1. Internal structure of f0(980) meson by fragmentation functions
M. Hirai (TUS)
Collaborators: S. Kumano(KEK), M. Oka(TiTech), K. Sudoh (Nishogakusha)
Phys. Rev D (2008);
arXiv:   [hep-ph]
2008, Dec.

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

3. Internal structure of exotic hadrons
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 e+e- scattering
p, k, p, a0, f0, et al.
Fragmentation functions (FFs)
Information about internal structure of produced hadrons

4. Fragmentation Functions (FFs)
Information of hadronization
Containing no perturbative object
Determined by a global analysis with experimental data in e++e 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
Favored F
Disfavored F
Z=Eh/Eq

5. Global analysis of FF Cross sections: observable DGLAP equation:
Scale Q=mF=mR =s: center of mass energy
Coefficient Function
calculable in pQCD
Fragmentation Function
extracted from experiments
: scaling variable
: j →i splitting function

6. Fragmentation functions of f0(980)
Functional form of initial distributions at Q02
Constraint condition
2nd moment should be finite and less than 1

7. Possible f0(980) configurations

8. Results c2/d.o.f. = 0.907 Tetra quark configuration SS configuration
Total # of data: 23
Tetra quark configuration
Becoming favored FFs for light and strange quarks
Peak position at large-z (z~0.85)
zumax ~ zsmax
SS configuration
Mu/Ms=0.43  6.73
Mu < Ms
Large uncertainty
Need precise measurements to reduce their huge uncertainties
2nd moments
Mu= 
Ms= 
Mg= 

9. 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 Bell, BaBar experiments
Model predictions for the FFs
Relation between behavior of FFs and quark configurations

11. Global analysis of FFs Q2 dependence of pol-PDFs Data sets of f0(980)
HRS:4 (s=29.0 GeV, 0.165< z <0.554)
PRL 57, 1990 (1986)
OPAL:8 (s=91.2 GeV, 0.092< z < 0.75)
EPJ C4,19 (1998)
DELPHI:10 (s=91.2 GeV, 0.078< z < 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
Q2 dependence of pol-PDFs
DGLAP eq
Q02 = 1GeV2
Minimizing c2
Error estimation
Hessian method
D2 (N=12) = 13.74

12. 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 s~10 GeV
Heavy quark tagged data
Charm, bottom quark → f0(980)