This paper presents a measurement of forward-forward and forward-central dijet azimuthal angular correlations and conditional yields in proton-proton ($pp$) and proton-lead ($p$+Pb) collisions as a probe of the nuclear gluon density in regions where the fraction of the average momentum per nucleon carried by the parton entering the hard scattering is low. In these regions, gluon saturation can modify the rapidly increasing parton distribution function of the gluon. The analysis utilizes 25 pb$^{-1}$ of $pp$ data and 360 $\mu \mathrm{b}^{-1}$ of $p$+Pb data, both at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, collected in 2015 and 2016, respectively, with the ATLAS detector at the LHC. The measurement is performed in the center-of-mass frame of the nucleon-nucleon system in the rapidity range between $-$4.0 and 4.0 using the two highest transverse momentum jets in each event, with the highest transverse momentum jet restricted to the forward rapidity range. No significant broadening of azimuthal angular correlations is observed for forward-forward or forward-central dijets in $p$+Pb compared to $pp$ collisions. For forward-forward jet pairs in the proton-going direction, the ratio of conditional yields in $p$+Pb collisions to those in $pp$ collisions is suppressed by approximately 20%, with no significant dependence on the transverse momentum of the dijet system. No modification of conditional yields is observed for forward-central dijets.

Measurements of the suppression and correlations of dijets is performed using 3 $\mu$b$^{-1}$ of Xe+Xe data at $\sqrt{s_{\mathrm{NN}}} = 5.44$ TeV collected with the ATLAS detector at the LHC. Dijets with jets reconstructed using the $R=0.4$ anti-$k_t$ algorithm are measured differentially in jet $p_{\text{T}}$ over the range of 32 GeV to 398 GeV and the centrality of the collisions. Significant dijet momentum imbalance is found in the most central Xe+Xe collisions, which decreases in more peripheral collisions. Results from the measurement of per-pair normalized and absolutely normalized dijet $p_{\text{T}}$ balance are compared with previous Pb+Pb measurements at $\sqrt{s_{\mathrm{NN}}} =5.02$ TeV. The differences between the dijet suppression in Xe+Xe and Pb+Pb are further quantified by the ratio of pair nuclear-modification factors. The results are found to be consistent with those measured in Pb+Pb data when compared in classes of the same event activity and when taking into account the difference between the center-of-mass energies of the initial parton scattering process in Xe+Xe and Pb+Pb collisions. These results should provide input for a better understanding of the role of energy density, system size, path length, and fluctuations in the parton energy loss.

A measurement of $W^\pm$ boson production in lead-lead collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV is reported using data recorded by the ATLAS experiment at the LHC in 2015, corresponding to a total integrated luminosity of $0.49\;\mathrm{nb^{-1}}$. The $W^\pm$ bosons are reconstructed in the electron or muon leptonic decay channels. Production yields of leptonically decaying $W^\pm$ bosons, normalised by the total number of minimum-bias events and the nuclear thickness function, are measured within a fiducial region defined by the detector acceptance and the main kinematic requirements. These normalised yields are measured separately for $W^+$ and $W^-$ bosons, and are presented as a function of the absolute value of pseudorapidity of the charged lepton and of the collision centrality. The lepton charge asymmetry is also measured as a function of the absolute value of lepton pseudorapidity. In addition, nuclear modification factors are calculated using the $W^\pm$ boson production cross-sections measured in $pp$ collisions. The results are compared with predictions based on next-to-leading-order calculations with CT14 parton distribution functions as well as with predictions obtained with the EPPS16 and nCTEQ15 nuclear parton distribution functions. No dependence of normalised production yields on centrality and a good agreement with predictions are observed for mid-central and central collisions. For peripheral collisions, the data agree with predictions within 1.7 (0.9) standard deviations for $W^-$ ($W^+$) bosons.

To assess the properties of the quark-gluon plasma formed in heavy-ion collisions, the ATLAS experiment at the LHC measures a correlation between the mean transverse momentum and the magnitudes of the flow harmonics. The analysis uses data samples of lead-lead and proton-lead collisions obtained at the centre-of-mass energy per nucleon pair of 5.02 TeV, corresponding to total integrated luminosities of $22 ~\mu b^{-1}$ and $28~nb^{-1}$, respectively. The measurement is performed using a modified Pearson correlation coefficient with the charged-particle tracks on an event-by-event basis. The modified Pearson correlation coefficients for the $2^{nd}$-, 3$^{rd}$-, and 4$^{th}$-order harmonics are measured as a function of event centrality quantified as the number of charged particles or the number of nucleons participating in the collision. The measurements are performed for several intervals of the charged-particle transverse momentum. The correlation coefficients for all studied harmonics exhibit a strong centrality evolution in the lead-lead collisions, which only weakly depends on the charged-particle momentum range. In the proton-lead collisions, the modified Pearson correlation coefficient measured for the second harmonics shows only weak centrality dependence. The data is qualitatively described by the predictions based on the hydrodynamical model.

The azimuthal variation of jet yields in heavy-ion collisions provides information about the path-length dependence of the energy loss experienced by partons passing through the hot, dense nuclear matter known as the quark-gluon plasma. This paper presents the azimuthal anisotropy coefficients $v_2$, $v_3$, and $v_4$ measured for jets in Pb+Pb collisions at $\sqrt{s_{NN}} =$ 5.02 TeV using the ATLAS detector at the LHC. The measurement uses data collected in 2015 and 2018, corresponding to an integrated luminosity of 2.2 nb$^{-1}$. The $v_n$ values are measured as a function of the transverse momentum of the jets between 71 GeV and 398 GeV and the event centrality. A nonzero value of $v_2$ is observed in all but the most central collisions. The value of $v_2$ is largest for jets with lower transverse momentum, with values up to 0.05 in mid-central collisions. A smaller, nonzero value of $v_3$ of approximately 0.01 is measured with no significant dependence on jet $p_T$ or centrality, suggesting that fluctuations in the initial state play a small but distinct role in jet energy loss. No significant deviation of $v_4$ from zero is observed in the measured kinematic region.

Two-particle long-range azimuthal correlations are measured in photonuclear collisions using 1.7 nb$^{-1}$ of 5.02 TeV Pb+Pb collision data collected by the ATLAS experiment at the LHC. Candidate events are selected using a dedicated high-multiplicity photonuclear event trigger, a combination of information from the zero-degree calorimeters and forward calorimeters, and from pseudorapidity gaps constructed using calorimeter energy clusters and charged-particle tracks. Distributions of event properties are compared between data and Monte Carlo simulations of photonuclear processes. Two-particle correlation functions are formed using charged-particle tracks in the selected events, and a template-fitting method is employed to subtract the non-flow contribution to the correlation. Significant nonzero values of the second- and third-order flow coefficients are observed and presented as a function of charged-particle multiplicity and transverse momentum. The results are compared with flow coefficients obtained in proton-proton and proton-lead collisions in similar multiplicity ranges, and with theoretical expectations. The unique initial conditions present in this measurement provide a new way to probe the origin of the collective signatures previously observed only in hadronic collisions.

Azimuthal anisotropies of muons from charm and bottom hadron decays are measured in Pb+Pb collisions at $\sqrt{s_\mathrm{NN}}= 5.02$ TeV. The data were collected with the ATLAS detector at the Large Hadron Collider in 2015 and 2018 with integrated luminosities of $0.5~\mathrm{nb}^{-1}$ and $1.4~\mathrm{nb^{-1}}$, respectively. The kinematic selection for heavy-flavor muons requires transverse momentum $4 < p_\mathrm{T} < 30$ GeV and pseudorapidity $|\eta|<2.0$. The dominant sources of muons in this $p_\mathrm{T}$ range are semi-leptonic decays of charm and bottom hadrons. These heavy-flavor muons are separated from light-hadron decay muons and punch-through hadrons using the momentum imbalance between the measurements in the tracking detector and in the muon spectrometers. Azimuthal anisotropies, quantified by flow coefficients, are measured via the event-plane method for inclusive heavy-flavor muons as a function of the muon $p_\mathrm{T}$ and in intervals of Pb+Pb collision centrality. Heavy-flavor muons are separated into contributions from charm and bottom hadron decays using the muon transverse impact parameter with respect to the event primary vertex. Non-zero elliptic ($v_{2}$) and triangular ($v_{3}$) flow coefficients are extracted for charm and bottom muons, with the charm muon coefficients larger than those for bottom muons for all Pb+Pb collision centralities. The results indicate substantial modification to the charm and bottom quark angular distributions through interactions in the quark-gluon plasma produced in these Pb+Pb collisions, with smaller modifications for the bottom quarks as expected theoretically due to their larger mass.

Heavy-flavour hadron production provides information about the transport properties and microscopic structure of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions. A measurement of the muons from semileptonic decays of charm and bottom hadrons produced in Pb+Pb and $pp$ collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV with the ATLAS detector at the Large Hadron Collider is presented. The Pb+Pb data were collected in 2015 and 2018 with sampled integrated luminosities of $208~\mathrm{\mu b}^{-1}$ and $38~\mathrm{\mu b^{-1}}$, respectively, and $pp$ data with a sampled integrated luminosity of $1.17~\mathrm{pb}^{-1}$ were collected in 2017. Muons from heavy-flavour semileptonic decays are separated from the light-flavour hadronic background using the momentum imbalance between the inner detector and muon spectrometer measurements, and muons originating from charm and bottom decays are further separated via the muon track's transverse impact parameter. Differential yields in Pb+Pb collisions and differential cross sections in $pp$ collisions for such muons are measured as a function of muon transverse momentum from 4 GeV to 30 GeV in the absolute pseudorapidity interval $|\eta| < 2$. Nuclear modification factors for charm and bottom muons are presented as a function of muon transverse momentum in intervals of Pb+Pb collision centrality. The measured nuclear modification factors quantify a significant suppression of the yields of muons from decays of charm and bottom hadrons, with stronger effects for muons from charm hadron decays.

Studies of the fragmentation of jets into charged particles in heavy-ion collisions can provide information about the mechanism of jet-quenching by the hot and dense QCD matter created in such collisions, the quark-gluon plasma. This paper presents a measurement of the angular distribution of charged particles around the jet axis in $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV Pb+Pb and $pp$ collisions, using the ATLAS detector at the LHC. The Pb+Pb and $pp$ data sets have integrated luminosities of 0.49 nb$^{-1}$ and 25 pb$^{-1}$, respectively. The measurement is performed for jets reconstructed with the anti-$k_{t}$ algorithm with radius parameter $R = 0.4$ and is extended to an angular distance of $r= 0.8$ from the jet axis. Results are presented as a function of Pb+Pb collision centrality and distance from the jet axis for charged particles with transverse momenta in the 1$-$63 GeV range, matched to jets with transverse momenta in the 126$-$316 GeV range and an absolute value of jet rapidity of less than 1.7. Modifications to the measured distributions are quantified by taking a ratio to the measurements in $pp$ collisions. Yields of charged particles with transverse momenta below 4 GeV are observed to be increasingly enhanced as a function of angular distance from the jet axis, reaching a maximum at $r=0.6$. Charged particles with transverse momenta above 4 GeV have an enhanced yield in Pb+Pb collisions in the jet core for angular distances up to $r = 0.05$ from the jet axis, with a suppression at larger distances.

Jet quenching is the process of color-charged partons losing energy via interactions with quark-gluon plasma droplets created in heavy-ion collisions. The collective expansion of such droplets is well described by viscous hydrodynamics. Similar evidence of collectivity is consistently observed in smaller collision systems, including $pp$ and $p$+Pb collisions. In contrast, while jet quenching is observed in Pb+Pb collisions, no evidence has been found in these small systems to date, raising fundamental questions about the nature of the system created in these collisions. The ATLAS experiment at the Large Hadron Collider has measured the yield of charged hadrons correlated with reconstructed jets in 0.36 nb$^{-1}$ of $p$+Pb and 3.6 pb$^{-1}$ of $pp$ collisions at 5.02 TeV. The yields of charged hadrons with $p_\mathrm{T}^\mathrm{ch} >0.5$ GeV near and opposite in azimuth to jets with $p_\mathrm{T}^\mathrm{jet} > 30$ or $60$ GeV, and the ratios of these yields between $p$+Pb and $pp$ collisions, $I_{p\mathrm{Pb}}$, are reported. The collision centrality of $p$+Pb events is categorized by the energy deposited by forward neutrons from the struck nucleus. The $I_{p\mathrm{Pb}}$ values are consistent with unity within a few percent for hadrons with $p_\mathrm{T}^\mathrm{ch} >4$ GeV at all centralities. These data provide new, strong constraints which preclude almost any parton energy loss in central $p$+Pb collisions.