The particle emitter size dependence on energy in e^+ e^- annihilations into hadrons

The nearly energy independent hadron emitter dimension $r$, measured in $e^+e^-$ annihilation in the energy range 10 to 91 GeV via the Bose-Einstein correlation of two identical charged pions, is shown to be well accounted for by choosing the hadron jets as independent pion sources. To this end the known normalised factorial cumulant moments dependence on particle sources is adapted to the Bose-Einstein correlation formalism to yield a relation between $r$ and these sources. This approach is also able to account for the measured $r$ values obtained for the $Z^0$ decays into two and three hadron jets. Finally the estimated $r$ value of the hadronic $\Upsilon(9.46)$ decay via three gluons is expected to be higher by about 6 to 11 % over that predicted for its one photon hadronic decay mode.