Measurements of charged-particle production in pp, p$-$Pb, and Pb$-$Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum ($p_{\mathrm{T}}^{\rm trig}$) in the range $8<p_{\mathrm{T}}^{\rm trig}<15$ GeV$/c$. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, $R_{\mathrm{T}}=N_{\mathrm{ch}}^{\mathrm{T}}/\langle N_{\mathrm{ch}}^{\mathrm{T}}\rangle$, is used to group events according to their UE activity, where $N_{\mathrm{ch}}^{\mathrm{T}}$ is the charged-particle multiplicity per event in the transverse region and $\langle N_{\mathrm{ch}}^{\mathrm{T}}\rangle$ is the mean value over the whole analysed sample. The energy dependence of the $R_{\mathrm{T}}$ distributions in pp collisions at $\sqrt{s}=2.76$, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle $p_{\rm T}$ spectra as a function of $R_{\mathrm{T}}$ in the three azimuthal regions in pp, p$-$Pb, and Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p$-$Pb).

Measurements of the production cross sections of prompt ${\rm D^0}$, ${\rm D^+}$, ${\rm D^{\ast +}}$, ${\rm D_s^+}$, ${\rm \Lambda_{c}^{+}}$, and ${\rm \Xi_{c}^{+}}$ charm hadrons at midrapidity in proton$-$proton collisions at $\sqrt{s}=13$ TeV with the ALICE detector are presented. The D-meson cross sections as a function of transverse momentum ($p_{\rm T}$) are provided with improved precision and granularity. The ratios of $p_{\rm T}$-differential meson production cross sections based on this publication and on measurements at different rapidity and collision energy provide a constraint on gluon parton distribution functions at low values of Bjorken-$x$ ($10^{-5}-10^{-4}$). The measurements of ${\rm \Lambda_{c}^{+}}$ (${\rm \Xi_{c}^{+}}$) baryon production extend the measured $p_{\rm T}$ intervals down to $p_{\rm T}=0(3)$~GeV$/c$. These measurements are used to determine the charm-quark fragmentation fractions and the ${\rm c\overline{c}}$ production cross section at midrapidity ($|y|<0.5$) based on the sum of the cross sections of the weakly-decaying ground-state charm hadrons ${\rm D^0}$, ${\rm D^+}$, ${\rm D_s^+}$, ${\rm \Lambda_{c}^{+}}$, ${\rm \Xi_{c}^{0}}$ and, for the first time, ${\rm \Xi_{c}^{+}}$, and of the strongly-decaying J/$psi$ mesons. The first measurements of ${\rm \Xi_{c}^{+}}$ and ${\rm \Sigma_{c}^{0,++}}$ fragmentation fractions at midrapidity are also reported. A significantly larger fraction of charm quarks hadronising to baryons is found compared to e$^+$e$^-$ and ep collisions. The ${\rm c\overline{c}}$ production cross section at midrapidity is found to be at the upper bound of state-of-the-art perturbative QCD calculations.

We report on new measurements of elliptic flow ($v_2$) of electrons from heavy-flavor hadron decays at mid-rapidity ($|y|<0.8$) in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$ = 27 and 54.4 GeV from the STAR experiment. Heavy-flavor decay electrons ($e^{\rm HF}$) in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}$ = 54.4 GeV exhibit a non-zero $v_2$ in the transverse momentum ($p_{\rm T}$) region of $p_{\rm T}<$ 2 GeV/$c$ with the magnitude comparable to that at $\sqrt{s_{_{\rm NN}}}=200$ GeV. The measured $e^{\rm HF}$$v_2$ at 54.4 GeV is also consistent with the expectation of their parent charm hadron $v_2$ following number-of-constituent-quark scaling as other light and strange flavor hadrons at this energy. These suggest that charm quarks gain significant collectivity through the evolution of the QCD medium and may reach local thermal equilibrium in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=54.4$ GeV. The measured $e^{\rm HF}$$v_2$ in Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=$ 27 GeV is consistent with zero within large uncertainties. The energy dependence of $v_2$ for different flavor particles ($\pi,\phi,D^{0}/e^{\rm HF}$) shows an indication of quark mass hierarchy in reaching thermalization in high-energy nuclear collisions.

A study of multiplicity and pseudorapidity distributions of inclusive photons measured in pp and p$-$Pb collisions at a center-of-mass energy per nucleon$-$nucleon collision of $\sqrt{s_{\rm NN}} = 5.02$ TeV using the ALICE detector in the forward pseudorapidity region $2.3 < \eta_{\rm lab} < 3.9$ is presented. Measurements in p$-$Pb collisions are reported for two beam configurations in which the directions of the proton and lead ion beam were reversed. The pseudorapidity distributions in p$-$Pb collisions are obtained for seven centrality classes which are defined based on different event activity estimators, i.e., the charged-particle multiplicity measured at midrapidity as well as the energy deposited in a calorimeter at beam rapidity. The inclusive photon multiplicity distributions for both pp and p$-$Pb collisions are described by double negative binomial distributions. The pseudorapidity distributions of inclusive photons are compared to those of charged particles at midrapidity in \pp collisions and for different centrality classes in p$-$Pb collisions. The results are compared to predictions from various Monte Carlo event generators. None of the generators considered in this paper reproduces the inclusive photon multiplicity distributions in the reported multiplicity range. The pseudorapidity distributions are, however, better described by the same generators.

A newly developed observable for correlations between symmetry planes, which characterize the direction of the anisotropic emission of produced particles, is measured in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV with ALICE. This so-called Gaussian Estimator allows for the first time the study of these quantities without the influence of correlations between different flow amplitudes. The centrality dependence of various correlations between two, three and four symmetry planes is presented. The ordering of magnitude between these symmetry plane correlations is discussed and the results of the Gaussian Estimator are compared with measurements of previously used estimators. The results utilizing the new estimator lead to significantly smaller correlations than reported by studies using the Scalar Product method. Furthermore, the obtained symmetry plane correlations are compared to state-of-the-art hydrodynamic model calculations for the evolution of heavy-ion collisions. While the model predictions provide a qualitative description of the data, quantitative agreement is not always observed, particularly for correlators with significant non-linear response of the medium to initial state anisotropies of the collision system. As these results provide unique and independent information, their usage in future Bayesian analysis can further constrain our knowledge on the properties of the QCD matter produced in ultrarelativistic heavy-ion collisions.

Femtoscopic correlations of non-identical charged kaons ($\rm K^+ K^-$) are studied in Pb$-$Pb collisions at a center-of-mass energy per nucleon$-$nucleon collision $\sqrt{s_{\mathrm{NN}}} =2.76$ TeV by ALICE at the LHC. One-dimensional $\rm K^+ K^-$ correlation functions are analyzed in three centrality classes and eight intervals of particle-pair transverse momentum. The Lednický and Luboshitz interaction model used in the $\rm K^+ K^-$ analysis includes the final-state Coulomb interactions between kaons and the final-state interaction through $a_{0}$(980) and $f_{0}$(980) resonances. The mass of $f_{0}$(980) and coupling were extracted from the fit to $\rm K^+ K^-$ correlation functions using the femtoscopic technique for the first time. The measured mass and width of the $f_{0}$(980) resonance are consistent with other published measurements. The height of the $\phi$(1020) meson peak present in the $\rm K^+ K^-$ correlation function rapidly decreases with increasing source radius, qualitatively in agreement with an inverse volume dependence. A phenomenological fit to this trend suggests that the $\phi$(1020) meson yield is dominated by particles produced directly from the hadronization of the system. The small fraction subsequently produced by FSI could not be precisely quantified with data presented in this paper and will be assessed in future work.

Multiplicity ($N_{\rm ch}$) distributions and transverse momentum ($p_{\rm T}$) spectra of inclusive primary charged particles in the kinematic range of $|\eta| < 0.8$ and 0.15 GeV/$c$$< p_{T} <$ 10 GeV/$c$ are reported for pp, p-Pb, Xe-Xe and Pb-Pb collisions at centre-of-mass energies per nucleon pair ranging from $\sqrt{s_{\rm NN}} = 2.76$ TeV up to $13$ TeV. A sequential two-dimensional unfolding procedure is used to extract the correlation between the transverse momentum of primary charged particles and the charged-particle multiplicity of the corresponding collision. This correlation sharply characterises important features of the final state of a collision and, therefore, can be used as a stringent test of theoretical models. The multiplicity distributions as well as the mean and standard deviation derived from the $p_{\rm T}$ spectra are compared to state-of-the-art model predictions. Providing these fundamental observables of bulk particle production consistently across a wide range of collision energies and system sizes can serve as an important input for tuning Monte Carlo event generators.

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons $v_2${$\Psi_{\rm SP}$} in collisions of Pb ions at center-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}}$=2.76 TeV and Xe ions at $\sqrt{s_{\rm NN}}$=5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum. The ratio between $v_2${$\Psi_{\rm SP}$} and the elliptic flow coefficient relative to the participant plane $v_2$4, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models of initial state fluctuations. A significant transverse momentum dependence of the ratio $v_2${$\Psi_{\rm SP}$}/$v_2${4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state fluctuations. The ratios of $v_2${$\Psi_{\rm SP}$} and $v_2${4} to the corresponding initial state eccentricities for Xe-Xe and Pb-Pb collisions at similar initial entropy density show a difference of $(7.0 \pm 0.9)$% with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark-gluon plasma.

The measurement of direct photons from Au$+$Au collisions at $\sqrt{s_{_{NN}}}=39$ and 62.4 GeV in the transverse-momentum range $0.4<p_T<3$ Gev/$c$ is presented by the PHENIX collaboration at the Relativistic Heavy Ion Collider. A significant direct-photon yield is observed in both collision systems. A universal scaling is observed when the direct-photon $p_T$ spectra for different center-of-mass energies and for different centrality selections at $\sqrt{s_{_{NN}}}=62.4$ GeV is scaled with $(dN_{\rm ch}/d\eta)^{\alpha}$ for $\alpha=1.21{\pm}0.04$. This scaling also holds true for direct-photon spectra from Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV measured earlier by PHENIX, as well as the spectra from Pb$+$Pb at $\sqrt{s_{_{NN}}}=2760$ GeV published by ALICE. The scaling power $\alpha$ seems to be independent of $p_T$, center of mass energy, and collision centrality. The spectra from different collision energies have a similar shape up to $p_T$ of 2 GeV/$c$. The spectra have a local inverse slope $T_{\rm eff}$ increasing with $p_T$ of $0.174\pm0.018$ GeV/$c$ in the range $0.4<p_T<1.3$ GeV/$c$ and increasing to $0.289\pm0.024$ GeV/$c$ for $0.9<p_T<2.1$ GeV/$c$. The observed similarity of low-$p_T$ direct-photon production from $\sqrt{s_{_{NN}}}= 39$ to 2760 GeV suggests a common source of direct photons for the different collision energies and event centrality selections, and suggests a comparable space-time evolution of direct-photon emission.

We present the first measurement of event-by-event fluctuations in the kaon sector in Pb-Pb collisions at $\sqrt {s_{\rm NN}}=$ 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator $\nu_{\rm dyn}$ is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator $\nu_{\rm dyn}[\rm K^+,\rm K^-]$ exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, $\nu_{\rm dyn}[\rm K_S^0,\rm K^{\pm}]$ features a significant deviation from such scaling. Within uncertainties, the value of $\nu_{\rm dyn}[\rm K_S^0,\rm K^{\pm}]$ is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS-LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb-Pb collisions.