Glauber model for a small system using the anisotropic and inhomogeneous density profile of a proton

Abstract

Recent studies reveal that at high energies, collisions of a small system such as $p+p$ gives signatures similar to that widely observed in heavy ion collisions hinting toward the possibility of forming a medium with collective behavior. With this motivation, we have used the Glauber model, which is traditionally applied to heavy ion collisions, in a small system using the anisotropic and inhomogeneous density profile of a proton and found that the proposed model reproduces the charged particle multiplicity distribution of $p+p$ collisions at LHC energies very well. Collision geometric properties such as the mean impact parameter, the mean number of binary collisions ($⟨{N}_{\mathrm{coll}}⟩$), and the mean number of participants ($⟨{N}_{\mathrm{part}}⟩$) at different multiplicities are determined. Having estimated $⟨{N}_{\mathrm{coll}}⟩$, we have calculated the nuclear modificationlike factor (${R}_{\mathrm{HL}}$) in $p+p$ collisions. We also estimated eccentricity and elliptic flow as a function of charged particle multiplicity using the linear response to the initial geometry.