Extension of Glauber-like model for Proton-Proton collisions using anisotropic and inhomogeneous density profile

The formation of partonic medium in the relativistic heavy-ion collisions is always marked by the values of the ratio of certain observables assuming $pp$ collisions as a reference. But recent studies of small systems formed in $pp$ collisions at the LHC energies hint towards the possibility of production of medium with collective behaviour. Results from $pp$ collisions has routinely been used as baseline to analyse and understand the production of QCD matter expected to be produced in nuclear collisions. Therefore, results from $pp$ collisions required more careful investigation to understand whether QCD matter is produced in high multiplicity $pp$ collisions. With this motivation, the Glauber model traditionally used to study the heavy-ion collision dynamics at high energy is applied here to understand the dynamics of $pp$ collisions. We have used anisotropic and inhomogeneous quark/gluon based proton density profile, a realistic picture obtained from the results of deep inelastic scattering, and found that this model explains the charged particle multiplicity distribution of $pp$ collisions at LHC energies very well. Collision geometric properties like impact parameter and mean number of binary collisions ($\langle N_{coll} \rangle$), mean number of participants ($\langle N_{part} \rangle$) at different multiplicities are determined for $pp$ collisions. We further used these collision geometric properties to estimate average charged-particle pseudorapidity density ($\langle dN_{ch}/d\eta \rangle$) and found it to be comparable with the experimental results. Knowing $\langle N_{coll} \rangle$, we have for the first time obtained nuclear modification-like factor ($R_{pp}$) in $pp$ collisions.