Benchmarking the Non-flow Contributions to the Elliptic Flow Parameter ($v_{_2}$) in Proton-Proton Collisions

This manuscript reports on the elliptic flow parameter, $v_{_2}$, in proton-proton (p-p) collisions using PYTHIA8 event generator simulations. The typical Event Plane ($EP$) method $v_{_2}$($EP$) as the one used for the real data analysis has been adopted to measure the $v_{_2}$ of particles composed of different quark flavors, and produced at mid-pseudorapidity $|\eta| \le 1$ at center-of-mass energy $\sqrt{s}$ = 200 GeV and $\sqrt{s}$ = 13 TeV. The event plane has been constructed using the soft charged particles with transverse momentum ($p{_{_T}} <$ 2 GeV/c) produced in various $\eta$ ranges. The pseudorapidity gap technique ($\Delta\eta$) between the particle of interest and the soft charged particles contributed to the event plane constructions has been utilized to benchmark the non-flow contributions. The $v_{_2}^{\pi^{^\pm,}\pi^{^0}}$, $v_{_2}^{J/\psi,\Upsilon, K, D, B}$, and the $v_{_2}^{\gamma_{dir}}$ show similar pattern dependence on the transverse momentum for the same $\Delta\eta$, at both $\sqrt{s}$ = 200 GeV and $\sqrt{s}$ = 13 TeV. At each center-of-mass energy, the measured $v_{_2}$ shows obvious dependence on the quark flavor contents where $v_{_2}^{\gamma_{dir}}$ $\le$ $v_{_2}^{J/\psi, \Upsilon, K, D, B}$ $\le$ $v_{_2}^{\pi^{^\pm,}\pi^{^0}}$ for similar $\Delta\eta$ gap. The measured $v_{_2}$ shows slightly higher values at smaller $\sqrt{s}$ for particles of similar values of $\Delta\eta$ gaps, particularly at small $\Delta\eta$ gap. The measured $v_{_2}$ for all particles shows systematic decreases with increasing the $\Delta\eta$ gap as expected from the previous experimental results. Because PYTHIA8 simulations do not incorporate final state interactions, the $v_{_2}(EP)$ values reported here primarily reflect the non-flow contributions and its dependence on the quark contents, pseudorapidity gap as a function on $p_{T}$ at each center of mass-energy.