Charged-particle production as a function of multiplicity and transverse spherocity in pp collisions at $\sqrt{s} =5.02$ and 13 TeV

We present a study of the inclusive charged-particle transverse momentum ($p_{\rm T}$) spectra as a function of charged-particle multiplicity density at mid-pseudorapidity, ${\rm d}N_{\rm ch}/{\rm d}\eta$, in pp collisions at $\sqrt{s}=5.02$ and 13 TeV covering the kinematic range $|\eta|<0.8$ and $0.15 < p_{\rm{T}} < 20$ GeV/$c$. The results are presented for events with at least one charged particle in $|\eta|<1$ (INEL$\,>0$). The transverse momentum spectra are reported for two multiplicity estimators covering different pseudorapidity regions. While the $p_{\rm T}$ spectra exhibit a strong dependence on multiplicity and center-of-mass energy, they show little energy dependence when normalized to the $p_{\rm T}$ spectrum for INEL$\,>0$. The behavior of the multiplicity dependent spectra from intermediate to high transverse momentum ($6 < p_{\rm T} < 20$ GeV/$c$) is parametrised by the exponent of a power-law function. Going from low to high average charged-particle density, the exponent decreases from $\sim$6 to $\sim$5. Moreover, the high-$p_{\rm T}$ yields of charged particles increase faster than the charged-particle multiplicity density. The average $\it{p}_{\rm T}$ as a function of multiplicity and transverse spherocity is reported for pp collisions at $\sqrt{s}=13$ TeV. For low- (high-) spherocity events, corresponding to jet-like (isotropic) events, the average $p_{\rm T}$ as function of multiplicity is higher (smaller) than that measured in INEL$\,>0$ pp collisions. Moreover, within uncertainties the functional form of $\langle p_{\rm T} \rangle(N_{\rm ch})$ is not affected by the spherocity selection. However, in PYTHIA 6 (tune Perugia 2011) and PYTHIA 8 (tune Monash 2013) the functional form of $\langle p_{\rm T} \rangle(N_{\rm ch})$ is modified by the spherocity selection and in particular for jet-like events, the models overestimate the average $p_{\rm T}$. The general purpose QCD Monte Carlo generator EPOS LHC gives a good description of many features of data. The observations are discussed in terms of multi-parton interactions with large momentum transfer and color reconnection.