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, D’Alesio, 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 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 !

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 Fragmentation–thrust 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 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”

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 (  ) <0.9 Thrust axis in central area: abs(thrustz)<0.75 Thrust > 0.8 z had1,had2 >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(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at lower z) uds (main contribution)

Subprocess contributions (MC) 32 8x8 m 1 m 2 binning charged B(<5%, mostly at higher mass) Neutral B (<2%) charm( 20-60%, mostly at highest masses) uds (main contribution) Charm Asymmetries in simulated data consistent with zero! To be checked with charm enhanced sample Data not corrected for Charm contributions

Systematic Errors Dominant: –MC asymmetry + its statistical error (up to % level) Smaller contributions: –mixed asymmetries: per mille level – higher moments: sub per mille level –axis smearing, –tau contribution –Charm contributions Possible Gluon radiation not accounted for

Model predictions for e + e - Invariant mass 1 dependence for increasing z 1 z 1 dependence for increasing z 2 34 Bacchetta,Checcopieri, Mukherjee, Radici : Phys.Rev.D79:034029,2009.

Comparison to theory predictions 35 Leading order, experimental results might contain effects from gluon radiation not contained in the model Mass dependence : Magnitude at low masses comparable, high masses significantly larger (some contribution possibly from charm ) Z dependence : Rising behavior steeper However: Theory contains parameters based on HERMES data which already fail to explain COMPASS well

Projections for (     ) (     ) for 580 fb -1 a 12 M inv <0.4 GeV 0.4 GeV<M inv <0.55 GeV 0.55 GeV<M inv <0.77 GeV 0.77 GeV <M inv < 1.2 GeV 1.2 GeV M inv < 2.0 GeV a 12

Projections for (     ) (K    ) for 580 fb -1 M inv <0.7 GeV0.7 GeV<M inv <0.85 GeV 0.85 GeV<M inv <1.0 GeV 1.0 GeV<M inv A a 12

Combined Analysis: Extract Transversity Distributions Transversity, δq(x) Tensor Charge Lattice QCD: Tensor Charge Factorization + Evolution Theory SIDIS ~ δq(x) x CFF(z) ~ δq(x) x IFF(z) e + e - ~ CFF(z 1 ) x CFF(z 2 ) ~ IFF(z 1 ) x IFF(z 2 ) pp  jets ~ G(x 1 ) x δq(x 2 ) x CFF(z) pp  h + + h - + X ~ G(x 1 ) x δq(x 2 ) x IFF(z) pp  l + + l - + X ~ δq(x 1 ) x δq(x 2 )

39 Measurements of quark transversity p+p SIDIS e + +e - E704, 1991 Large forward SSA STAR, PHENIX, BRAHMS, 2004~2005 Inclusive A N HERMES 2005, COMPASS 2006 A UT BELLE 2006 Collins FF BELLE IFF RHIC IFF asym. RHIC Collins asym. JParc, RHIC, FAIR Drell-Yan COMPASS p target JLab 3 He and 12 GeV Underway Future BELLE k T dep. Pol. & upol FF, pol. Lambda FF

Summary First measurement of Interference Fragmentation Function! Asymmetry significant Combined Analysis of Di-hadron and single hadron measurements possible Systematic effects to be finalized Future goal: Combined analysis of SIDIS, pp, e + e - data –Extract transversity –Disentangle contributions to A N

Backup

Charm asymmetries Charm meeting, June 4th 42 Interference fragmentation functions

Charm Studies Look at Events with D 0 decay in Pi,K pair Asymmetries with and without Pi from D 0 decay Way to separate between QCD effects and weak decays? c/c D0D0 /u u   

Transverse Spin Asymmetries at RHIC QCD: : very small Single transverse spin asymmetries pick up: –Sivers Effect: k T in quark distribution –Quark transverse polarization x Collins fragmentation function: k T in fragmentation function δq x CFF 44 Transversity PHENIX, forward    at s = 62 GeV, nucl-ex/

Transversity Quark Distributions δq(x) from Transverse Single Spin Asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS) Collins- and IFF- asymmetries in semi-inclusive deep inelastic scattering (SIDIS) and pp measure ~ δq(x) x CFF(z)  combined analysis with CFF from e + e - annihilation Example: New COMPASS results for Collins Asymmetries on proton target (consistent with previous HERMES results)

46 Methods to eliminate gluon contributions: Double ratios and subtractions Double ratio method: Subtraction method: Pros: Acceptance cancels out Cons: Works only if effects are small (both gluon radiation and signal) Pros: Gluon radiation cancels out exactly Cons: Acceptance effects remain 2 methods give very small difference in the result

Final Collins results Belle 547 fb -1 data set (Phys.Rev.D78:032011,2008.) 47

48 Collins Fragmentation: Angles and Cross Section: cos(     ) Method (e+e- CMS frame)       2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins  e-e- e+e+ Observable: yield, N 12 ( φ 1 +φ 2 ) of π + π - pairs

49 Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 k ┴ transverse quark momentum in nucleon p ┴ transverse hadron momentum in fragmentation hadron FF quark pdf The transverse momentum dependencies are unknown and very Difficult to obtain experimentally! transversity Collins FF Collins Extraction of Transversity: unknown Transverse Momentum Dependences!

50 Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk and Melis at Transversity 2008, Ferrara. Previously: Phys. Rev. D75:05032,2007 HERMES SIDIS (p) + COMPASS SIDIS (d) + Belle e + e -  transversity dist. + Collins FF Fit includes: Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e + e - Soffer Bound Old fit New fit

Examples of fits to azimuthal asymmetries 51 D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0 22     ) Cosine modulations clearly visible P1 contains information on IFF

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

SSA from di-hadron production See Talk R. Yang

IFF in SIDIS  R defined by: R = (z 1 p 2 – z 2 p 1 )/(z 1 +z 2 ) (X. Artru, hep-ph/ ) R

Summary & Outlook Collins FF at Belle final ->global analysis 2H Interference FF Analysis underway Plans for k T dependent Pol. & Upol. FFs –Necessary for global analysis w/o model assumptions Polarized Lambda FF 2H Interference FF Measurements at Phenix, HERMES and COMPASS –Non vanishing effect at HERMES and COMPASS –Together with Belle results -> Independent extraction of transversity Proposed Transverse Spin Sum rule Bakker, Leader, Trueman Phys.Rev.D70:114001,2004 Gluon contribution is Small (Phenix, Compass results)

Models Main contribution: interference of hadron pairs produced in relative s and p wave P wave from Vector meson decay S wave from non-resonant background Signal around vector meson mass Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, (2006) Two different theoretical models gave different prediction of mass dependence Sign change is not observed in HERMES/COMPASS results

Interference fragmentation functions Motivation: Measure quark transverse spin distribution in the nucleon Successful global analysis of our Collins results together with HERMES and COMPASS data revealed first glimpse at quark transversity distribution: Open questions: evolution of Collins functions Independent access via interference fragmentation: nonzero HERMES results nonzero COMPASS results zero PHENIX results (so far) Alexei Prokudin, DIS2008, update of Anselmino et al: hep-ex

Models Main contribution: interference of hadron pairs produced in relative s and p wave P wave from Vector meson decay S wave from non-resonant background Look around  -mass Jaffe, Jin and Tang, PRL 80 (1998) 1166Bacchetta and Radici, Phys. Rev. D 74, (2006) Two different theoretical models gave different prediction of mass dependence Sign change is not observed in HERMES/COMPASS results Charm meeting, June 4th 58 Interference fragmentation functions

Combining experiments and on/off resonance Charm meeting, June 4th Interference fragmentation functions 59 Treat all experimets separately, Extract average value in each kinematic bin over all experiments Separate fit of on- resonance and continuum data Extract average of continuum and onresonance values 5x5 x 2x2 m1,m2,z1,z2 binning Red. Chi2 distribution, NDF onresonance 21, NDF continuum 19 Red. Chi2 distribution, NDF: 1 (onres, continuum)

60 Applied Cuts, Binning Two data sets: off-resonance data ( 29.1 fb -1 ) on-resonance data ( 547 fb -1 ) Track selection: –p T > 0.1GeV –vertex cut: dr < 2cm, |dz| <4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –N track  3 –Thrust > 0.8 –z 1, z 2 > 0.2 Hemisphere cut Q T < 3.5 GeV Pion PID selection z2z z1z1 (z 1, z 2 )-binning

MC asymmetries (no asymmetry expected) 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 61 PhPh No opening cut Opening cut>0.7 Opening cut >0.8 in %

Interference Fragmentation – thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Stay in the mass region around  -mass Find pion pairs in opposite hemispheres Observe angles  1 +  2 between the event-plane (beam, jet-axis) and the two two-pion planes. Transverse momentum is integrated (universal function, evolution easy  directly applicable to semi-inclusive DIS and pp) Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(19 96)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] 62 Interference fragmentation functions  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)] Charm meeting, June 4th

Central values in binning Charm meeting, June 4th Interference fragmentation functions 63 9x9 z 1 z 2 binning 8x8 m 1 m 2 binning Polarization factor: Hemispheres are independent of each other In same hemisphere: higher m also corresponds to higher z and higher sin(  decay1 ) cos(  decay1 ) marginal (important for possible other Legende contributions)

Decay angle moments sin mostly very large (85%-98%) cos very symmetric  mostly <1% Bin to bin values will be given in results table Need to take sin moments into account for theory comparison 64

Chiral odd FFs + _ + ? _   + _ Collins effect Hadronic Tensor Helicity base: independent amplitudes: q  ’’ N _ L z -1LzLz

Systematic Studies Mc asymmetries Reweighted asymmetries –Constant, linear weights Mixed events Single hemispheres Higher harmonics Binning Inverse thrust Relative process contributions Correlation studies Combining data from diff exp Kinematics correlations & center values Pid systematics Cross checks Asymmetries as polar angles Decay angle dependent asymmetries Mixed binning asymmetries

Interference Fragmentation–thrust method e + e -  (  +  - ) jet1 (     ) jet2 X Find pion pairs in opposite hemispheres Observe angles  1 +  2 between the event- plane (beam, jet-axis) and the two two- pion planes. Transverse momentum is integrated (universal function, evolution easy  directly applicable to semi-inclusive DIS and pp) collinear factorization Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] Independent Measurement Favourable in pp: no Sivers 67  2   1 Model predictions by: Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

Expected sensitivities for ~580 fb -1 (     ) (     ) M inv <0.4 GeV0.4 GeV<M inv <0.55 GeV0.55 GeV<M inv <0.77 GeV 0.77 GeV <M inv < 1.2 GeV 1.2 GeV M inv < 2.0 GeV A AA A A

Cuts and Binning Similar to Collins analysis, full off-resonance and on- resonance data (7-55): ~73 fb fb -1 Visible energy >7GeV PID 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: abs(thrustz)<0.75 Thrust > 0.8 z had1,had2 >0.1 z 1 = z had1 +z had2 and z 2 in 9x9 bins: [0.2, 0.275, 0.35, 0.425, 0.5, 0.575, 0.65, 0.725, 0.825, 1.0] m  and m  in 8x8 bins: [0.25, 0.4, 0.5, 0.62, 0.77, 0.9, 1.1, 1.5, 2.0] Mixed single hemisphere binning 8x8 z 1 x m 1 Scattering angular binning and sin decay angle binnings for consistency checks Orientation of first hadron is positive, second negative, angle and plane defined by R=(P1-P2)/2 69

Pi+ Pi- Purities