Charged particle production in $pp$ collisions at $\sqrt{s}$=8, 7 and 2.76 TeV at the LHC -- a case study

Abstract: We analyse the charged${\text -}$particle multiplicity distributions measured by the ALICE experiment, over a wide pseudorapidity range, for $pp$ collisions at $\sqrt{s}$=8,\,7\,and\, 2.76~TeV at the LHC.~The analysis offers an understanding of particle production in high energy collisions in the purview of a new distribution, the shifted Gompertz distribution.~Data are compared with the distribution and moments of the distributions are calculated.~A modified version of the distribution is also proposed and used to improve the description of the data consisting of two different event classes; the inelastic and the non${\text -}$single${\text -}$diffractive and their subsets in different windows of pseudorapidity, $\eta$.~The distribution used to analyse the data has a wide range of applicability to processes in different fields and complements the analysis done by the ALICE collaboration in terms of various LHC event generators and IP-Glasma calculations.