Light front analysis towards the study of thermalisation in pp collisions at $\sqrt{s}= 13$ TeV

An analysis involving the light front variables of inclusively produced hadrons in proton-proton (pp) collisions to study the thermalisation and formation of a QGP-like medium is presented in this paper. Two schemes of analysis are discussed and performed with inclusively produced $\pi^{\pm}$, $K^{\pm}$ and $p(\bar{p})$ in the central pp collisions at $\sqrt{s} = 13$ TeV simulated using the PYTHIA 8 event generator. It is shown that a group of $\pi^{\pm}$ and $K^{\pm}$ falling inside a paraboloid defined by a certain constant value of the light front variable in their respective phase space follows the Bose-Einstein statistics while the $p(\bar{p})$ inside the similar paraboloid in its phase space follows the Fermi-Dirac statistics. It is also shown that for the $\pi^{\pm}$, $K^{\pm}$ and $p(\bar{p})$ with transverse momentum $p_{T} < 1$ GeV in these collisions, a polynomial in $p_T$ can be constructed for a specific light front variable of the particle $\zeta_c (p_T)$ such that the $\pi^{\pm}$ and $K^{\pm}$ with their light front variable $\zeta^{\pm} > \zeta_c (p_T)$ follows Bose-Einstein statistics while the $p(\bar{p})$ with $\zeta^{\pm} > \zeta_c (p_T)$ follows the Fermi-Dirac statistics. The analysis can serve as a baseline for an investigation towards the QGP formation and thermalisation in the pp collisions at LHC.