Illinois-Indiana Fragmentation workshop, December 11, 2013 Ralf Seidl (RIKEN) for the Belle Collaboration

Illinois-Indiana Fragmentation workshop, December 11, 2013 Ralf Seidl (RIKEN) for the Belle Collaboration

What are fragmentation functions? How do quasi-free partons fragment into confined hadrons? Does spin play a role?flavor dependence? What about transverse momentum ( and its Evolution)? What experiments measure: Normalized hadron momentum in CMS: e + e - h(z) X ; z = 2E h / s Hadron pairs azimuthal distributions: e + e - h 1 h 2 X ; <cos(f 1 +f 2 )> ; Collins FF Interference(IFF) Cross sections or multiplicities differential in z: ep->hx, pp->hx Additional benefits of the FF measurements: Pol FFs necessary input to transverse spin SIDIS und pp measurements to extract Transversity distributions function Flavor separation of all Parton distribution functions (PDFs) via FFs (including unpolarized PDFs) Baseline for any Heavy Ion measurement Access to exotics? FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 2

Transverse quark polarization Unpolarized distribution function q(x) Helicity distribution function Dq(x) Sum of quarks with parallel and antiparallel polarization q(x),g(x) relative to proton spin (well known from Collider DIS experiments) Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton (known from fixed target (SI)DIS experiments) Dq(x), DG(x) Difference of quarks with parallel and antiparallel polarization relative to transversely polarized dq(x) proton (first results from HERMES and COMPASS with the help of Belle) Transversity distribution function dq(x) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 3

Transversity properties Helicity flip amplitude Chiral odd Since all interactions conserve chirality one needs another chiral odd object Does not couple to gluons adifferent QCD evolution than Dq(x) Valence dominateda Comparable to Lattice calculations, especially tensor charge Positivity bound: δq x q x Soffer bound: x qx qx δq 2 1 D FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 4

How to access Transversity: another chiral-odd function Drell Yan: Combine two Transversity distributions with each other SIDIS/pp: Combine Transversity distributions with chiralodd 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 F workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 5

Towards a global transversity analysis: Chiral odd Fragmentation functions RHIC and SIDIS experiments measure: Transversity dq(x) X Collins Fragmentation function H 1 z 2 Unknown Functions measured together or Interference Fragmentation function (IFF) Universality understood Evolution? Transversity Belle measures: Collins X Collins or IFF X IFF FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 6

Fragmentation functions in e + e - annihilation e - e + h 2Eh z, s 10 52. GeV s Process: e + e - hx At leading order sum of unpolarized fragmentation functions from quark and antiquark side FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 9

FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 10

Collins fragmentation function J. Collins, Nucl. Phys. B396, (1993) 161 s q q k h, p h f p h Spin of quark correlates with hadron transverse momentum translates into azimuthal anisotropy of final state hadrons FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 11

j 2 -p P h2 Collins fragmentation in e + e - : Angles and Cross section cos(f 1 +f 2 ) method e + e - CMS frame: e - P h1 2Eh z, s 10 52. GeV s j 1 j 2 j 1 - dσ e e h1h 2 ddz dz d q 1 2 cm 2 y1 - y sin B y 2 T e + 2-hadron inclusive transverse momentum dependent cross section: X 1 4 B y 1 1 cos j j H z H z 1 2 1 1 1 2 [D.Boer: PhD thesis(1998)] Nucl.Phys. B806 (2009) 23-6 Net (anti-)alignment of transverse quark spins FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 12

Inclusion of Upsilon(4S) data e + e - qq, q uds e + e - cc thrust i i p i p ˆ n i B B - 13 R.Seidl: Spin dependent fragmenation at Belle B 0 B 0 e + e - q q (u d s) MC U(4S) B + B - MC U(4S) B 0 B 0 MC Charm-tagged Data sample (used for charm correction) also increases with statistics Largest systematic errors reduce with more statistics FF workshop, Dec11 2013

systematic errors Tau contribution (not shown) Quark axis correction PID systematics MC uncertainties Charged ratios (p + p + /p - p - ) higher moments in Fit (not shown) difference double ratio-subtraction method Beam polarization studies consistent with zero Correction for charm events 14 R.Seidl: Spin dependent fragmenation at Belle FF workshop, Dec11 2013

Belle Collins asymmetries Red points : cos(f 1 + f 2 ) moment of Unlike sign pion pairs over like sign pion pair ratio : A UL Green points : cos(f 1 + f 2 ) moment of Unlike sign pion pairs over any charged pion pair ratio : A UC Collins fragmentation is large effect Consistent with SIDIS indication of sign change between favored and disfavored Collins FF RS et al (Belle), PRL96: 232002 PRD 78:032011, Erratum D86:039905 FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 15

Global Fit of Collins FF and Transversity (HERMES, COMPASS d, Belle) Collins function Transversity Latest SIDIS data not included infit Open questions: TMD evolution unknown(however from Belle to HERMES no large differences seen) Kt dependence from Assumption(Belle measurements planned) Interference FF(IFF) as independent Cross check FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 20 Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.191:98-107,2009

Global Fit of Collins FF and Transversity (HERMES, COMPASS d, Belle) Collins function Transversity Latest SIDIS data not included infit Open questions: TMD evolution unknown(however from Belle to HERMES no large differences seen) Kt dependence from Assumption(Belle measurements planned) Interference FF(IFF) as independent Cross check FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 21 Phys.Rev.D75:054032,2007, update in Nucl.Phys.Proc.Suppl.191:98-107,2009

One comment on Babar consistency See next talk: Babar results consistent except for highest z bin (0.75-1 vs 0.75-0.95) Potential reason tau dilution at very high z As we did not see any overall asymmetry of a tau enhanced sample we only assigned global systematic uncertainty However, tau mostly dominant at very highest z: Some asymmetry dilution due to tau contribution likely in last bin FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 22

Collins outlook Kaons: Francesca (UIUC) Need Kaon Collins fragmentation: to understand HERMES/COMPASS kaon data Flavor separation of transversity Inflation of FF functions: u,d p: 2 u,d,s p,k: 6+ Analysis ongoing, preliminary results expected soon F. Giordano (UIUC) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 23

Collins outlook p 0,h: Hairong Li (Indiana) Slight indication by STAR that h AN larger than p 0 (though consistent in PHENIX) h strange component could be cause for differences (see also HERMES, Brahms Kaon data) p 0 ( ½ fav + ½ disfavored) as crosscheck for charged Collins results Status: Analysis started, extracted p 0 and h Developing asymmetry code Unpolarized h FF only poorly known Measure also at Belle QCDN, October 24, 2012 spin dependent Fragmentation at Belle 24

Interference fragmentation Again azimuthal anisotropy of distribution of hadron pairs wrt transverse quark spin Collinear treatment of interference fragmentation evolution known (Cecciopieri et al: Phys.Lett. B650 (2007) 81-89) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 25

Interference Fragmentation thrust method e + e - (p + p - ) jet1 (p p - ) jet2 X Look in the mass region around r- mass (largest interference expected) Find pion pairs in opposite hemispheres Observe angles j 1 +j 2 between the event-plane (beam, jet-axis) and the two two-pion planes. Transverse momentum is integrated (universal function, evolution known directly applicable to semi-inclusive DIS and pp) Theoretical guidance by papers of Boer,Jakob,Radici[PRD 67,(2003)] and Artru,Collins[ZPhysC69(1996)] Early work by Collins, Heppelmann, Ladinsky [NPB420(1994)] A H FF workshop, Dec11 2013 z, m H z, cos j j 1 1 1 1 2 m2 1 R.Seidl: Spin dependent fragmenation at Belle 2 j 2 -p P h1 P P h 1 Ph 2 h2 Model predictions by: 26 p-j 1 Jaffe et al. [PRL 80,(1998)] Radici et al. [PRD 65,(2002)]

Asymmetry extraction Build normalized yields: N( f f2), Fit with: FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 27 27 or a c 12 12 a 1 N 12 cos( f1 f2) cos( f f ) b 1 cos 2( f f ) d 1 2 2 b 12 12 12 sin( f f ) Amplitude a 12 directly measures ( IFF ) x ( -IFF ) (no double ratios) 1 2

Zero tests: Mixed Events FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 28 (Red/blue points: Thrust axis last or current event)

Weighted MC asymmetries 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 Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 29

Systematic Errors Dominant: MC asymmetry + its statistical error (up to % level) Smaller contributions: PID: per mille level higher moments: sub per mille level Uncertainty on axis smearing correction mixed asymmetries: per mille level Tau asymmetries Note: asymmetries contain events from u,d,s and c events FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 30

Belle IFF asymmetries: (z 1 x z 2 ) Binning PRL107:072004(2011) Magnitude increasing with z FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 31

Belle IFF asymmetries: (z 1 x m 1 ) Binning PRL107:072004(2011) 2 d distributions of one hemisphere FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 32

(m 1 x z 1 ) Binning FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 33

First transversity extraction from HERMES, COMPASS and Belle IFF data Using Belle IFF and HERMES or COMPASS to extract transversity compared to Collins FF based global analysis: Courtoy, Bacchetta, Radici: Phys.Rev.Lett. 107 (2011) 012001 and arxiv:1206.1836 HERMES: JHEP 0806 (2008) COMPASS: Phys.Lett. B713 (2012) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle recent IFF analysis and Collins Transversity comparable CollinsFF evolution weak? But many assumptions at this point STAR and PHENIX Preliminary data not yet used 34

IFF outlook Kaons: Noriaki Kobayashi (TiTech) Kaon related IFF analysis equally necessary for flavor decomposition Charged combinations (eg p 0 p analysis also required Goal: flavor decomposition of transversity via IFF channel However: Requirements for flavor decomposition: Unpolarized di-hadron FFs as baseline Treatment of charm contribution FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 35

Summary and outlook Significant, nonzero Collins asymmetries Data used already in Global analysis Kaon related asymmetries will be ready soon p 0,h Collins analysis making good progress kt dependence of Collins function First direct measurement of the interference fragmentation function Large asymmetries seen, rising with z and invariant mass No sign change at r mass No double ratios make interpretation simple Collinear transversity extraction pk, KK IFFanalysis resumed New di-hadron fragmentation function analysis started Information of favored/disfavored FF Vector meson (r,k*,f) FF VM Collins analysis logical continuation Artru Model test Continue to measure precise spin dependent fragmentation functions at Belle FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 36

Belle Fragmentation activity Unpol FFs e + e - hx: e + e - (hh)x, (h)(h)x,hhx: Unpol k T dependence: RIKEN/RBRC Illinois Indiana Bilbao Titech Charged dihadrons: Ralf Seidl Charged hadrons (p,k,p): Martin Leitgab p 0,h 0: Hairong Li P, long prd Charlotte Hulse Charlotte Hulse Black: about to start Green:ongoing Grey: finished Collins FFs e + e - (h)(h)x: k T dependence: pr 0 : Ralf Seidl pp: Ralf Seidl pk,kk: Francesca Giordano Francesca Giordano pp 0 : Hairong Li Charlotte Hulse Interference FF: e + e - (hh)(hh)x Charged pp : Ralf Seidl Charged pp: Anselm Vossen pp 0 : Anselm Vossen Charged pk, KK: Nori-aki Kobayashi Local P : (polff,ssa) : Handetness: Jet-jet asy: Anselm Vossen Anselm Vossen QCDN, October 24, 2012 spin dependent Fragmentation at Belle 37

Backup Slides FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 38

The Collins effect in the Artru fragmentation model A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: String breaks and a dd-pair with spin -1 is inserted. π + picks up L=1 to compensate for the pair S=1 and is emitted to the right. In Artru Model: favored (ie up ) and disfavored (ie up - ) Collins function naturally of opposite sign R.Seidl: Spin dependent fragmenation at Belle 39 FF workshop, Dec11 2013

P h2 Collins fragmentation in e + e - : Angles and Cross section cos(2f 0 ) method 2 e - e + e - CMS frame: P h1 Independent of thrust-axis Convolution integral I over transverse momenta involved e + j 0 [Boer,Jakob,Mulders: NPB504(1997)345] 2-hadron inclusive transverse momentum dependent cross section: B - e e h 1h2 X Bcos2j I 2ĥ k ĥ p - k p dσ ddz dz d cm 1 1 4 2 2 q T 2 sin 0 T T T T H1 H M M 1 1 2 Net (anti-)alignment of transverse quark spins FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 40

Interference Fragmentation f 0 method Similar to previous method Observe angles j 1R j 2R between the event-plane (beam, twopion-axis) and the two two-pion planes. Theoretical guidance by Boer,Jakob,Radici j R2 P h P 3 h4 P h3 P h1 P h4 P P h 1 Ph 2 h2 p-j R1 A H z, m H z, cos j j 1 1 1 1 2 m2 1R 2R FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 41

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) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 42

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) FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 43

Zero tests: MC No opening cut Opening cut>0.7 Opening cut >0.8 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 P h P ˆ h n cos( P, n) P FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle h 44 44

Weighted MC asymmetries 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 Smearing In azimuthal Angle of thrust Axis in CMS Black: injected Purple reconstructed Hadron13, November 7, 2013 R.Seidl: Fragmentation function measurements 45

Heavy flavor fragmentation Rolf Seuster: Phys.Rev.D73:032002,2006, 103 fb -1 Charmed hadron fragmentation much harder than light hadron fragmentation heavy quark more likely to stay in heavy hadron FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 46

Unpolarized outlook: overcoming the flavor blindness of e+e- Unlike-sign pion pairs (U): (favored x favored + unfavored x unfavored) Like-sign pion pairs (L): (favored x unfavored + unfavored x favored) Reconstructed udsc Monte Carlo (Pythia/Evtgen in Belle acceptance) opposite hemisphere pion pairs Hadron13, November 7, 2013 R.Seidl: Fragmentation function measurements 47

Sample MC (udsc) distributions - pp same hemisphere: Distributions falling off rapidly Naturally as z 1 +z 2 <1 For same hemisphere also interesting: z Pair,m Pair distribution Corresponding resonances FF (r, K *, F) Also unpol Baseline for IFF FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 48

Higher statistics available at high z B decays almost at rest no hadrons above 0.5 Instead of about 90 pb -1 almost 1000 fb -1 available Useful at high z, where statistics is low FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 49

Rho Collins similar plans for p 0,h Measure Collins effect for e + e - p ± r 0 X According to Artru model sign change expected wrt. pion Collins: sgn a 12 (p ± r 0 ) = - sgn a 12 (p ± p ± ) Instead of double ratios to eliminate acceptance/radiative effects use combinatoric BG Normally: FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 50

MC (uds) Rho Collins example Acceptance effect visible in all three mass ranges Magnitude similar, but need more statistics to confirm method FF workshop, Dec11 2013 R.Seidl: Spin dependent fragmenation at Belle 51