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Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration(PYTHIA 6), we examine the necessity of applying the three-negative binomialdistribution (T-NBD). By making use of the T-NBD formulation, we analyze themultiplicity distribution (MD) and the Bose-Einstein correlation (BEC) at theLarge Hadron Collider (LHC). In the T-NBD framework, the BEC is expressed bytwo degrees of coherence $\lambda_1$ and $\lambda_2$ and two kinds of exchangefunctions $E_1^2$ 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 theT-NBD, along with free $\lambda_1$ and $\lambda_2$, we analyze the BEC data at0.9 and 7 TeV. The estimated parameters $R_1$ and $R_2$ are almost coincidentand seem to be consistent with $pp$ collisions. We also present an enlargedKoba-Nielsen-Olesen (KNO) scaling function based on the T-NBD, and apply it toKNO scaling at LHC energies. The enlarged scaling function describes theobserved violation of the KNO scaling.

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