Fragmentation in the phi^3 Theory and the LPHD Hypothesis

TL;DR

This paper analytically solves the DGLAP equation in a hypothetical phi^3 theory to explore jet parton distributions and demonstrates that the LPHD hypothesis fails without detailed hadronisation modeling, emphasizing the importance of hadronisation in jet physics.

Contribution

It provides the first analytic solution of the DGLAP equation in phi^3 theory and critically examines the LPHD hypothesis in this context.

Findings

LPHD does not hold in the phi^3 theory scenario.

Hadronisation modeling is crucial for accurate jet hadron distributions.

Analytic solutions offer insights into parton evolution in simplified theories.

Abstract

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.