???????f0(980)????????

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???????f0(980)????????

• ???? (?????)
• ???????(???), ????(KEK),
• ????(KEK)
• To be published in PRD
• arXiv0708.1816 hep-ph
• 2008, Jan. 12 _at_KEK

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Contents

• Introduction
• Fragmentation functions (FFs)
• Global analysis
• Possible f0(980) configurations
• Results discussion
• Behavior of obtained FFs
• 2nd moments of FFs
• Summary

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Introduction

• Internal structure of exotic hadrons
• Parton distribution functions (PDFs)
• Measured by deeply inelastic scattering (DIS )
  experiments
• Need stable targets (ex. proton)
• Exotic hadron ?
• Decay
• Short life time, no stable target
• Produced hadrons in ee- scattering
• p, k, p, a0, f0, et al.
• Fragmentation functions (FFs)
• Information about internal structure of produced
  hadrons

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Fragmentation Functions (FFs)

• Information of hadronization
• Probability to find the hadron h from a parton i
  with energy fraction z Dhi(z)
• Containing no perturbative object
• Determined by a global analysis with experimental
  data in ee?? h X
• Similar behavior to PDFs
• Favored FF like valence quarks
• A constituent of produced hadrons
• Peak position at medium and large-z
• Disfavored FF like sea quarks
• Peak position at small-z

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Global analysis of FF

• Cross sections observable
• DGLAP equation
• Scale QmFmR ?s center of mass energy

Coefficient Function - calculable in pQCD
Fragmentation Function - extracted from
experiments
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Fragmentation functions of f0(980)

• Functional form of initial distributions at Q02
• Constraint condition
• 2nd moment should be finite and less than 1

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Possible f0(980) configurations
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Results

• c2/d.o.f. 0.907
• Total of data 23
• Tetra quark configuration
• Becoming favored FFs for light and strange quarks
• Peak position at large-z (z0.85)
• zumax zsmax
• SS configuration
• Mu/Ms0.43 ? 6.73
• Mu lt Ms
• Large uncertainty
• Need precise measurements to reduce their huge
  uncertainties

• 2nd moments
• Mu0.0012 ? 0.0107
• Ms0.0027 ? 0.0183
• Mg0.0090 ? 0.0046

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Comparison of data with theory

• Large uncertainty
• Consistent with deviation of experimental data
  with their errors
• Rather large uncertainty at low Q2
• Reducing the uncertainties
• Needs of precise data
• Wide rage of Q2
• Determination of gluon FF
• Belle experiment ?s11 GeV
• Heavy quark tagged data
• Charm, bottom quarks ? f0(980)

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Summary

• Internal structure of the exotic hadron from
  fragmentation functions
• Global analysis of FFs with the data of the
  f0(980) production
• Favored disfavored FFs valence sea quarks
• Peak position zmax
• Relation between the 2nd moments of FFs
• Intuitive estimation of order counting for the
  f0(980) production in various quark
  configurations
• Indicating tetra-quark and ss configuration
• Tetra-quark peak position of the up(down)
  strange quark FFs
• SS relation of the 2nd moments
• Huge uncertainties of the FFs and 2nd moments
• Low accuracy of experimental data
• Need precise measurements from the Belle
  experiments
• Model predictions for the FFs
• Relation between behavior of FFs and quark
  configurations

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Global analysis of FFs

• Q2 dependence of FFs
• DGLAP eq
• Q02 1GeV2
• Minimizing c2
• Error estimation
• Hessian method
• D?2 (N12) 13.74

• Data sets of f0(980)
• HRS4 (?s29.0 GeV, 0.165lt z lt0.554)
• PRL 57, 1990 (1986)
• OPAL8 (?s91.2 GeV, 0.092lt z lt 0.75)
• EPJ C4,19 (1998)
• DELPHI10 (?s91.2 GeV, 0.078lt z lt 0.7)
• PL 449B,364 (1999),ZP C65, 587 (1995)
• Total of data 23
• NLO analysis
• MS scheme
• Reduction of theoretical uncertainty
• c2/d.o.f. 0.907