Multiplicity and Transverse Spherocity dependence of $\langle p_{\rm T} \rangle$ fluctuations of charged particles in p$-$p collisions at $\sqrt{s}$ = 7 and 13 TeV

The multiplicity dependence of event-by-event fluctuations in mean transverse momentum, $\langle p_{\rm T} \rangle$, of charged particles has been studied in p$-$p collisions at $\sqrt{s}$ = 7 TeV and 13 TeV using the PYTHIA 8 event generator. The charged particles were selected in kinematic range of $0.15 < p_{\rm T}<2$ GeV$/c$ and $|\eta| < 0.8$. The dynamical fluctuations would indicate towards the correlated emission of particles. The measurements in A$-$A and p$-$p collisions has shown a decrease in the strength of $ \langle p_{\rm T} \rangle$ fluctuations with the average charged particle multiplicity. The effects of various microscopic processes like color reconnection and multi-partonic interactions has been studied. A minimal dependency on the collision energy is also observed. Furthermore, the fluctuation observables are investigated in the intervals of transverse spherocity in order to comprehend the relative contributions resulting from hard scattering and underlying events. The present study would act as a baseline for future measurements in A$-$A as well as p$-$p collisions at the LHC.