Measurement of (Interference) Fragmentation Functions in e + e - at Anselm Vossen and Di-Hadron Correlations and DiFF Mini Workshop Pavia, Italy, September 5 th - 8 th

Outline IFF measurements at Belle – Observables – Kinematic Distributions – Flavor decomposition (Charm Contributions) – Results – Future Plans Phenix – Experiment – Results Star – Current status – Future possibilities 2

3 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:

4 o Quark spin direction unknown: measurement of Interference Fragmentation function in one hemisphere is not possible sin φ modulation will average out. o Correlation between two hemispheres with sin φ Ri single spin asymmetries results in cos(φ R1 +φ 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 !

5 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  Observable:cos( φ R1 +φ R2 ) modulation measures Measuring di-Hadron Correlations In e + e - Annihilation into Quarks electron positron q2q2 quark-2 spin z 1,2 relative pion pair momenta z2z2 z1z1 φ R1 φ R2

6 KEKB: L>2.11 x cm -2 s -1 !! Asymmetric collider 8GeV e GeV e + √s = 10.58GeV (  (4S)) e + e -   (4S)  B  B Off-resonance production: GeV e + e -  q  q (u,d,s,c) Integrated Luminosity: > 1000 fb -1 >70 fb -1 => continuum 6 Belle detector KEKB

7 Large acceptance, good tracking and particle identification! He/C 2 H 6

Interference Fragmentation–thrust method e + e -  (  +  - ) jet1 (     ) jet2 X transverse spin projection 8  2   1 

9 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  R2  R1 Interference Fragmentation – “   “ method

10 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 for di-pion pairs > 90% Same Hemisphere cut within pair (     ), opposite hemisphere between pairs All 4 hadrons in barrel region:-0.6 < cos (  ) <0.9 Thrust axis in central area: cosine of thrust axis around beam <0.75 Thrust > 0.8 to remove B-events  < 1% B events in sample z had1,had2 >0.1 z 1 = z had1 +z had2 and z 2 in 9x9 bins m  and m  in 8x8 bins: [ ] GeV New: Mixed binning

Kinematics 11

Opening Cut and Energy Flow 12 Opening Cut of 0.8Opening Cut of 0.9

13 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 13 PhPh No opening cut Opening cut>0.7 Opening cut >0.8

14 (z 1 x m 1 ) Binning arXiv: PRL 107, (2011)

(m 1 x z 1 ) Binning arXiv: PRL 107, (2011) 15

16 Subprocess contributions (MC) 8x8 m 1 m 2 binning tau contribution (only significant at high z) charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution)

Subprocess contributions (MC) tau contribution (only significant at high z) charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution) 17 9x9 z 1 z 2 binning

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Accessing QCD vacuum fluctuations in Quark Fragmentation QCD vacuum is superposition of theta vacua On microscopic scale this could be accessible in experiments – First results in STAR – Planned measurements in Belle: – Needed as a ‘tie breaker’ – Model Calculations predict 2% effect Access to nonperturpative properties of QCD Transition instantons/sphalerons: Role in Early Universe, baryogenesis …

Anselm Vossen 20 q1q1 quark-1 spin Event Topology electron positron q2q2 quark-2 spin z2z2 z1z1 z 1,2 relative pion momenta Jet Axis   : Momentum : Spin Fragmentation in P-odd bubble leads to left right asymmetry – Difference in ‘Winding number’ gives effective increment in chirality – Spin alignment via chromomagnetic effect – Azimuthal event by event modulation – Measurement: Extract width of distribution of first moments – Analysis already underway: Is there a Di-hadron Analogue?

Currently underway: Belle II is a significant upgrade to Belle and will sample 2 orders of magnitude higher luminosity High precision data will enable measurement of – P-odd FFs – Transverse momentum dependent FFs – Charm suppression possible IU will develop FEE for Barrel KLM detector crucial for high precision FF measurement of identified particles

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 Black: about to start Green: ongoing Grey: finished 22

Same Hemisphere Correlations? Motivation: P-odd FF x Collins (in Single hadron) does not average out 23

p+p complementary and increased kinematic reach in x, z Kinematic reach of SIDIS data Kinematic reach in p+p for single pions at 3<eta<4 Relative hadron momentum z for p+p (3<eta<4) collisions and SIDIS (COMPASS), only single hadron, di- hadron z 1 +z 2 ‘less different ’ ptpt z Mean z: 0.64 PTPT PTPT

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

26 PHENIX Detectors used for IFF Analysis Use 2 separate spectrometer arms at central rapidity, |  | < 0.35 Azimuthal coverage: 90° + 90° Electromagnetic Calorimeters – PbSC + PbGl – High granularity  =0.01  0.01 Tracking of charged particles – Drift chamber, pad chambers Little p_t dependence of x at mid rapidity, low x

27 vs Invariant Mass of the Pair First measurement of IFF in pp Results and Projections From run 12+13

Planned Transversity measurements at STAR Measurements with current detector – Transversity in Di-Hadron correlations –   in FMS and Encap,     inTPC – Sivers effect in jets in EEMC – Explore jet –jet and gamma – jet asymmetries Full azimuth spanned with nearly contiguous electromagnetic calorimetry from -1<  <4  approaching full acceptance detector

29 R&D for planned STAR forward upgrade Forward instrumentation optimized for p+A and transverse spin physics – Charged Tracking upgrade covering FMS will enable di-hadron measurements and jet measurements – Star decadal plans calls additionally for PID (e.g. RICH) and pi0/gamma separation (preshower) FMS ~ 6 GEM disks Tracking: 2.5 < η < 4 proton nucleus Transverse spin effect dominated by valence quarks accessed in forward direction

30 Projections for Belle Measurements of IFF in STAR, Channel: (     ) (     ) Errors one order of magnitude smaller than average asymmetry in (     ) Hadron pair in second hemisphere: 0.77 GeV <M inv < 1.2 GeV a 12 (580 fb -1 integrated luminosity)

31 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 73 fb -1  662 fb -1 e + e -  qq̅, q ∈ uds e + e -  cc̅ s “off”