Fragmentation in the phi³ Theory and the LPHD Hypothesis

We present analytic solution of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation at leading order (LO) in the phi^3 theory in 6 space-time dimensions. If the phi^3 model was the theory of strong interactions, the obtained solution would describe the distribution of partons in a jet. We point out that the local parton-hadron duality (LPHD) conjecture does not work in this hypothetical situation. That is, treatment of hadronisation of shower partons is essential for the description of hadron distributions in jets stemming from proton-proton (pp) collisions at \sqrt{s} = 7 TeV and from electron-positron (e+e-) annihilations at various collision energies. We use a statistical model for the description of hadronisation.