A search for the production of three massive vector bosons in proton--proton collisions is performed using data at $\sqrt{s}=13\,TeV$ recorded with the ATLAS detector at the Large Hadron Collider in the years 2015--2017, corresponding to an integrated luminosity of $79.8\,\text{fb}^{-1}$. Events with two same-sign leptons $\ell$ (electrons or muons) and at least two reconstructed jets are selected to search for $WWW\to\ell\nu\ell\nu qq$. Events with three leptons without any same-flavour opposite-sign lepton pairs are used to search for $WWW\to\ell\nu\ell\nu\ell\nu$, while events with three leptons and at least one same-flavour opposite-sign lepton pair and one or more reconstructed jets are used to search for $WWZ\to\ell\nu qq \ell\ell$. Finally, events with four leptons are analysed to search for $WWZ\to\ell\nu\ell\nu\ell\ell$ and $WZZ\to qq \ell\ell\ell\ell$. Evidence for the joint production of three massive vector bosons is observed with a significance of 4.0 standard deviations, where the expectation is 3.1 standard deviations.

A measurement of the four-lepton invariant mass spectrum is made with the ATLAS detector, using an integrated luminosity of 36.1 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}$ = 13 TeV delivered by the Large Hadron Collider. The differential cross-section is measured for events containing two same-flavour opposite-sign lepton pairs. It exhibits a rich structure, with different mass regions dominated in the Standard Model by single $Z$ boson production, Higgs boson production, and $Z$ boson pair production, and non-negligible interference effects at high invariant masses. The measurement is compared with state-of-the-art Standard Model calculations, which are found to be consistent with the data. These calculations are used to interpret the data in terms of $gg\rightarrow ZZ \rightarrow 4\ell$ and $Z \rightarrow 4\ell$ subprocesses, and to place constraints on a possible contribution from physics beyond the Standard Model.

The prevalence of hadronic jets at the LHC requires that a deep understanding of jet formation and structure is achieved in order to reach the highest levels of experimental and theoretical precision. There have been many measurements of jet substructure at the LHC and previous colliders, but the targeted observables mix physical effects from various origins. Based on a recent proposal to factorize physical effects, this Letter presents a double-differential cross-section measurement of the Lund jet plane using 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collision data collected with the ATLAS detector using jets with transverse momentum above 675 GeV. The measurement uses charged particles to achieve a fine angular resolution and is corrected for acceptance and detector effects. Several parton shower Monte Carlo models are compared with the data. No single model is found to be in agreement with the measured data across the entire plane.

Inclusive jet production cross-sections are measured in proton--proton collisions at a centre-of-mass energy of $\sqrt{s}=$8 TeV recorded by the ATLAS experiment at the Large Hadron Collider at CERN. The total integrated luminosity of the analysed data set amounts to $20.2$ fb$^{-1}$. Double-differential cross-sections are measured for jets defined by the anti-$k_{t}$ jet clustering algorithm with radius parameters of $R=0.4$ and $R=0.6$ and are presented as a function of the jet transverse momentum, in the range between 70 GeV and 2.5 TeV and in six bins of the absolute jet rapidity, between 0 and 3.0. The measured cross-sections are compared to predictions of quantum chromodynamics, calculated at next-to-leading order in perturbation theory, and corrected for non-perturbative and electroweak effects. The level of agreement with predictions, using a selection of different parton distribution functions for the proton, is quantified. Tensions between the data and the theory predictions are observed.

Multi-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in $pp$ collisions at $\sqrt{s}$ = 5.02 and 13 TeV and in $p$+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, and compared to the results obtained for low-multiplicity Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. These measurements aim to assess the collective nature of particle production. The measurements of multi-particle cumulants confirm the evidence for collective phenomena in $p$+Pb and low-multiplicity Pb+Pb collisions. On the other hand, the $pp$ results for four-particle cumulants do not demonstrate collective behaviour, indicating that they may be biased by contributions from non-flow correlations. A comparison of multi-particle cumulants and derived Fourier harmonics across different collision systems is presented as a function of the charged-particle multiplicity. For a given multiplicity, the measured Fourier harmonics are largest in Pb+Pb, smaller in $p$+Pb and smallest in $pp$ collisions. The $pp$ results show no dependence on the collision energy, nor on the multiplicity.

The dynamics of isolated-photon plus two-jet production in $pp$ collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset corresponding to an integrated luminosity of 36.1 fb$^{-1}$. Cross sections are measured as functions of a variety of observables, including angular correlations and invariant masses of the objects in the final state, $\gamma+jet+jet$. Measurements are also performed in phase-space regions enriched in each of the two underlying physical mechanisms, namely direct and fragmentation processes. The measurements cover the range of photon (jet) transverse momenta from 150 GeV (100 GeV) to 2 TeV. The tree-level plus parton-shower predictions from SHERPA and PYTHIA as well as the next-to-leading-order QCD predictions from SHERPA are compared with the measurements. The next-to-leading-order QCD predictions describe the data adequately in shape and normalisation except for regions of phase space such as those with high values of the invariant mass or rapidity separation of the two jets, where the predictions overestimate the data.

A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.

The dynamics of isolated-photon plus one-, two- and three-jet production in $pp$ collisions at a centre-of-mass energy of 8 TeV are studied with the ATLAS detector at the LHC using a data set with an integrated luminosity of 20.2 fb$^{-1}$. Measurements of isolated-photon plus jets cross sections are presented as functions of the photon and jet transverse momenta. The cross sections as functions of the azimuthal angle between the photon and the jets, the azimuthal angle between the jets, the photon-jet invariant mass and the scattering angle in the photon-jet centre-of-mass system are presented. The pattern of QCD radiation around the photon and the leading jet is investigated by measuring jet production in an annular region centred on each object; enhancements are observed around the leading jet with respect to the photon in the directions towards the beams. The experimental measurements are compared to several different theoretical calculations, and overall a good description of the data is found.

A dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy $\sqrt{s}=8$ TeV is used to study inclusive single diffractive dissociation, $pp \rightarrow Xp$. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system $X$ are measured in the central detector components. The fiducial range of the measurement is $-4.0 < \log_{10} \xi < -1.6$ and $0.016 < |t| < 0.43 \ {\rm GeV^2}$, where $\xi$ is the proton fractional energy loss and $t$ is the squared four-momentum transfer. The total cross section integrated across the fiducial range is $1.59 \pm 0.13 \ {\rm mb}$. Cross sections are also measured differentially as functions of $\xi$, $t$, and $\Delta \eta$, a variable that characterises the rapidity gap separating the proton and the system $X$. The data are consistent with an exponential $t$ dependence, ${\rm d} \sigma / {\rm d} t \propto \text{e}^{Bt}$ with slope parameter $B = 7.65 \pm 0.34 \ {\rm GeV^{-2}}$. Interpreted in the framework of triple Regge phenomenology, the $\xi$ dependence leads to a pomeron intercept of $\alpha(0) = 1.07 \pm 0.09$.

This Letter presents direct searches for lepton flavour violation in Higgs boson decays, $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$, performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton-proton collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $36.1\,\mathrm{fb}^{-1}$. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95 % confidence-level upper limits on the lepton-flavour-violating branching ratios are $0.47\%$ ($0.34^{+0.13}_{-0.10}\,\%$) and $0.28\%$ ($0.37^{+0.14}_{-0.10}\,\%$) for $H\to e\tau$ and $H\to\mu\tau$, respectively.

This paper reports a search for triboson $W^{\pm}W^{\pm}W^{\mp}$ production in two decay channels ($W^{\pm}W^{\pm}W^{\mp}\rightarrow \ell^{\pm}\nu\ell^{\pm}\nu\ell^{\mp}\nu$ and $W^{\pm}W^{\pm}W^{\mp}\rightarrow \ell^{\pm}\nu\ell^{\pm}\nu{}jj$ with $\ell=e, \mu$) in proton-proton collision data corresponding to an integrated luminosity of 20.3 fb$^{-1}$ at a centre-of-mass energy of 8 TeV with the ATLAS detector at the Large Hadron Collider. Events with exactly three charged leptons, or two leptons with the same electric charge in association with two jets, are selected. The total number of events observed in data is consistent with the Standard Model (SM) predictions. The observed 95 % confidence level upper limit on the SM $W^{\pm}W^{\pm}W^{\mp}$ production cross section is found to be 730 fb with an expected limit of 560 fb in the absence of SM $W^{\pm}W^{\pm}W^{\mp}$ production. Limits are also set on $WWWW$ anomalous quartic gauge couplings.

The production of two prompt $J/\psi$ mesons, each with transverse momenta $p_{\mathrm{T}}>8.5$ GeV and rapidity $|y| < 2.1$, is studied using a sample of proton-proton collisions at $\sqrt{s} = 8$ TeV, corresponding to an integrated luminosity of 11.4 fb$^{-1}$ collected in 2012 with the ATLAS detector at the LHC. The differential cross-section, assuming unpolarised $J/\psi$ production, is measured as a function of the transverse momentum of the lower-$p_{\mathrm{T}}$ $J/\psi$ meson, di-$J/\psi$ $p_{\mathrm{T}}$ and mass, the difference in rapidity between the two $J/\psi$ mesons, and the azimuthal angle between the two $J/\psi$ mesons. The fraction of prompt pair events due to double parton scattering is determined by studying kinematic correlations between the two $J/\psi$ mesons. The total and double parton scattering cross-sections are compared with predictions. The effective cross-section of double parton scattering is measured to be $\sigma_{\mathrm{eff}} = 6.3 \pm 1.6 \mathrm{(stat)} \pm 1.0 \mathrm{(syst)}$ mb.

Inclusive four-jet events produced in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 7$ TeV are analysed for the presence of hard double-parton scattering using data corresponding to an integrated luminosity of 37.3 pb$^{-1}$, collected with the ATLAS detector at the LHC. The contribution of hard double-parton scattering to the production of four-jet events is extracted using an artificial neural network, assuming that hard double-parton scattering can be approximated by an uncorrelated overlaying of dijet events. For events containing at least four jets with transverse momentum $p_{\mathrm{T}} \geq 20$ GeV and pseudorapidity $\eta \leq 4.4$, and at least one having $p_{\mathrm{T}} \geq 42.5$ GeV, the contribution of hard double-parton scattering is estimated to be $f_{\mathrm{DPS}} = 0.092 ^{+0.005}_{-0.011} (\mathrm{stat.}) ^{+0.033}_{-0.037} (\mathrm{syst.})$. After combining this measurement with those of the inclusive dijet and four-jet cross-sections in the appropriate phase space regions, the effective overlap area between the interacting protons, $\sigma_{\mathrm{eff}}$, was determined to be $\sigma_{\mathrm{eff}} = 14.9 ^{+1.2}_{-1.0} (\mathrm{stat.}) ^{+5.1}_{-3.8} (\mathrm{syst.})$ mb. This result is consistent within the quoted uncertainties with previous measurements of $\sigma_{\mathrm{eff}}$, performed at centre-of-mass energies between 63 GeV and 8 TeV using various final states, and it corresponds to $21^{+7}_{-6}$% of the total inelastic cross-section measured at $\sqrt{s} = 7$ TeV. The distributions of the observables sensitive to the contribution of hard double-parton scattering, corrected for detector effects, are also provided.

A search for supersymmetric partners of top quarks decaying as $\tilde{t}_1\to c\tilde\chi^0_1$ and supersymmetric partners of charm quarks decaying as $\tilde{c}_1\to c\tilde\chi^0_1$, where $\tilde\chi^0_1$ is the lightest neutralino, is presented. The search uses 36.1 ${\rm fb}^{-1}$ $pp$ collision data at a centre-of-mass energy of 13 TeV collected by the ATLAS experiment at the Large Hadron Collider and is performed in final states with jets identified as containing charm hadrons. Assuming a 100% branching ratio to $c\tilde\chi^0_1$, top and charm squarks with masses up to 850 GeV are excluded at 95% confidence level for a massless lightest neutralino. For $m_{\tilde{t}_1,\tilde{c}_1}-m_{\tilde\chi^0_1}

Inclusive isolated-photon production in $pp$ collisions at a centre-of-mass energy of 13 TeV is studied with the ATLAS detector at the LHC using a data set with an integrated luminosity of 3.2 fb$^{-1}$. The cross section is measured as a function of the photon transverse energy above 125 GeV in different regions of photon pseudorapidity. Next-to-leading-order perturbative QCD and Monte Carlo event-generator predictions are compared to the cross-section measurements and provide an adequate description of the data.

This paper presents results of searches for electroweak production of supersymmetric particles in models with compressed mass spectra. The searches use 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider. Events with missing transverse momentum and two same-flavor, oppositely charged, low transverse momentum leptons are selected, and are further categorized by the presence of hadronic activity from initial-state radiation or a topology compatible with vector-boson fusion processes. The data are found to be consistent with predictions from the Standard Model. The results are interpreted using simplified models of $R$-parity-conserving supersymmetry in which the lightest supersymmetric partner is a neutralino with a mass similar to the lightest chargino, the second-to-lightest neutralino or the slepton. Lower limits on the masses of charginos in different simplified models range from 193 GeV to 240 GeV for moderate mass splittings, and extend down to mass splittings of 1.5 GeV to 2.4 GeV at the LEP chargino bounds (92.4 GeV). Similar lower limits on degenerate light-flavor sleptons extend up to masses of 251 GeV and down to mass splittings of 550 MeV. Constraints on vector-boson fusion production of electroweak SUSY states are also presented.

The differential cross section for isolated-photon production in $pp$ collisions is measured at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 36.1 fb$^{-1}$. The differential cross section is presented as a function of the photon transverse energy in different regions of photon pseudorapidity. The differential cross section as a function of the absolute value of the photon pseudorapidity is also presented in different regions of photon transverse energy. Next-to-leading-order QCD calculations from JETPHOX and SHERPA as well as next-to-next-to-leading-order QCD calculations from NNLOJET are compared with the measurement, using several parameterisations of the proton parton distribution functions. The predictions provide a good description of the data within the experimental and theoretical uncertainties.

The production cross-sections for $W^{\pm}$ and $Z$ bosons are measured using ATLAS data corresponding to an integrated luminosity of 4.0 pb$^{-1}$ collected at a centre-of-mass energy $\sqrt{s}=2.76$ TeV. The decay channels $W \rightarrow \ell \nu$ and $Z \rightarrow \ell \ell $ are used, where $\ell$ can be an electron or a muon. The cross-sections are presented for a fiducial region defined by the detector acceptance and are also extrapolated to the full phase space for the total inclusive production cross-section. The combined (average) total inclusive cross-sections for the electron and muon channels are: \begin{eqnarray} \sigma^{\text{tot}}_{W^{+}\rightarrow \ell \nu}& = & 2312 \pm 26\ (\text{stat.})\ \pm 27\ (\text{syst.}) \pm 72\ (\text{lumi.}) \pm 30\ (\text{extr.})\text{pb} \nonumber, \\ \sigma^{\text{tot}}_{W^{-}\rightarrow \ell \nu}& = & 1399 \pm 21\ (\text{stat.})\ \pm 17\ (\text{syst.}) \pm 43\ (\text{lumi.}) \pm 21\ (\text{extr.})\text{pb} \nonumber, \\ \sigma^{\text{tot}}_{Z \rightarrow \ell \ell}& = & 323.4 \pm 9.8\ (\text{stat.}) \pm 5.0\ (\text{syst.}) \pm 10.0\ (\text{lumi.}) \pm 5.5 (\text{extr.}) \text{pb} \nonumber. \end{eqnarray} Measured ratios and asymmetries constructed using these cross-sections are also presented. These observables benefit from full or partial cancellation of many systematic uncertainties that are correlated between the different measurements.

The production of a prompt photon in association with a $Z$ boson is studied in proton-proton collisions at a centre-of-mass energy $\sqrt{s} =$ 13 TeV. The analysis uses a data sample with an integrated luminosity of 139 fb$^{-1}$ collected by the ATLAS detector at the LHC from 2015 to 2018. The production cross-section for the process $pp \rightarrow \ell^+\ell^-\gamma+X$ ($\ell = e, \mu$) is measured within a fiducial phase-space region defined by kinematic requirements on the photon and the leptons, and by isolation requirements on the photon. An experimental precision of 2.9% is achieved for the fiducial cross-section. Differential cross-sections are measured as a function of each of six kinematic variables characterising the $\ell^+\ell^-\gamma$ system. The data are compared with theoretical predictions based on next-to-leading-order and next-to-next-to-leading-order perturbative QCD calculations. The impact of next-to-leading-order electroweak corrections is also considered.

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 yield and nuclear modification factor, $R_\mathrm{ AA}$, for inclusive jet production are performed using 0.49 nb$^{-1}$ of Pb+Pb data at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV and 25 pb$^{-1}$ of $pp$ data at $\sqrt{s}=5.02$ TeV with the ATLAS detector at the LHC. Jets are reconstructed with the anti-$k_t$ algorithm with radius parameter $R=0.4$ and are measured over the transverse momentum range of 40-1000 GeV in six rapidity intervals covering $|y|<2.8$. The magnitude of $R_\mathrm{ AA}$ increases with increasing jet transverse momentum, reaching a value of approximately 0.6 at 1 TeV in the most central collisions. The magnitude of $R_\mathrm{ AA}$ also increases towards peripheral collisions. The value of $R_\mathrm{ AA}$ is independent of rapidity at low jet transverse momenta, but it is observed to decrease with increasing rapidity at high transverse momenta.

This Letter presents a search for heavy charged long-lived particles produced in proton-proton collisions at $\sqrt{s} = 13$ TeV at the LHC using a data sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ collected by the ATLAS experiment in 2015 and 2016. These particles are expected to travel with a velocity significantly below the speed of light, and therefore have a specific ionisation higher than any high-momentum Standard Model particle of unit charge. The pixel subsystem of the ATLAS detector is used in this search to measure the ionisation energy loss of all reconstructed charged particles which traverse the pixel detector. Results are interpreted assuming the pair production of $R$-hadrons as composite colourless states of a long-lived gluino and Standard Model partons. No significant deviation from Standard Model background expectations is observed, and lifetime-dependent upper limits on $R$-hadron production cross-sections and gluino masses are set, assuming the gluino always decays in two quarks and a stable neutralino. $R$-hadrons with lifetimes above 1.0 ns are excluded at the 95% confidence level, with lower limits on the gluino mass ranging between 1290 GeV and 2060 GeV. In the case of stable $R$-hadrons, the lower limit on the gluino mass at the 95% confidence level is 1890 GeV.

This Letter presents a normalized differential cross-section measurement in a fiducial phase-space region where interference effects between top-quark pair production and associated production of a single top quark with a $W$ boson and a $b$-quark are significant. Events with exactly two leptons ($ee$, $\mu\mu$, or $e\mu$) and two $b$-tagged jets that satisfy a multi-particle invariant mass requirement are selected from $36.1$ fb$^{-1}$ of proton-proton collision data taken at $\sqrt{s}=13$ TeV with the ATLAS detector at the LHC in 2015 and 2016. The results are compared with predictions from simulations using various strategies for the interference. The standard prescriptions for interference modeling are significantly different from each other but are within $2\sigma$ of the data. State-of-the-art predictions that naturally incorporate interference effects provide the best description of the data in the measured region of phase space most sensitive to these effects. These results provide an important constraint on interference models and will guide future model development and tuning.

This paper describes precision measurements of the transverse momentum $p_\mathrm{T}^{\ell\ell}$ ($\ell=e,\mu$) and of the angular variable $\phi^{*}_{\eta}$ distributions of Drell-Yan lepton pairs in a mass range of 66-116 GeV. The analysis uses data from 36.1 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV collected by the ATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair and muon-pair final states are performed in the same fiducial volumes, corrected for detector effects, and combined. Compared to previous measurements in proton-proton collisions at $\sqrt{s}=$7 and 8 TeV, these new measurements probe perturbative QCD at a higher centre-of-mass energy with a different composition of initial states. They reach a precision of 0.2% for the normalized spectra at low values of $p_\mathrm{T}^{\ell\ell}$. The data are compared with different QCD predictions, where it is found that predictions based on resummation approaches can describe the full spectrum within uncertainties.

Differential cross sections are presented for the prompt and non-prompt production of the hidden-charm states $X(3872)$ and $\psi(2S)$, in the decay mode $J/\psi \pi^+\pi^-$, measured using 11.4 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 8$ TeV by the ATLAS detector at the LHC. The ratio of cross-sections $X(3872)/\psi(2S)$ is also given, separately for prompt and non-prompt components, as well as the non-prompt fractions of $X(3872)$ and $\psi(2S)$. Assuming independent single effective lifetimes for non-prompt $X(3872)$ and $\psi(2S)$ production gives $R_B = \frac{\mathcal{B}(B \rightarrow X(3872)\textrm{ + any}) \mathcal{B}(X(3872 \rightarrow J/\psi\pi^+\pi^-)}{\mathcal{B}(B \rightarrow \psi(2S)\textrm{ + any}) \mathcal{B}(\psi(2S) \rightarrow J/\psi\pi^+\pi^-)} = (3.95 \pm 0.32 \mathrm{(stat)} \pm 0.08\mathrm{(sys)}) \times 10^{-2}$, while separating short- and long-lived contributions, assuming that the short-lived component is due to $B_c$ decays, gives $R_B = (3.57 \pm 0.33\mathrm{(stat)} \pm 0.11\mathrm{(sys)}) \times 10^{-2}$, with the fraction of non-prompt $X(3872)$ produced via $B_c$ decays for $p_\mathrm{T}(X(3872)) > 10$ GeV being $(25 \pm 13\mathrm{(stat)} \pm 2\mathrm{(sys)} \pm 5\mathrm{(spin)})\%$. The distributions of the dipion invariant mass in the $X(3872)$ and $\psi(2S)$ decays are also measured and compared to theoretical predictions.