This article reports measurements characterizing the Underlying Event (UE) associated with hard scatterings at midrapidity in pp collisions at $\sqrt{s}=13$ TeV. The hard scatterings are identified by the leading particle, the charged particle with the highest transverse momentum ($p_{\rm T}^{\rm leading}$) in the event. Charged-particle number and summed transverse-momentum densities are measured in different azimuthal regions defined with respect to the leading particle direction: Toward, Transverse, and Away. The Toward and Away regions contain the fragmentation products of the hard scatterings in addition to the UE contribution, whereas particles in the Transverse region are expected to originate predominantly from the UE. The study is performed as a function of $p_{\rm T}^{\rm leading}$ with three different $p_{\rm T}$ thresholds for the associated particles, $p_{\rm T}^{\rm min} >$ 0.15, 0.5, and 1.0 GeV/$c$. The charged-particle density in the Transverse region rises steeply for low values of $p_{\rm T}^{\rm leading}$ and reaches a plateau. The results confirm the trend that the charged-particle density in the Transverse region shows a stronger increase with $\sqrt{s}$ than the inclusive charged-particle density at midrapidity. The UE activity is increased by approximately 20% when going from 7 to 13 TeV. The plateau in the Transverse region ($5 < p_{\rm T}^{\rm leading} < ~ 40$ GeV/$c$ ) is further characterized by the probability distribution of its charged-particle multiplicity normalized to its average value (relative transverse activity, $R_{T}$) and the mean transverse momentum as a function of $R_{T}$. Experimental results are compared to model calculations using PYTHIA 8 and EPOS LHC. The overall agreement between models and data is within 30%. These measurements provide new insights on the interplay between hard scatterings and the associated UE in pp collisions.

The cross section of jets reconstructed from charged particles is measured in the transverse momentum range of $5<p_\mathrm{T}<100\ \mathrm{GeV}/c$ in pp collisions at the center-of-mass energy of $\sqrt{s} = 5.02\ \mathrm{TeV}$ with the ALICE detector. The jets are reconstructed using the anti-$k_\mathrm{T}$ algorithm with resolution parameters $R=0.2$, $0.3$, $0.4$, and $0.6$ in the pseudorapidity range $|\eta|< 0.9-R$. The charged jet cross sections are compared with the leading order (LO) and to next-to-leading order (NLO) perturbative Quantum ChromoDynamics (pQCD) calculations. It was found that the NLO calculations agree better with the measurements. The cross section ratios for different resolution parameters were also measured. These ratios increase from low $p_\mathrm{T}$ to high $p_\mathrm{T}$ and saturate at high $p_\mathrm{T}$, indicating that jet collimation is larger at high $p_\mathrm{T}$ than at low $p_\mathrm{T}$. These results provide a precision test of pQCD predictions and serve as a baseline for the measurement in Pb$-$Pb collisions at the same energy to quantify the effects of the hot and dense medium created in heavy-ion collisions at the LHC.

The production of $\phi$ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $2.5 < y < 4$. Measurements of the differential cross section ${\rm d}^2\sigma/{\rm d}y {\rm d}p_{\rm T}$ are presented as a function of the transverse momentum ($p_{\rm T}$) at the center-of-mass energies $\sqrt{s}=5.02$, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $\sqrt{s}=5.02$ and 13 TeV are also studied in several rapidity intervals as a function of $p_{\rm T}$, and as a function of rapidity in three $p_{\rm T}$ intervals. A hardening of the $p_{\rm T}$-differential cross section with the collision energy is observed, while, for a given energy, $p_{\rm T}$ spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $p_{\rm T}$. The new results, complementing the published measurements at $\sqrt{s}=2.76$ and 7 TeV, allow one to establish the energy dependence of $\phi$ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $p_{\rm T}$ and rapidity at all the energies.

The production rates and the transverse momentum distribution of strange hadrons at mid-rapidity ($\ |y\ | < 0.5$) are measured in proton-proton collisions at $\sqrt{s}$ = 13 TeV as a function of the charged particle multiplicity, using the ALICE detector at the LHC. The production rates of $\rm{K}^{0}_{S}$, $\Lambda$, $\Xi$, and $\Omega$ increase with the multiplicity faster than what is reported for inclusive charged particles. The increase is found to be more pronounced for hadrons with a larger strangeness content. Possible auto-correlations between the charged particles and the strange hadrons are evaluated by measuring the event-activity with charged particle multiplicity estimators covering different pseudorapidity regions. When comparing to lower energy results, the yields of strange hadrons are found to depend only on the mid-rapidity charged particle multiplicity. Several features of the data are reproduced qualitatively by general purpose QCD Monte Carlo models that take into account the effect of densely-packed QCD strings in high multiplicity collisions. However, none of the tested models reproduce the data quantitatively. This work corroborates and extends the ALICE findings on strangeness production in proton-proton collisions at 7 TeV.

The production cross section of inclusive J/$\psi$ pairs in pp collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV is measured with ALICE. The measurement is performed for J/$\psi$ in the rapidity interval $2.5 < y < 4.0$ and for transverse momentum $p_{\rm T} > 0$. The production cross section of inclusive J/$\psi$ pairs is reported to be $10.3 \pm 2.3 {\rm (stat.)} \pm 1.3 {\rm (syst.)}$ nb in this kinematic interval. The contribution from non-prompt J/$\psi$ (i.e. originated from beauty-hadron decays) to the inclusive sample is evaluated. The results are discussed and compared with data.

Two-particle azimuthal correlations are measured with the ALICE apparatus in pp collisions at $\sqrt{s} = 13$ TeV to explore strangeness- and multiplicity-related effects in the fragmentation of jets and the transition regime between bulk and hard production, probed with the condition that a strange meson (K$^{0}_{\rm S}$) or baryon ($\Lambda$) with transverse momentum $p_{\rm T} > 3$ GeV/c is produced. Azimuthal correlations between kaons or $\Lambda$ hyperons with other hadrons are presented at midrapidity for a broad range of the trigger ($3 < p_{\rm T}^{\rm trigg} < 20$ GeV/$c$) and associated particle $p_{\rm T}$ (1 GeV/$c$$< p_{\rm T}^{\rm assoc} < p_{\rm T}^{\rm trigg}$), for minimum-bias events and as a function of the event multiplicity. The near- and away-side peak yields are compared for the case of either K$^{0}_{\rm S}$ or $\Lambda$($\overline{\Lambda}$) being the trigger particle with that of inclusive hadrons (a sample dominated by pions). In addition, the measurements are compared with predictions from PYTHIA 8 and EPOS LHC event generators.

Measurements of identified hadrons as a function of the charged-particle multiplicity in pp collisions enable a search for the onset of collective effects in small collision systems. With such measurements, it is possible to study the mechanisms that determine the shapes of hadron transverse momentum ($p_{\rm{T}}$) spectra, to search for possible modifications of the yields of short-lived hadronic resonances due to scattering effects in the hadron-gas phase, and to investigate different explanations for the multiplicity evolution of strangeness production provided by phenomenological models. In this paper, these topics are addressed through measurements of the $\rm{K}^{*}(892)^{0}$ and $\phi(1020)$ mesons at midrapidity in pp collisions at $\sqrt{s}$ = 13 TeV as a function of the charged-particle multiplicity. The results include the $p_{\rm{T}}$ spectra, $p_{\rm{T}}$-integrated yields, mean transverse momenta, and the ratios of the yields of these resonances to those of longer-lived hadrons. Comparisons with results from other collision systems and energies, as well as predictions from phenomenological models, are also discussed.

The production of prompt $D^{0}$, $D^{+}_{\rm s}$, and $\Lambda_{\rm c}^{+}$ hadrons, and their ratios, $D^{+}_{\rm s}$/$D^{0}$ and $\Lambda_{\rm c}^{+}$/$D^{0}$, are measured in proton-proton collisions at $\sqrt{s}$ = 13 TeV at midrapidity ($|y| <0.5$) with the ALICE detector at the LHC. The measurements are performed as a function of the charm-hadron transverse momentum ($p_{\rm T}$) in intervals of charged-particle multiplicity, measured with two multiplicity estimators covering different pseudorapidity regions. While the strange to non-strange $D^{+}_{\rm s}$/$D^{0}$ ratio indicates no significant multiplicity dependence, the baryon-to-meson $p_{\rm T}$-differential $\Lambda_{\rm c}^{+}$/$D^{0}$ ratio shows a multiplicity-dependent enhancement, with a significance of 5.3$\sigma$ for $1< p_{\rm T} < 12$ GeV/$c$, comparing the highest multiplicity interval with respect to the lowest one. The measurements are compared with a theoretical model that explains the multiplicity dependence by a canonical treatment of quantum charges in the statistical hadronisation approach, and with predictions from event generators that implement colour reconnection mechanisms beyond the leading colour approximation to model the hadronisation process. The $\Lambda_{\rm c}^{+}$/$D^{0}$ ratios as a function of $p_{\rm T}$ present a similar shape and magnitude as the $\Lambda/K^{0}_{s}$ ratios in comparable multiplicity intervals, suggesting a potential common mechanism for light- and charm-hadron formation, with analogous multiplicity dependence. The $p_{\rm T}$-integrated ratios, extrapolated down to $p_{\rm T}$=0, do not show a significant dependence on multiplicity within the uncertainties.