1. Measurements of chiral-odd fragmentation functions at Belle D. Gabbert (University of Illinois and RBRC) M. Grosse Perdekamp (University of Illinois and RBRC) K. Hasuko (RIKEN/RBRC) S. Lange (Frankfurt University) A. Ogawa (BNL/RBRC) R. Seidl (University of Illinois and RBRC) V. Siegle (RBRC) for the Belle Collaboration SSA workshop June1 st – 3 rd, BNL, NY

2. measurements of chiral-odd fragmentation functions at Belle2 SSA workshop, June, 2 nd Outline Motivation –Global transversity analysis –Feasibility  LEP analysis [hep-ph/9901216] The BELLE detector Collins analysis –Angular definitions and cross sections –Double Ratios to eliminate radiative/momentum correlation effects –An experimentalist’s interpretation Summary

3. measurements of chiral-odd fragmentation functions at Belle3 SSA workshop, June, 2 nd SIDIS experiments (HERMES and COMPASS) measure  q(x) together with either Collins Fragmentation function or Interference Fragmentation function Motivation: Global Transversity Analysis RHIC measures the same combinations of quark Distribution (DF) and Fragmentation Functions (FF) plus unpolarized DF q(x) There are always 2 unknown functions involved which cannot be measured independently The Spin dependent Fragmentation function analysis yields information on the Collins and the Interference Fragmentation function ! Universality appears to be proven in LO by Collins and Metz: [PRL93:( 2004)252001 ]

4. measurements of chiral-odd fragmentation functions at Belle4 SSA workshop, June, 2 nd KEKB: L>1.5x10 34 cm -2 s -1 !! KEKB –Asymmetric collider –8GeV e - + 3.5GeV e + –  s = 10.58GeV (  (4S)) e + e -   S    –Off-resonance: 10.52 GeV e + e -  q  q (u,d,s,c) –Integrated Luminosity: >400 fb -1 >30fb -1 => off-resonance Belle detector KEKB

5. measurements of chiral-odd fragmentation functions at Belle5 SSA workshop, June, 2 nd Good tracking and particle identification!

6. measurements of chiral-odd fragmentation functions at Belle6 SSA workshop, June, 2 nd Good detector performance (acceptance, momentum resolution, pid) Jet production from light quarks  off-resonance (60 MeV below resonance) (~10% of all data) Intermediate Energy  Sufficiently high scale (Q 2 ~ 110 GeV 2 ) - can apply pQCD  Not too high energy (Q 2 << M Z 2 ) -avoids additional complication from Z interference Sensitivity = A 2 sqrt(N) ~ x19 (60) compared to LEP A Belle / A LEP ~ x2 (A scales as ln Q 2 ) L Belle / L LEP ~ x23 (230) Belle is well suited for FF measurements:

7. measurements of chiral-odd fragmentation functions at Belle7 SSA workshop, June, 2 nd e-e- e+e+ Jet axis: Thrust = 6.4 Near-side Hemisphere: h i, i=1,N n with z i Far-side: h j, j=1,N f with z j  Event Structure at Belle e + e - CMS frame: Spin averaged cross section:

8. measurements of chiral-odd fragmentation functions at Belle8 SSA workshop, June, 2 nd Collins fragmentation: Angles and Cross section cos(     ) method       2-hadron inclusive transverse momentum dependent cross section: Net anti-alignment of transverse quark spins  e + e - CMS frame: e-e- e+e+

9. measurements of chiral-odd fragmentation functions at Belle9 SSA workshop, June, 2 nd Collins fragmentation: 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]

10. measurements of chiral-odd fragmentation functions at Belle10 SSA workshop, June, 2 nd Applied cuts, binning Off-resonance data (in the future also resonance) Track selection: –pT > 0.1GeV –vertex cut: dr<2cm, |dz|<4cm Acceptance cut –-0.6 < cos  i < 0.9 Event selection: –Ntrack  3 –Thrust > 0.8 –Z 1, Z 2 >0.2 Light quark selection Hemisphere cut <0 Opening angule cuts: - cos(2   ) method:  - cos(     ) method:      z2z2 0123 4 5 6 78 9 0.2 0.3 0.5 0.7 1.0 0.20.30.50.71.0 5 86 1 2 3 z1z1 z-binning: 0.2 0.3 0.5 0.7 1.0

11. measurements of chiral-odd fragmentation functions at Belle11 SSA workshop, June, 2 nd Examples of fitting the azimuthal asymmetries Cosine modulations clearly visible No change in cosine moments when including higher harmonics (even though double ratios will contain them) D 1 : spin averaged fragmentation function, H 1 : Collins fragmentation function N(  )/N 0

12. measurements of chiral-odd fragmentation functions at Belle12 SSA workshop, June, 2 nd Raw asymmetries vs Q T      Q T describes transverse momentum of virtual photon in  CMS system Significant nonzero Asymmetries visible in MC (w/o Collins) Acceptance, radiative and momentum correlation effects similar for like and unlike sign pairs uds MC (  ) Unlike sign pairs uds MC (  ) Like sign pairs

13. measurements of chiral-odd fragmentation functions at Belle13 SSA workshop, June, 2 nd 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

14. measurements of chiral-odd fragmentation functions at Belle14 SSA workshop, June, 2 nd Testing the double ratios with MC Asymmetries do cancel out for MC Double ratios of         compatible to zero Mixed events also show zero result Asymmetry reconstruction works well for  MC (weak decays) Single hemisphere analysis yields zero  Double ratios are safe to use uds MC (  pairs ) charm MC  pairs  Data (         )

15. measurements of chiral-odd fragmentation functions at Belle15 SSA workshop, June, 2 nd Results for  -pairs for 30fb -1 Significant non- zero asymmetries Rising behaviour vs. z cos      double ratios only marginally larger First direct measurement of the Collins function z1z1 z2z2

16. measurements of chiral-odd fragmentation functions at Belle16 SSA workshop, June, 2 nd Systematics: charm contribution? Weak (parity violating) decays could also create asymmetries (seen in    overall  dilution 5%) Especially low dilution in combined z-bins with large pion asymmetry Double ratios from charm MC compatible to zero  Charm decays cannot explain large double ratios seen in the data  Systematic errors from charm are preliminary Charm fraction N(charm)/N(all)

17. measurements of chiral-odd fragmentation functions at Belle17 SSA workshop, June, 2 nd Take unpolarized parameterizations (Kretzer at Q 2 =2.5GeV 2 ) Assume (PDF-like behaviour) Assume Sensitivity studies in progress An experimentalist’s interpretation: fitting parameterizations of the Collins function(s)

18. measurements of chiral-odd fragmentation functions at Belle18 SSA workshop, June, 2 nd Take simple parameterization to test sensitivity on favored to disfavored Ratio Favored/Disfavored contribution  Sensitivity c b

19. measurements of chiral-odd fragmentation functions at Belle19 SSA workshop, June, 2 nd Summary and outlook Double ratios: –double ratios from data –most systematic errors cancel Analysis procedure passes zero tests Main systematic uncertainties understood Significant nonzero double ratios  Naïve LO analysis shows significant Collins effect Finalize analysis On resonance  10 x statistics Include    into analysis:  Better distinction between favored and disfavored Collins function Include VMs into analysis:  Possibility to test string fragmentation models used to describe Collins effect Expansion of analysis to Interference fragmentation function straightforward Summary:Outlook:

20. measurements of chiral-odd fragmentation functions at Belle20 SSA workshop, June, 2 nd What is the transverse momentum Q T of the virtual photon? In the lepton CMS frame e - =-e + and the virtual photon is only time-like: q  =(e -  +p +  )=(Q,0,0,0) Radiative (=significant BG) effects are theoretically best described in the hadron CMS frame where P h1 +P h2 =0  q  ’ =(q ’ 0,q ’ ) Inclusive Cross section for radiative events (acc. to D.Boer): P h1 e+e+ e-e- P h2 e-’e-’ e+’e+’ q’ P’ h1 P’ h2 qTqT Lepton-CMS Hadron-CMS

21. measurements of chiral-odd fragmentation functions at Belle21 SSA workshop, June, 2 nd Different charge combinations  additional information Unlike sign pairs contain either only favored or only unfavored fragmentation functions on quark and antiquark side: Like sign pairs contain one favored and one unfavored fragmentation function each: Favored= u   ,d   ,cc. Unfavored= d   ,u   ,cc.

22. measurements of chiral-odd fragmentation functions at Belle22 SSA workshop, June, 2 nd Raw asymmetries vs transverse photon momentum Q T      Already MC contains large asymmetries Strong dependence against transverse photon Momentum Q T Expected to be due to radiative effects Difference of DATA and MC is signal  not so easy to determine DATA (  ) fiducial cut DATA (KK) fiducial cut UDS-MC fiducial cut CHARM-MC fiducial cut Unlike sign pairs Like sign pairs