Transverse Spin Dependent Di-Hadron Fragmentation Functions at 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) Outline Motivation Analysis of Transverse Spin Effects in SIDIS, proton-proton Recent experimental results Transversity extraction Measuring Fragmentation Functions at Belle Experimental techniques Interference Fragmentation Function Measurement Comparison with theory Summary & Outlook Transverse Spin Asymmetries Experimental results in SIDIS and pp Transverse Spin Asymmetries - Single Hadrons Large transverse single spin effects persist at large scale Convolution of different effects 4 Transversity PHENIX, forward at s = 62 GeV, nucl-ex/ Transverse Spin Asymmetries Experimental results in SIDIS and pp Access to fundamental aspects of QCD and nucleon structure: TMDs, orbital angular momentum Initial, final state interactions Gauge invariance of correlators Prominent effects: Transversity * Collins Sivers Effect Separation of different effects requires measurements at multiple experiments, channels -> pp, SIDIS, e + e - Measuring Transversity in SIDIS _ + _ + Transversity base: _ Difference in densities for , quarks in nucleon Helicity base: Need chiral odd partner => Fragmentation function Chiral odd FFs + _ + _ + _ Collins effect q N : Collins FF Collins Fragmentation at Belle First extraction of transversity quark distribution Together with HERMES, COMPASS First, still model dependent transversity Extraction : Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex Belle 547 fb -1 data set (Phys.Rev.D78:032011,2008.) Collins Extraction of Transversity: model dependence from Transverse Momentum Dependences! Anselmino, Boglione, DAlesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 k transverse quark momentum in nucleon p transverse hadron momentum in fragmentation transversity Collins FF hadron FF quark pdf The transverse momentum dependencies are unknown and difficult to obtain experimentally! Chiral odd FFs + _ + _ + q N _ L z -1LzLz Interference Fragmentation Function Advantages of IFF Independent Measurement Favourable in pp: no Sivers Transverse momentum is integrated Collinear factorization No assumption about k t in evolution Universal function evolution known, collinear scheme can be used directly applicable to semi-inclusive DIS and pp First experimental results from HERMES, COMPASS, PHENIX Interference FF in Quark Fragmentation q Interference Fragmentation Function: Fragmentation of a transversely polarized quark q into two spin-less hadron h1, h2 carries an azimuthal dependence: Di-Hadron SSA in SIDIS (both on proton target, sign convention different) Added statistics from 2008 running As expected: No significant asymmetries seen at central-rapidity. SSA from di-hadron production Extended kinematic regime compared with SIDIS Hard scale 15 General Form of Fragmentation Functions Number density for finding Hadron pair with invariant mass M Pair from a transversely polarized quark, q: unpolarized FF Interference FF o Quark spin direction unknown: measurement of Interference Fragmentation function in one hemisphere is not possible sin modulation will average out. o Correlation between two hemispheres with sin Ri single spin asymmetries results in cos( R1 + R2 ) modulation of the observed di-hadron yield. Measurement of azimuthal correlations for di-pion pairs around the jet axis in two-jet events! Spin Dependent FF in e + e - : Need Correlation between Hemispheres ! 17 q1q1 quark-1 spin Interference 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 Measuring di-Hadron Correlations In e + e - Annihilation into Quarks electron positron q2q2 quark-2 spin z2z2 z1z1 z 1,2 relative pion pair momenta KEKB: L>2.11 x 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: ~ 950 fb -1 >70 fb -1 => continuum 18 Belle detector KEKB Collins Asymmetries in Belle19 May 28 th Large acceptance, good tracking and particle identification! He/C 2 H 6 Interference Fragmentationthrust method e + e - ( + - ) jet1 ( ) jet2 X Find pion pairs in opposite hemispheres Measure azimuthal correlations of Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 20 2 1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)] (Here: z 1, (z 2 )relative momenta of first (second) pair) Amplitude of modulation directly measures IFF! (squared) 21 Measuring Light Quark Fragmentation Functions on the (4S) Resonance small B contribution (75% of X-section continuum under (4S) resonance 73 fb -1 662 fb -1 e + e - qq, q uds e + e - cc s off Asymmetry extraction Build normalized yields: Fit with: or 22 Amplitude a 12 directly measures IFF! (squared) Zero tests: MC A small asymmetry seen due to acceptance effect Mostly appearing at boundary of acceptance Opening cut in CMS of 0.8 (~37 degrees) reduces acceptance effect to the sub-per-mille level 23 PhPh No opening cut Opening cut>0.7 Opening cut >0.8 Zero tests: Mixed Events False Asymmetries consistent with zero (Red/blue points: Thrust axis last or current event) Inject asymmetries in Monte Carlo Reconstruction smears thrust axis, ~94% of input asymmetry is reconstructed (Integrated over thrust axis: 98%) Effect is understood, can be reproduced in Toy MC Asymmetries corrected 25 Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed Weighted MC asymmetries Cuts and Binning Similar to Collins analysis, full off-resonance and on- resonance data (7-55): ~73 fb fb -1 Visible energy >7GeV PID: Purities in Pion/Pion Sample > 90% Same Hemisphere cut within pair ( ), opposite hemisphere between pairs All 4 hadrons in barrel region:-0.6 < cos ( ) 0.1 z 1 = z had1 +z had2 and z 2 in 9x9 bins m and m in 8x8 bins: [ ] GeV 26 First observation of IFF asymmetries in in e + e - coming up Results including systematic errors 8x8 m 1 m 2 binning 28 Preliminary 9x9 z 1 z 2 binning Preliminary Comparison with Collins FF extraction a 12 Asymmetries directly measure IFF squared IFF asymmetries can be integrated over k t No double ratios necessary to cancel gluon radiation effects Subprocess contributions (MC) 9x9 z 1 z 2 binning tau contribution (only significant at high z) charged B(