Monte-Carlo Approach to Calculating the Fragmentation Functions in NJL-Jet Model

TL;DR

This paper introduces a Monte Carlo simulation method for calculating fragmentation functions within the NJL-Jet model, enabling more flexible and detailed modeling of hadron emission processes in quark cascades.

Contribution

The paper develops a Monte Carlo approach to solve the NJL-Jet model's fragmentation functions, relaxing previous assumptions and paving the way for more comprehensive hadronization modeling.

Findings

MC simulations closely match integral equation solutions for large hadron emissions

MC method allows inclusion of additional hadronic channels and resonance decays

Enables study of transverse momentum dependence in fragmentation functions

Abstract

Recent studies of the fragmentation functions using the Nambu--Jona-Lasinio (NJL) - Jet model have been successful in describing the quark fragmentation functions to pions and kaons. The NJL-Jet model employs the integral equation approach to solve for the fragmentation functions in quark-cascade description of the hadron emission process, where one assumes that the initial quark has infinite momentum and emits an infinite number of hadrons. Here we introduce a Monte Carlo (MC) simulation method to solve for the fragmentation functions,, that allows us to relax the above mentioned approximations. We demonstrate that the results of MC simulations closely reproduce the solutions of the integral equations in the limit where a large number of hadrons are emitted in the quark cascade. The MC approach provides a strong foundation for the further development of the NJL-Jet model that might include many more hadronic emission channels with decays of the possible produced resonances, as well as inclusion of the transverse momentum dependence (TMD), all of which are of considerable importance to the experimental studies of the transverse structure of hadrons.