On the $\xi$-Distribution of Inclusively Produced Particles in $e^+e^-$ Annihilation

TL;DR

This paper analyzes the momentum distributions of particles produced in electron-positron annihilation, demonstrating how the peak positions of the spectra depend on particle mass through fragmentation functions and energy-momentum conservation.

Contribution

It provides a theoretical explanation for the mass dependence of the spectral maxima in particle production using fragmentation functions and conservation laws.

Findings

Maxima positions of $\xi$ spectra depend on particle mass

Dependence derived from fragmentation functions with energy-momentum conservation

The approach explains experimental observations of particle spectra

Abstract

We discuss the momentum distributions of inclusively produced particles in $e^+e^-$ annihilation. We show that the dependence of the position of the maxima of the $\xi=\ln(1/z)$ spectra on the mass of the produced particles follows naturally from the general definition of fragmentation functions when energy-momentum conservation is correctly incorporated.