for pion pairs around the jet axis in two-jet events! Measurement of Collins Asymmetries at Belle 9

10 Event Structure at Belle Near-side Hemisphere: h i, i=,n n with z i e + e - CMS frame: Θ e - Eh z =, s = 0 5. GeV s <N h+,- > = ( e e h h X ) dωdz dz 3α = Q e + Spin averaged cross section: dσ A ( y) e D ( z ) D ( z ) a, a a Jet axis: Thrust Far-side: h j, j=,n f with z j A ( y) = y + y ( cm) = 4 ( + cos Θ) Measurement of Collins Asymmetries at Belle 0

11 Collins Fragmentation: Angles and Cross Section cos(φ +φ ) Method e + e - CMS frame: ϕ π Θ e - Observables: N (φ +φ ), A (z,z ) P r h P r h ϕ ϕ ϕ + ( e e h h X) dσ dωdz dz cm = LB y ( ) = y( y) = sin Θ B y d q T e + -hadron inclusive transverse momentum dependent cross section: 4 [] [] ( ) cos ( ϕ + ϕ ) H ( z ) H ( z ) Net anti-alignment of transverse quark spins Measurement of Collins Asymmetries at Belle

12 Collins Fragmentation: Angles and Cross Section cos(φ 0 ) Method Observables: N 0 (φ 0 ), A (z,z ) e + e - CMS frame: P r h Θ e - A 0 P r h Independent of thrust-axis Convolution integral I over transverse momenta involved + ( e e h h X) dσ dωdz dz cm = LB y ( ) = y( y) = sin Θ B y e + -hadron inclusive transverse momentum dependent cross section: d q T 4 ϕ 0 ( ) cos ( ϕ ) I ( h ˆ k h ˆ p k p ) 0 T T T [Boer,Jakob,Mulders: NPB504(997)345] T H H M M Net anti-alignment of transverse quark spins Measurement of Collins Asymmetries at Belle

13 Hadronic Events observed with Belle Î.5 x 09 hadronic events in analysis v p i nˆ On resonance: 547fb-,i = s=0.5 GeV (published) particles ~ 0.5 ~ thrust- = v Off resonance: 9fb, s=0.58 pi GeV (preliminary) i May 4th Measurement of Collins Asymmetries at Belle 3

14 Gluon Emission dn dωdz dz dq T Q qt + Q T sin θ cos(φ ) D 0 ( z ) D ( z ) z Q T e- e+ Frame: v v p = p z Measurement of Collins Asymmetries at Belle 4

15 Examples of Fits to Azimuthal Asymmetries N(φ)/N 0 φ 0 (φ +φ ) D : spin averaged fragmentation function, H : Collins fragmentation function Measurement of Collins Asymmetries at Belle 5

16 Method to eliminate gluon contributions: Double ratios for unlike- and like sign pions Double ratio method: F sin ( θ ) e q + cos ( θ ) e q ( H ( D Fav H ) cos( φ ) ) ~ 0 Fav Fav Unf Unf D Fav + H + D Unf H D Unf A 0 (z,z ) Measurement of Collins Asymmetries at Belle 6

17 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 ± π 0 pairs UL (favored + unfavored) x (favored + unfavored) A. Efremov et al. ([hep-ph/ ]): charged ππ pairs are similar (and easier to handle) (C): (favored + unfavored) x (favored + unfavored) UC Observables: A (UL), A (UC) A 0 (UL), A 0 (UC) published and input to fit by Anselmino et al. Measurement of Collins Asymmetries at Belle 7

18 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 Final Charm Corrected Results for e + e - ππ X (9fb -, off-resonance Data) Phys.Rev.Lett.96:300,006 A 0 (UL/L) (3.06 ± 0.57 ± 0.55)% A (UL/L) (4.6 ± 0.68 ± 0.68)% A 0 (UL/C) (.7 ± 0.49 ± 0.35)% A (UL/C) (.75 ± 0.59 ± 0.4)% Measurement of Collins Asymmetries at Belle 8

19 Preliminary Charm Corrected Results for e + e - ππ X (547 fb -,on-resonance) Significance largely increased Behavior unchanged Reduced systematics Precise measurements of the Collins function Preliminary Integrated results: A 0 (UL/L) (.67 ± 0.0 ± 0.6)% A (UL/L) (3.55 ± 0.08 ± 0.5)% A 0 (UL/C) (. ± 0. ± 0.)% A (UL/C) (.46 ± 0.09 ± 0.3)% Measurement of Collins Asymmetries at Belle 9

20 Summary and Outlook Summary: Observation of large azimuthal asymmetries in light quark fragmentation. Updated statistics: Ldt = 9 fb fb - Double ratios reliably cancel contributions from detector acceptance and gluon radiation. important input for the transverse spin physics programs at RHIC, HERMES, COMPASS and JLab Outlook: Future spin dependent FFs: update Collins FF measure p T dependence interference fragmentation Collins FF for VMs Lambdas Precision measurement of spin averaged fragmentation functions as input to RHIC program with inclusive hadrons and future precision measurements in SIDIS. Measurement of Collins Asymmetries at Belle 0

21 Input also for precision measurements of quark helicity distributions in SIDIS, Compilation in particular of data a possible available future for the electronpolarizeged hadron proton FF char- collider. FF Belle Impact on the Knowledge of FFs Belle: Charged h +/-, pions, kaons, protons FF Belle MC h+,- pions kaons protons <% of data sample work in progress precision at high z! z = E h s / z = Measurement of Collins Asymmetries at Belle E h s /

22 What is Known Experimentally? Hirai, Kumano, Nagai, Sudo hep-ph/06009 (including errors!) Earlier work: Kretzer Binnewies, Potter, Albino Kniehl, Kramer, Potter Albino, Kniehl, Kramer Measurement of Collins Asymmetries at Belle

23 Motivation I G from QCD Analysis of A LL for inclusive hadrons: π 0,+,-, η, K +,- PHENIX π 0 cross section a η <0.35 Phys.Rev.Lett.9:4803,003 Idea: QCD analysis of LEP and Belle data will fix uncertainty in knowledge of FFs (gluon FF, flavor separation) Deviation connected to uncertainties in FFs gluon FF! Measurement of Collins Asymmetries at Belle 3

24 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 Measurement of Collins Asymmetries at Belle 4

25 Measurement of Collins Asymmetries at Belle 5

26 KEKB: L>.6 x 0 34 cm - s -!!.5 x 0 9 hadronic events in analysis KEKB Asymmetric collider 8GeV e GeV e + s = 0.58GeV (Υ(4S)) e + e - Υ(4S) Β Β Off-resonance: 0.5 GeV e + e - q q (u,d,s,c) Integrated Luminosity: > 600 fb - > 60fb - => off-resonance Average Trigger rates: Υ(4S) BB q q μμ + ττ Bhabha γ.5hz 8 Hz 6 Hz 4.4 Hz 35 Hz KEKB Belle detector Measurement of Collins Asymmetries at Belle 6

27 Good tracking and particle identification! Measurement of Collins Asymmetries at Belle 7

28 Belle is Well Suited for FF Measurements: Good detector performance (acceptance, momentum resolution, pid) 5 Jet production from light quarks off-resonance (60 MeV below resonance) 0 (~0% of all data) Intermediate Energy 5 Sufficiently high scale (Q ~ 0 GeV ) 0 - can apply pqcd Not too high energy (Q << M Z ) 5 -avoids complication from Z interference Sensitivity = A ϒ(S) ϒ(S) ϒ(3S) sqrt(n) ~ x 5 (00) compared to 0LEP A Belle / A LEP ~ x (A scales as ln Q ) L Belle dt / L LEP dt ~ x 46 (600) Total number of hadronic events ~.5 x 0 9 σ(e + e - hadrons)(nb) ϒ(4S) e + e - Center-of-Mass Energy (GeV) Measurement of Collins Asymmetries at Belle 8

29 Applied Cuts, Binning Originally off_resonance data, now also on_resonance data ( fb - ) Track selection: pt > 0.GeV vertex cut: dr<cm, dz <4cm Acceptance cut -0.6 < cosθ i < 0.9 Event selection: Ntrack 3 Thrust > 0.8 Z, Z >0. Hemisphere cut (P h n ˆ ) n ˆ (P h n ˆ ) n ˆ < 0 Q T < 3.5 GeV Pion PID selection z z Measurement of Collins Asymmetries at Belle 9

30 Experimental Issues Cosφ 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(φ) asymmetries for jets or γγ False asymmetries from weak decays Study effect in τ decays, constrain through D tagging False asymmetries from misidentified hemispheres Q T 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 Measurement of Collins Asymmetries at Belle 30

31 Why is it Possible to Include Data on Resonance? Different Thrust Distributions e + e - qq, q uds e + e - cc σ(e + e - hadrons)(nb) B + B B 0 B 0 thrust = i i p i p ˆ n i ϒ(S) ϒ(S) ϒ(3S) ϒ(4S) e + e - Center-of-Mass Energy (GeV) small B contribution (<%) in high thrust sample >75% of X-section continuum under Υ (4S) resonance 9 fb fb - many systematic errors reduce with more statistics Charm-tagged Data sample also increases Measurement of Collins Asymmetries at Belle 3

32 Collins Asymmetries I: 4x4 z, z binning A 0 (cos(φ 0 )) moments A (cos(φ +φ )) moments PRELIMINAR Y PRELIMINAR Y 547 fb - charm corrected data sample, UL and UC double ratios Measurement of Collins Asymmetries at Belle 3

33 Collins Asymmetries II: sin θ/(+cos θ) Binning (UL) thrustz θ PRELIMINARY Nonzero quark polarization ~ sin θ Unpolarized denominator ~ +cos θ Clear linear behavior seen when using either thrustz or nd hadron as polar angle Better agreement for thrust axis (~approximate quark axis) UC plots similar Measurement of Collins Asymmetries at Belle 33

34 Collins Asymmetries III: Q T Binning (UL) PRELIMINARY Reduced asymmetries in low thrust sample At low thrust significant B contribution (for t<0.8 ~0 % B for t>0.8 < % B) A thrust axis dependent High Q T (>3.5 GeV) asymmetries from beam related BG UC plots similar Thrust>0.8 Thrust<0.8 (not corrected for heavy quark contributions) Measurement of Collins Asymmetries at Belle 34

35 Improved Systematic Errors (UC) Tau contributions PID systematics MC double ratios Charged ratios (π + π + /π π ) Higher order terms Double ratio-subtraction method A 0 (cos(φ 0 )) moments A (cos(φ +φ )) moments Reweighting asymmetries: underestimation of cos(φ +φ ) asymmetries rescaled by. Correlation studies: statistical errrors rescaled by.0 (UL) and 0.55 (UC) Beam polarization studies consistent with zero Measurement of Collins Asymmetries at Belle 35

36 Collins Asymmetry Collins FF QCD analysis: (I) Efremov, Goeke, Schweitzer (Phys.Rev.D73:09405,006): consistency between Belle, HERMES and COMPASS asymmetries. (II) Anselmino, Boglione, D Alesio, Kotzinian, Murgia, Prokudin and Tuerk (hep-ph/ ) extract transversity distributions and the Collins FF (see tomorrow). (III) UIUC fit to Belle data (work in progress): Measurement of Collins Asymmetries at Belle 36

37 Spin Averaged FF + Collins Asymmetry Kretzer FFs (also KKP) Experimental double ratio: Measurement of Collins Asymmetries at Belle 37

38 Fits of the Belle Collins Asymmetries A 0 with Ldt = 9 fb- Measurement of Collins Asymmetries at Belle 38

39 Fits of the Belle Collins Asymmetries A with Ldt = 9 fb - Measurement of Collins Asymmetries at Belle 39

40 Results for the Collins FF A 0 A H D fav fav H D H D fav fav fav fav H D dis dis H D fav fav H D fav fav H D dis dis 0 < z < Measurement of Collins Asymmetries at Belle 40