# Statistical method in quark combination model

## TL;DR

This paper introduces a simplified generating function method to solve probability distributions of hadrons in the quark combination model, aiding the study of multiplicity fluctuations and phase transitions in heavy-ion collisions.

## Contribution

It presents a new, more straightforward method using generating functions for the quark combination rule, enhancing analysis of hadronization and multiplicity distributions.

## Key findings

- Derived probability distributions for baryons, antibaryons, and mesons.
- Analyzed multiplicity cumulant ratios of net-protons.
- Discussed potential for studying phase transitions in heavy-ion collisions.

## Abstract

We present a new method of solving the probability distribution for baryons, antibaryons and mesons at the hadronization of constituent quark and antiquark system. The hadronization is governed by the quark combination rule in the quark combination model developed by the Shandong Group. We use the method of the generating function to derive the outcome of the quark combination rule, which is much simpler and easier to be generalized than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of multiplicity distribution of net-protons. Taking a naive case of quark number fluctuations and correlations at hadronization, we calculate ratios of multiplicity cumulants of final-state net-protons and discuss the potential applicability of quark combination model in studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions.