The fractions of non-prompt (i.e. originating from beauty-hadron decays) D$^0$ and D$^+$ mesons with respect to the inclusive yield are measured as a function of the charged-particle multiplicity in proton$-$proton collisions at a centre-of-mass energy of $\sqrt{s} = 13$ TeV with the ALICE detector at the LHC. The results are reported in intervals of transverse momentum ($p_{\rm T}$) and integrated in the range $1 < p_{\rm T} < 24$ GeV/$c$. The fraction of non-prompt D$^0$ and D$^+$ mesons is found to increase slightly as a function of $p_{\rm T}$ in all the measured multiplicity intervals, while no significant dependence on the charged-particle multiplicity is observed. In order to investigate the production and hadronisation mechanisms of charm and beauty quarks, the results are compared to PYTHIA 8 as well as EPOS 3 and EPOS 4 Monte Carlo simulations, and to calculations based on the colour glass condensate including three-pomeron fusion.

The measurements of the inclusive J/$\psi$ yield at midrapidity ($\left | y \right | < 0.9$) and forward rapidity (2.5 $< y <$ 4) in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ALICE detector at the LHC are reported. The inclusive J/$\psi$ production yields and nuclear modification factors, $R_{\rm AA}$, are measured as a function of the collision centrality, J/$\psi$ transverse momentum ($p_{\rm T}$), and rapidity. The J/$\psi$ average transverse momentum and squared transverse momentum ($\langle p_{\mathrm{T}}\rangle$ and $\langle p_{\mathrm{T}}^{\mathrm{2}}\rangle$) are evaluated as a function of the centrality at midrapidity. Compared to the previous ALICE publications, here the entire Pb$-$Pb collisions dataset collected during the LHC Run 2 is used, which improves the precision of the measurements and extends the $p_{\rm T}$ coverage. The $p_{\rm T}$-integrated $R_{\rm AA}$ shows a hint of an increasing trend towards unity from semicentral to central collisions at midrapidity, while it is flat at forward rapidity. The $p_{\rm T}$-differential $R_{\rm AA}$ shows a strong suppression at high $p_{\rm T}$ with less suppression at low $p_{\rm T}$ where it reaches a larger value at midrapidity compared to forward rapidity. The ratio of the $p_{\rm T}$-integrated yields of J/$\psi$ to those of D$^{0}$ mesons is reported for the first time for the central and semicentral event classes at midrapidity. Model calculations implementing charmonium production via the coalescence of charm quarks and antiquarks during the fireball evolution (transport models) or in a statistical approach with thermal weights are in good agreement with the data at low $p_{\rm T}$. At higher $p_{\rm T}$, the data are well described by transport models and a model based on energy loss in the strongly-interacting medium produced in nuclear collisions at the LHC.

The Quark Gluon Plasma (QGP) produced in ultra relativistic heavy-ion collisions at the Large Hadron Collider (LHC) can be studied by measuring the modifications of jets formed by hard scattered partons which interact with the medium. We studied these modifications via angular correlations of jets with charged hadrons for jets with momenta 20 < $p_{\rm{T}}^{\rm{jet}}$ < 40 GeV/$c$ as a function of the associated particle momentum. The reaction plane fit (RPF) method is used in this analysis to remove the flow modulated background. The analysis of angular correlations for different orientations of the jet relative to the second order event plane allows for the study of the path length dependence of medium modifications to jets. We present the dependence of azimuthal angular correlations of charged hadrons with respect to the angle of the axis of a reconstructed jet relative to the event plane in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. The dependence of particle yields associated with jets on the angle of the jet with respect to the event plane is presented. Correlations at different angles relative to the event plane are compared through ratios and differences of the yield. No dependence of the results on the angle of the jet with respect to the event plane is observed within uncertainties, which is consistent with no significant path length dependence of the medium modifications for this observable.

Mid-rapidity production of $\pi^{\pm}$, $\rm{K}^{\pm}$ and ($\bar{\rm{p}}$)p measured by the ALICE experiment at the LHC, in Pb-Pb and inelastic pp collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV, is presented. The invariant yields are measured over a wide transverse momentum ($p_{\rm{T}}$) range from hundreds of MeV/$c$ up to 20 GeV/$c$. The results in Pb-Pb collisions are presented as a function of the collision centrality, in the range 0$-$90%. The comparison of the $p_{\rm{T}}$-integrated particle ratios, i.e. proton-to-pion (p/$\pi$) and kaon-to-pion (K/$\pi$) ratios, with similar measurements in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV show no significant energy dependence. Blast-wave fits of the $p_{\rm{T}}$ spectra indicate that in the most central collisions radial flow is slightly larger at 5.02 TeV with respect to 2.76 TeV. Particle ratios (p/$\pi$, K/$\pi$) as a function of $p_{\rm{T}}$ show pronounced maxima at $p_{\rm{T}}$ $\approx$ 3 GeV/$c$ in central Pb-Pb collisions. At high $p_{\rm{T}}$, particle ratios at 5.02 TeV are similar to those measured in pp collisions at the same energy and in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Using the pp reference spectra measured at the same collision energy of 5.02 TeV, the nuclear modification factors for the different particle species are derived. Within uncertainties, the nuclear modification factor is particle species independent for high $p_{\rm{T}}$ and compatible with measurements at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. The results are compared to state-of-the-art model calculations, which are found to describe the observed trends satisfactorily.

The pseudorapidity density of charged particles ($\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$) at mid-rapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of $\sqrt{s_{\rm NN}}$ = 5.02 TeV. It increases with centrality and reaches a value of $1943 \pm 54$ in $|\eta|<0.5$ for the 5% most central collisions. A rise in $\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$ as a function of $\sqrt{s_{\rm NN}}$ for the most central collisions is observed, steeper than that observed in proton-proton collisions and following the trend established by measurements at lower energy. The centrality dependence of $\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta$ as a function of the average number of participant nucleons, ${\langle N_\mathrm{part} \rangle}$, calculated in a Glauber model, is compared with the previous measurement at lower energy. A constant factor of about 1.2 describes the increase in $\frac{2}{\langle N_\mathrm{part} \rangle}\langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta \rangle$ from $\sqrt{s_{\rm NN}}$ = 2.76 TeV to $\sqrt{s_{\rm NN}}$ = 5.02 TeV for all centrality intervals, within the measured range of 0-80% centrality. The results are also compared to models based on different mechanisms for particle production in nuclear collisions.

The elliptic flow, $v_{2}$, of muons from heavy-flavour hadron decays at forward rapidity ($2.5 < y < 4$) is measured in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$~=~2.76 TeV with the ALICE detector at the LHC. The scalar product, two- and four-particle $Q$ cumulants and Lee-Yang zeros methods are used. The dependence of the $v_2$ of muons from heavy-flavour hadron decays on the collision centrality, in the range 0--40\%, and on transverse momentum, $p_{\rm T}$, is studied in the interval $3 < p_{\rm T} < 10$~GeV/$c$. A positive $v_2$ is observed with the scalar product and two-particle $Q$ cumulants in semi-central collisions (10--20\% and 20--40\% centrality classes) for the $p_{\rm T}$ interval from 3 to about 5 GeV/$c$. The $v_2$ magnitude tends to decrease towards more central collisions and with increasing $p_{\rm T}$. It becomes compatible with zero in the interval $6<p_{\rm T}<10~{\rm GeV/}c$. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions. The model calculations describe the measured $v_2$ within uncertainties.

The production of the hypertriton nuclei $^{3}_{\Lambda}\mathrm H$ and $^{3}_{\bar{\Lambda}} \overline{\mathrm H}$ has been measured for the first time in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE experiment at LHC energies. The total yield, d$N$/d$y$ $\times \mathrm{B.R.}_{\left( ^{3}_{\Lambda}\mathrm H \rightarrow ^{3}\mathrm{He},\pi^{-} \right)} = \left( 3.86 \pm 0.77 (\mathrm{stat.}) \pm 0.68 (\mathrm{syst.})\right) \times 10^{-5}$ in the 0-10% most central collisions, is consistent with the predictions from a statistical thermal model using the same temperature as for the light hadrons. The coalescence parameter $B_3$ shows a dependence on the transverse momentum, similar to the $B_2$ of deuterons and the $B_3$ of $^{3}\mathrm{He}$ nuclei. The ratio of yields $S_3$ = $^{3}_{\Lambda}\mathrm H$/($^{3}\mathrm{He}$ $\times \Lambda/\mathrm{p}$) was measured to be $S_3$ = 0.60 $\pm$ 0.13 (stat.) $\pm$ 0.21 (syst.) in 0-10% centrality events; this value is compared to different theoretical models. The measured $S_3$ is fully compatible with thermal model predictions. The measured $^{3}_{\Lambda}\mathrm H$ lifetime, $ \tau = 181^{+54}_{-39} (\mathrm{stat.}) \pm 33 (\mathrm{syst.})\ \mathrm{ps}$ is compatible within 1$\sigma$ with the world average value.

In ultrarelativistic heavy-ion collisions, the event-by-event variation of the elliptic flow $v_2$ reflects fluctuations in the shape of the initial state of the system. This allows to select events with the same centrality but different initial geometry. This selection technique, Event Shape Engineering, has been used in the analysis of charge-dependent two- and three-particle correlations in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}} =2.76$ TeV. The two-particle correlator $\langle \cos(\varphi_\alpha - \varphi_\beta) \rangle$, calculated for different combinations of charges $\alpha$ and $\beta$, is almost independent of $v_2$ (for a given centrality), while the three-particle correlator $\langle \cos(\varphi_\alpha + \varphi_\beta - 2\Psi_2) \rangle$ scales almost linearly both with the event $v_2$ and charged-particle pseudorapidity density. The charge dependence of the three-particle correlator is often interpreted as evidence for the Chiral Magnetic Effect (CME), a parity violating effect of the strong interaction. However, its measured dependence on $v_2$ points to a large non-CME contribution to the correlator. Comparing the results with Monte Carlo calculations including a magnetic field due to the spectators, the upper limit of the CME signal contribution to the three-particle correlator in the 10-50% centrality interval is found to be 26-33% at 95% confidence level.

The transverse momentum ($p_{\rm T}$) differential cross section of the charm-strange baryon $\Xi^0_{\rm c}$ is measured at midrapidity ($|y|<$ 0.5) via its semileptonic decay into ${\rm e^{+}}\Xi^{-}\nu_{\rm e}$ in pp collisions at $\sqrt{s}$ = 5.02 TeV with the ALICE detector at the LHC. The ratio of the $p_{\rm T}$-differential $\Xi^0_{\rm c}$-baryon and ${\rm D^0}$-meson production cross sections is also reported. The measurements are compared with simulations with different tunes of the PYTHIA 8 event generator, with predictions from a statistical hadronisation model (SHM) with a largely augmented set of charm-baryon states beyond the current lists of the Particle Data Group, and with models including hadronisation via quark coalescence. The $p_{\rm T}$-integrated cross section of prompt $\Xi^0_{\rm c}$-baryon production at midrapidity is also reported, which is used to calculate the baryon-to-meson ratio $\Xi^0_{\rm c}/{\rm D^0} = 0.20 \pm 0.04~{\rm (stat.)} ^{+0.08}_{-0.07}~{\rm (syst.)}$. These results provide an additional indication of a modification of the charm fragmentation from $\rm e^+e^-$ and $\rm e^{-}p$ collisions to pp collisions.

We report measurements of the production of prompt D$^0$, D$^+$, D$^{*+}$ and D$^+_{\rm s}$ mesons in Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}}=5.02$ TeV, in the centrality classes 0-10%, 30-50% and 60-80%. The D-meson production yields are measured at mid-rapidity ($|y|<0.5$) as a function of transverse momentum ($p_{\rm T}$). The $p_{\rm T}$ intervals covered in central collisions are: $1<p_{\rm T}<50$ Gev/$c$ for D$^0$, $2<p_{\rm T}<50$ GeV/$c$ for D$^+$, $3<p_{\rm T}<50$ GeV/$c$ for D$^{*+}$, and $4<p_{\rm T}<16$ GeV/$c$ for D$^+_{\rm s}$ mesons. The nuclear modification factors ($R_{\rm AA}$) for non-strange D mesons (D$^0$, D$^+$, D$^{*+}$) show minimum values of about 0.2 for $p_{\rm T}$ = 6-10 GeV/$c$ in the most central collisions and are compatible within uncertainties with those measured at $\sqrt{s_{\rm NN}}=2.76$ TeV. For D$^+_{\rm s}$ mesons, the values of $R_{\rm AA}$ are larger than those of non-strange D mesons, but compatible within uncertainties. In central collisions the average $R_{\rm AA}$ of non-strange D mesons is compatible with that of charged particles for $p_{\rm T} > 8$ GeV/$c$, while it is larger at lower $p_{\rm T}$. The nuclear modification factors for strange and non-strange D mesons are also compared to theoretical models with different implementations of in-medium energy loss.