# Unified Description of Multiplicity Distributions and Bose-Einstein Correlations at the LHC Based on the Three-Negative Binomial Distribution

## TL;DR

This paper introduces a unified approach using the three-negative binomial distribution to describe multiplicity distributions and Bose-Einstein correlations at the LHC, providing new insights into particle interactions and scaling behaviors.

## Contribution

The study applies the T-NBD framework to analyze multiplicity and BEC data at LHC energies, revealing consistent interaction ranges and explaining KNO scaling violations.

## Key findings

- T-NBD effectively models multiplicity distributions and BEC at LHC energies.
- Estimated interaction ranges R1 and R2 are nearly identical and consistent with pp collisions.
- The enlarged KNO scaling function accounts for observed violations at high energies.

## Abstract

Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration (PYTHIA 6), we examine the necessity of applying the three-negative binomial distribution (T-NBD). By making use of the T-NBD formulation, we analyze the multiplicity distribution (MD) and the Bose-Einstein correlation (BEC) at the Large Hadron Collider (LHC). In the T-NBD framework, the BEC is expressed by two degrees of coherence $\lambda_1$ and $\lambda_2$ and two kinds of exchange functions $E_1^2$ and $E_2^2$ that act over interaction ranges $R_1$ and $R_2$, respectively. Using the calculated $\lambda_1$ and $\lambda_2$ based on the T-NBD, along with free $\lambda_1$ and $\lambda_2$, we analyze the BEC data at 0.9 and 7 TeV. The estimated parameters $R_1$ and $R_2$ are almost coincident and seem to be consistent with $pp$ collisions. We also present an enlarged Koba-Nielsen-Olesen (KNO) scaling function based on the T-NBD, and apply it to KNO scaling at LHC energies. The enlarged scaling function describes the observed violation of the KNO scaling.