Finite $V_{\rm 2\Delta}$ puzzle in low-multiplicity pp collisions from ultra-long-range azimuthal correlations in the string-shoving model

Ultra-long range angular correlations have been recently reported by the ALICE collaboration in pp collisions at $\sqrt{s}=13$ TeV below ${\rm d}N_{\rm ch}/{\rm d}\eta=7$. The measurements have been performed as a function of the charged-particle multiplicity at midrapidity ($N_{\rm ch}$ in $|\eta|<0.8$), which is known to be strongly sensitive to local multiplicity fluctuations. The present work investigates the impact of the event-activity estimator on ultra-long range angular correlations. The study is conducted in the framework of PYTHIA8 with the string shoving mechanism since it gives a non-zero elliptic flow coefficient, $V_{2\Delta}$. The analysis is conducted as a function of $N_{\rm ch}$, the number of parton-parton scatterings ($N_{\rm mpi}$) and flattenicity. Surprisingly, for ultra-long range correlations, pp collisions with $N_{\rm mpi}=1$ (dijets) seems to be the most sensitive to string shoving. The effect diminishes with increasing $N_{\rm mpi}$. While in data, within uncertainties, $V_{2\Delta}$ exhibits a weak multiplicity dependence; the string shoving mechanism gives a $V_{2\Delta}$ that decreases with the increase in $N_{\rm ch}$. The present work therefore supports the picture stating that mechanisms such as string shoving might explain the low multiplicity limit, whereas, hydro becomes relevant in high-multiplicity pp collisions. This work also suggests that flattenicity might be more effective than $N_{\rm ch}$ to better handle non-flow effects.