8 th Circum Pan Pacific Symposium on High Energy Spin Physics Cairns, June 21, 2011 Ralf Seidl (RIKEN) for the Belle Collaboration Transverse quark polarization Pac Spin, June 21, 2011 polarized fragmentation functions from Belle2 q(x), G(x) Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton (known from fixed target (SI)DIS experiments) q(x),G(x) q(x) Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton (first results from HERMES and COMPASS with the help of Belle) Unpolarized distribution function q(x) Helicity distribution function q(x) Transversity distribution function q(x) Sum of quarks with parallel and antiparallel polarization relative to proton spin (well known from Collider DIS experiments) Transversity properties Pac Spin, June 21, 2011 polarized fragmentation functions from Belle3 Helicity flip amplitude Chiral odd Since all interactions conserve chirality one needs another chiral odd object Does not couple to gluons different QCD evolution than q(x) Valence dominated Comparable to Lattice calculations, especially tensor charge Positivity bound: Soffer bound: How to access Transversity: another chiral-odd function Drell Yan: Combine two Transversity distributions with each other SIDIS/pp: Combine Transversity distributions with chiral- odd fragmentation function (FF) Total process is chiral-even: OK Possible Partners: Collins FF Interference FF Transverse L FF Most require single spin asymmetries in the fragmentation Pac Spin, June 21, 2011 polarized fragmentation functions from Belle4 Towards a global transversity analysis: Chiral odd Fragmentation functions Pac Spin, June 21, 2011 polarized fragmentation functions from Belle5 RHIC and SIDIS experiments measure: Transversity q(x) X Collins Fragmentation function or Interference Fragmentation function (IFF) 2 Unknown Functions measured together Universality understood Evolution ? Belle measures: Collins X Collins - finished for charged pion pairs or IFF X IFF charged pions about to be published Transversity Pac Spin, June 21, 2011 polarized fragmentation functions from Belle6 KEKB: L>2.1x10 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: >1000 fb -1 >70fb -1 => continuum Belle detector KEKB Main research at Belle: CP violation and determination of Cabibbo Kobayashi Maskawa (CKM) matrix / K L detection 14/15 lyr. RPC+Fe C entral D rift C hamber small cell +He/C 2 H 6 CsI(Tl) 16X 0 Aerogel Cherenkov cnt. n=1.015~1.030 Si vtx. det. 3/4 lyr. DSSD TOF counter SC solenoid 1.5T 8 GeV e 3.5 GeV e Belle Detector Good tracking and particle identification! (K)~85%, ( K)0.7) hardly available Current knowledge on fragmentation functions DSS, HKNS,AKK Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 28 DeFlorian, Sassot, Stratmann, Phys.Rev.D75:114010,2007. Differences between different global fits still large for high-z gluon contributions, kaons and disfavored fragmentation Hirai, Kumano, Nagai, Sudoh, Phys.Rev.D75: ,2007 Systematic studies: Particle identification Particle identification: create PID efficiency matrix for K, ,p,e, PID responses from MC not reliable, use well identified decays from data: Use D * slow D 0 slow fast K for K, identification Use p for p, identification J/ + -, e + e - for leptons (if needed also (1S)) Unfolding 29 polarized fragmentation functions from Belle REAL Particles Reconstructed particles Kp e K p e = Pac Spin, June 21, 2011 polarized fragmentation functions from Belle30 Martin Leitgabs Spin 2010 talk D* Extraction final extraction: large acceptance region covered K+K+ K-K- P Lab Cos Lab Pac Spin, June 21, polarized fragmentation functions from Belle Status of FF analysis: PID study finished Smearing correction finished Acceptance correction + nonQCD contribution removal ongoing Plan: have results soon Pac Spin, June 21, 2011 polarized fragmentation functions from Belle32 Event Structure for hadron pairs in e + e - annihilation = 6.4 e + e - CMS frame: e-e- e+e+ Spin averaged cross section: Jet axis: Thrust Pac Spin, June 21, 2011 polarized fragmentation functions from Belle33 Unpolarized 2-hadron fragmentation Detect two hadrons simultaneously: e + e - hhX If two hadrons in opposite hemispheres one obtains sensitivity to favored/ disfavored fragmentation: Difficulty: contribution from one quark fragmentation q hhX measure all three: (hh) jet1 X (h) jet1 (h) jet2 X hhX, ( ) requires thrust cut Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) any charge hadron pairs (C): (favored + unfavored) x (favored + unfavored) Favored= u ,d ,cc. Unfavored= d ,u ,cc. Sample MC (udsc) distributions - 45 fb -1 sampled (~50% of off resonance data) PID corrected using Martins Matrices Smearing not yet corrected (but small) Acceptance not yet corrected Statistic reasonable out to high z Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 34 Sample MC (udsc): ratio Yield ratios will be almost directly sensitive to disfavored/favored FF ratio Acceptance effects cancel Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 35 Summary and outlook First direct measurement of the interference fragmentation function Large asymmetries seen, rising with z and invariant mass No sign change at mass No double ratios make interpretation simple Submitted to PRL Significant, nonzero Collins asymmetries, Data used already in Global analysis Measure precise unpolarized fragmentation functions of many final states Important input for general QCD physics and helicity structure measurements Analysis progressing: PID studies finished smearing correction finished Acceptance correction ongoing New di-hadron fragmentation function analysis started Information of favored/disfavored FF Vector meson FFs VM Collins analysis started Artru Model test Continue to measure precise spin dependent fragmentation functions at Belle kT dependence of Collins function, , K Collins, pK, KK IFF Measure other interesting QCD- related quantities at Belle: Chiral-odd -fragmentation function single spin asymmetry Pac Spin, June 21, 2011 polarized fragmentation functions from Belle 36 Belle Fragmentation activity RIKEN/RBRCIllinoisIndianaTitech Unpol FFs e + e - hX: e + e - (hh)X, (h)(h)X,hhX: Unpol k T dependence: Neutral hadrons: ( ) John Koster Charged di- hadrons: Ralf Seidl Charged hadrons ( ,K,P): Martin Leitgab Collins FFs e + e - (h)(h)X: k T dependence: 0 : John Koster : Ralf Seidl : Ralf Seidl 0 : John Koster K,KK: Francesca Giordano Francesca Giordano : ? Interference FF: e + e - (hh)(hh)X Charged Ralf Seidl Charged : Anselm Vossen 0 : Anselm Vossen Charged K, KK: Nori-aki Kobayashi Local P : (polFF,SSA) : Jet-jet asy: Anselm Vossen 37 Black: about to start Green: ongoing Grey: finished Pac Spin, June 21, 2011 polarized fragmentation functions from Belle Pac Spin, June 21, 2011 polarized fragmentation functions from Belle38 Backup Slides polarized fragmentation functions from Belle 39 Pac Spin, June 21, 2011 The Collins effect in the Artru fragmentation model + picks up L=1 to compensate for the pair S=1 and is emitted to the right. String breaks and a dd-pair with spin -1 is inserted. A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: In Artru Model: favored (ie u ) and disfavored (ie u ) Collins function naturally of opposite sign Pac Spin, June 21, 2011 polarized fragmentation functions from Belle40 Collins fragmentation in e + e - : Angles and Cross section cos(2 ) method 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 involved e + e - CMS frame: e-e- e+e+ [Boer,Jakob,Mulders: NPB504(1997)345] Pac Spin, June 21, 2011 polarized fragmentation functions from Belle41 Similar to previous method Observe angles 1R 2R between the event-plane (beam, two- pion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici Interference Fragmentation method R2 R1 42 Subprocess contributions (MC) 8x8 m 1 m 2 binning tau contribution (only significant at high z) charged B(