Generalised Tsallis Statistics in Electron-Positron Collisions

The scaling of charged hadron fragmentation functions to the Tsallis distribution for $0.01 \lessapprox x \lessapprox 0.2$ is presented for various $e^+e^-$ collision energies. A possible microcanonical generalisation of the Tsallis distribution is proposed, which gives good agreement with measured data up to $x\approx1$. The proposal is based on superstatistics and a $KNO$ like scaling of multiplicity distributions in $e^+e^-$ experiments.