Fragmentation Functions, Flavor Dependence

1. Fragmentation Functions, Flavor Dependence M. Grosse Perdekamp, Illinois • Motivation • What is known from the analysis of inclusive hadron production in • e+e-  h + X • eN  h + X • pp  h + X • New Results from Belle • Spin dependent fragmentation • Projections for Super Belle Workshop on Flavor Structure of the Nucleon Sea at ECT, Trento, July 1st, 2013

2. Hadron Fragmentation Functions (FFs) q Number density for finding hadron h from a quark, q:

3. Importance of Fragmentation Functions • The extraction of spin dependent quark and gluon distributions • through global QCD analysis relies on the knowledge of hadron • fragmentation functions: • pp at RHIC, • SIDIS at HERMES, COMPASS, Jlab and in the future EIC • e+e- at Belle and Babar • pp-baseline for heavy ion measurements at RHIC and LHC; • determination of nuclear PDFs. • Characterization of hadron backgrounds at the LHC.

4. Example I: Helicity Distributions from SIDIS at EIC EIC: projected uncertainties for anti-quark helicity distributions from SIDIS (A. Accardi et al. EIC White Paper arXiv:1212.1701)

5. Example II: Quark Transversity Distribution Extraction from SIDIS and e+e- Data J.C. Collins, Nucl. Phys. B396, 161(1993) Collins Effect in Quark Fragmentation q Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence:

6. Example II: Quark Transversity Distribution Extraction from SIDIS and e+e- Data √s=10 GeV e++ e-  π+ + π- +X Program: Combined analysis of Collins asymmetries in SIDIS (HERMES & COMPASS) + Collins asymmetries in e+e- (Belle)  extract quark transversity distributions and Collins fragmentation functions 27.5 GeV e+p  π + X 160 GeV μ+d  π + X 5

7. SIDIS AUT is sensitive to the Product of [Transversity,δq(x) ] x [Collins FF, CFF (z)] Collins Asymmetries from HERMES, eg. Luciano Pappalardo, DIS 2009, Madrid Collins Asymmetries in semi- inclusive deep inelastic scattering e+p  e + π + X ~ Transversity (x) x Collins(z) cannot unfold δq(x) without additional information! x=0.3 AUT sin(f+fs) HERMES data cover x < 0.3

8. e+e- Annihilation into Quarks is sensitive to [Collins FF, CFF (z1)] x [Collins FF, CFF (z2)] R. Seidl, K. Hasuko, A. Ogawa, S. Lange, M. Grosse Perdekamp et al. Phys. Rev. Lett. 96 232002 2006 and Phys. Rev. D 78 032011, 2008 Collins Asymmetries in e+e- annihilation into hadrons e++e- π++ π- + X ~ Collins(z1) x Collins (z2) j2-p e- Q j1 e+ A12 cos(f1+f2) 8

9. Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS+e+e- Anselmino, Prokudin et al. Phys. Rev. D75:05032, 2007 Nucl. Phys. Proc. Suppl. 191, 2009 Extraction of Transversity & Collins FF including errors ! Belle: Collins Asymmetries + HERMES, & COMPASS data  first extraction of δq(x) :

10. Spin Averaged Fragmentation Functions from Global QCD Analysis of Single Hadron Production in e+e-, SIDIS and pp Global analysis of FFs have been carried out by several groups: List from Hiroyuki Kawamura

11. FFs from Global Analysis of e+e- Data Hiroyuki Kawamura at Fragmentation 2012 at RIKEN e+e- data on hadron cross sections: zh

12. FFs from Global Analysis of e+e- Data HKNS 2007 M. Hirai, S. Kumano, T.H. Nagai, K. Sudoh Phys.Rev. D75 (2007) 094009 Positive pion  favored FF at input scale  disfavored FF  Gluon FF  charm & bottom FFs Limited sensitivity to flavor structure and gluon FF !

13. FFs from Global Analysis of e+e- , pp and ep Single Hadron Data D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 • Global analysisof all availablee+e-­‐, ep, and pp data for single hadron production • requires flexible functional form • Reduce assumptions on flavor structure Pion Kaon

14. FFs from Global Analysis: Fit to e+e- D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 Fit to pions in e+e-  constrain flavor singlet

15. FFs from Global Analysis:Fit to e+e- with Heavy Flavor Tags D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 Fit to pions in e+e- charm and bottom tagged data

16. FFs from Global Analysis: Fit to SIDIS D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 Fit to pions in SIDIS  tag flavor structure

17. FFs from Global Analysis: pp data D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 Fit to pions in pp  tag gluon for large z

18. FFs from Global Analysis Results D. de Florian, R.Sassot, M. Stratmann PRD 75 (2007) 114010; 76 (2007) 074033 Pion FFs Kaon FFs Comparison to previous global analysis : Dg different at high z due to pp data! Significant flavor dependence compared to errors.

19. Lagrange Multiplier Method to Estimate Uncertainties Chi-2 Profiles for truncated moments

20. Motivation for High Statistics Measurement for Hadron Multiplicities at B-Factories limited data for z>0.7 and at low Q2

21. Belle (and BaBar): New Results for Pion and Kaon Multiplicites Martin Leitgab, UIUC at Fragmentation 2012

22. Pions: New Results vs Previous Martin Leitgab at Fragmentation 2012

23. Kaons: New Results vs Previous Martin Leitgab, at Fragmentation 2012

24. Impact of New Belle Results on HKNS at NLO Hiroyuki Kawamara at Fragmentation 2012 HKNS2007 Belle 2012 gluon favored disfavored bottom charm relative uncertainties

25. Re-Call Spin Dependent FFs Di-Hadron Measurement used in combined analysis with SIDIS Collins data to extract quark transversity distributions and the Collins FF for pions: Collins effect in e+e- quark fragmentation will lead to azimuthal asymmetries in di-hadron correlation measurements: Nπ1,π2(ϕ1+ϕ2) ~a12cos(ϕ1+ϕ2) a12~ Collins(z1) x Collins (z2) electron ϕ2 ϕ1 e++e- π++ π- + X θ q1 z2 z1 q2 quark-1 spin quark-2 spin z1,2 relative pion momenta positron

26. Favored and Dis-Favored Collins FF from Combined Analysis of e+e- and SIDIS Favored Collins FF Dis-Favored Collins FF

27. Projections for Super Belle KEKB Upgrade & Luminosity Backgrounds & Detectors Projections for di-hadron yields and kT dependent yields Combined analysis with SIDIS yields from Jlab 12 GeV and EIC

28. Asymmetric energy e+e- collider at ECM = m ((4S)) to be realized by upgrading the existing KEKB collider. • Initial target: 10×higher luminosity ~ 21035/cm2/sec • Final goal: L=81035/cm2/sec and ∫L dt = 50 ab-1 New IR with crab crossing and smaller by* More RF for higher beam current Damping ring for e+ Upgrade Plan for Super KEKB Crab cavity 8GeV e- 3.5GeV e+ Assume 5 ab- 1 off-resonance for FF analysis ! New beam-pipe with ante-chamber beam SR

29. Beam Background for Super Belle 1st layer New Belle detector must handle up to 20 times more background

30. New Detector Required for 20 Times Increased Background (Super -)

31. Super Belle Faster calorimeter with waveform sampling and pure CsI (endcap) New particle identifier with precise Cherenkov device: (i)TOP or fDIRC. KL/m detection with scintillator and next generation photon sensors Background tolerant super small cell tracking detector New dead time free pipelined readout and high speed computing systems Si vertex detector with high background tolerance & fast readout

32. Observe Yields for e+e- Annihilation into h1 and h2 in Opposite Jet-Hemispheres For hadrons observed in opposite hemispheres: electron q1 z2 z1 q2 Combinations: z1,2 relative hadron momenta positron

33. 1 10-1 10-2 10-3 10-4 10-5 1 10-1 10-2 10-3 10-4 10-5 0.5 < z1 < 0.55 0.2 < z1< 0.25 Relative Stat. Error Relative Stat. Error Future input to flavor sensitive FF analysis of SIDIS data z2 z2 1 10-1 10-2 10-3 10-4 10-5 1 10-1 10-2 10-3 10-4 10-5 0.7 < z1< 0.75 Relative Stat. Error Relative Stat. Error 0.9 < z1< 0.95 z2 z2 Martin Leitgab

34. Observe pT Dependence of Yields for e+e- Annihilation into hadron h electron Constrain kT-dependence of fragmentation functions q pT z Combinations: zrelative hadron momenta positron

35. 1 10-1 10-2 10-3 10-4 10-5 1 10-1 10-2 10-3 10-4 10-5 0.2 < z< 0.25 0.5 < z< 0.55 Relative Stat. Error Relative Stat. Error pT[GeV] pT[GeV] 1 10-1 10-2 10-3 10-4 10-5 1 10-1 10-2 10-3 10-4 10-5 0.7 < z< 0.75 0.9 < z< 0.95 Relative Stat. Error Relative Stat. Error pT[GeV] pT[GeV] Martin Leitgab

36. Precision TMDs in SIDIS at JLab12 GeV Collins and Sivers Asymmetries at Jlab 12 GeV high precision to x ~ 0.7 Collins Measure in x,z, pT bins with high precision. Sivers

37. Precision Measurements of TMDs at EIC SSA projections (Collins, Sivers, Pretzelosity) for e-proton

38. Precision Measurements of TMDs at EIC SSA projections (Collins, Sivers, Pretzelosity) for e-deuteron

39. Use Precision Data from e+e- and SIDIS for Best Knowledge of FFs and PDFs. Example: Analysis of Collins Asymmetries Collins FF transversity hadron FF quark pdf kTtransverse quark momentum in nucleon pT transverse hadron momentum in fragmentation Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 The transverse momentum dependencies are currently unknown and model assumptions are being made. A combined analysis of precise spin averaged and spin dependent observables measured as function of transverse momentum in SIDIS and e+e- might be possible in the future.

40. Summary o The simultaneous analysis of 1-hadron observables in e+e-, e-p and p-p gives first insight in the flavor structure of hadron fragmentation o New Belle data will be published soon. Main impact on knowledge of gluon FF from evolution and reduced errors in other FFs. o High statistics data samples from Jlab 12 GeV, Super Belle (including back-to-back di-hadron multiplicities) and in the future EIC will lead to the precise extraction of parton helicity distributions, TMDs and the relevant fragmentation functions.