Anisotropic flow and radial flow are two key probes of the expansion dynamics and properties of the quark-gluon plasma (QGP). While anisotropic flow has been extensively studied, radial flow, which governs the system's radial expansion, has received less attention. Notably, experimental evidence for the global and collective nature of radial flow has been lacking. This Letter presents the first measurement of transverse momentum ($p_{\mathrm{T}}$) dependence of radial flow fluctuations ($v_0(p_{\mathrm{T}})$) over $0.5<p_{\mathrm{T}}<10$ GeV, using a two-particle correlation method in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The data reveal three key features supporting the collective nature of radial flow: long-range correlation in pseudorapidity, factorization in $p_{\mathrm{T}}$, and centrality-independent shape in $p_{\mathrm{T}}$. The comparison with a hydrodynamic model demonstrates the sensitivity of $v_0(p_{\mathrm{T}})$ to bulk viscosity, a crucial transport property of the QGP. These findings establish a new, powerful tool for probing collective dynamics and properties of the QGP.
Data from Figure 2, panel a, $v_{0}$
Data from Figure 2, panel c, upper panel, Normalized Covariance $\times 10^{3}$ in 0-5% Centrality
Data from Figure 2, panel c, lower panel, Normalized Covariance $\times 10^{3}$ in 50-60% Centrality
Correlations among conserved quantum numbers, such as the net-electric charge, the net-baryon, and the net-strangeness in heavy-ion collisions, are crucial for exploring the QCD phase diagram. In this letter, these correlations are investigated using net-proton number (as a proxy for the net-baryon), net-kaon number (for the net-strangeness), and net-charged particle number in Pb-Pb collisions at $\sqrt{s_\text{NN}}=5.02$ TeV with the ALICE detector. The observed correlations deviate from the Poissonian baseline, with a more pronounced deviation at LHC energies than at RHIC. Theoretical calculations of the Thermal-FIST hadron resonance gas model, HIJING, and EPOS LHC event generators are compared with experimental results, where a significant impact of resonance decays is observed. Thermal-FIST calculations under the grand canonical and canonical ensembles highlight significant differences, underscoring the role of local charge conservation in explaining the data. Recent lattice QCD studies have demonstrated that the magnetic field generated by spectator protons in heavy-ion collisions affects susceptibility ratios, in particular those related to the net-electric charge and the net-baryon numbers. The experimental findings are in qualitative agreement with the expectations of lattice QCD.
$\kappa^{2}_{\pi}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 1 $p_\mathrm{T}$ acceptance.
$\kappa^{2}_{\pi}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 2 $p_\mathrm{T}$ acceptance.
$\kappa^{2}_\mathrm{K}$ as a function of centrality (%) in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for Set 1 $p_\mathrm{T}$ acceptance.
This paper presents the measurement of charged-hadron and identified-hadron ($K^\mathrm{0}_\mathrm{S}$, $Λ$, $Ξ^\mathrm{-}$) yields in photo-nuclear collisions using 1.7 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV Pb+Pb data collected in 2018 with the ATLAS detector at the Large Hadron Collider. Candidate photo-nuclear events are selected using a combination of tracking and calorimeter information, including the zero-degree calorimeter. The yields as a function of transverse momentum and rapidity are measured in these photo-nuclear collisions as a function of charged-particle multiplicity. These photo-nuclear results are compared with 0.1 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV $p$+Pb data collected in 2016 by ATLAS using similar charged-particle multiplicity selections. These photo-nuclear measurements shed light on potential quark-gluon plasma formation in photo-nuclear collisions via observables sensitive to radial flow, enhanced baryon-to-meson ratios, and strangeness enhancement. The results are also compared with the Monte Carlo DPMJET-III generator and hydrodynamic calculations to test whether such photo-nuclear collisions may produce small droplets of quark-gluon plasma that flow collectively.
The multiplicity distribution (#it{N}_{ch}^{rec}) from Pb+Pb photo-nuclear collisions.
The multiplicity distribution (#it{N}_{ch}^{rec}) from p+Pb collisions.
The Charged-hadron yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.
This paper presents the primary charged-particle multiplicity distributions in proton-lead collisions at a centre-of-mass energy per nucleon-nucleon collision of $\sqrt{s_{\rm NN}} = 5.02$ TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analysed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton-proton and nucleus-nucleus collisions across a wide range of collision energies.
Charged-particle multiplicity distributions for different pseudorapidity intervals measured in NSD p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.
The pseudorapidity dependence of the double NBD parameters $\langle n \rangle_1$, $\langle n \rangle_2$, $k_1$, and $k_2$ in NSD p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.
First four moments ($\langle N_{\mathrm{ch}}\rangle$, $\sigma$, $S$, and $\kappa$) of charged-particle multiplicity distributions for different pseudorapidity intervals in NSD p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.
Top-quark pair production is observed in lead-lead (Pb+Pb) collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV at the Large Hadron Collider with the ATLAS detector. The data sample was recorded in 2015 and 2018, amounting to an integrated luminosity of 1.9 nb$^{-1}$. Events with exactly one electron and one muon and at least two jets are selected. Top-quark pair production is measured with an observed (expected) significance of 5.0 (4.1) standard deviations. The measured top-quark pair production cross-section is $\sigma_{t\bar{t}} = 3.6\;^{+1.0}_{-0.9}\;\mathrm{(stat.)}\;^{+0.8}_{-0.5}\;\mathrm{(syst.)} ~\mathrm{\mu b}$, with a total relative uncertainty of 31%, and is consistent with theoretical predictions using a range of different nuclear parton distribution functions. The observation of this process consolidates the evidence of the existence of all quark flavors in the pre-equilibrium stage of the quark-gluon plasma at very high energy densities, similar to the conditions present in the early universe.
The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR1 (Signal Region 1 (SR\(_1\)):} Events with exactly one muon and one oppositely charged electron, a dilepton invariant mass \( m_{e\mu} \geq 30 \, \mathrm{GeV} \), at least two jets with \( p_T \geq 35 \, \mathrm{GeV} \), and a dilepton transverse momentum \( p_T^{e\mu} > 40 \, \mathrm{GeV} \). This region is expected to be signal-dominated) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.
The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR2 (Signal Region 2 (SR\(_2\)):} Events meeting the same criteria as SR\(_1\), but with a dilepton transverse momentum \( p_T^{e\mu} \leq 40 \, \mathrm{GeV} \). This region includes events with a lower \( p_T^{e\mu} \) and has a larger background contribution) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.
The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined fit of all channels. Only the 10 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.
Event-by-event fluctuations of the event-wise mean transverse momentum, $\langle p_{\mathrm{T}}\rangle$, of charged particles produced in proton$-$proton (pp) collisions at $\sqrt{s}$ = 5.02 TeV, Xe$-$Xe collisions at $\sqrt{s_{\mathrm{NN}}} =$ 5.44 TeV, and Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}} =$ 5.0 TeV are studied using the ALICE detector based on the integral correlator $\langle\langle Δp_{\rm T}Δp_{\rm T}\rangle\rangle $. The correlator strength is found to decrease monotonically with increasing produced charged-particle multiplicity measured at midrapidity in all three systems. In Xe$-$Xe and Pb$-$Pb collisions, the multiplicity dependence of the correlator deviates significantly from a simple power-law scaling as well as from the predictions of the HIJING and AMPT models. The observed deviation from power-law scaling is expected from transverse radial flow in semicentral to central Xe$-$Xe and Pb$-$Pb collisions. In pp collisions, the correlation strength is also studied by classifying the events based on the transverse spherocity, $S_0$, of the particle production at midrapidity, used as a proxy for the presence of a pronounced back-to-back jet topology. Low-spherocity (jetty) events feature a larger correlation strength than those with high spherocity (isotropic). The strength and multiplicity dependence of jetty and isotropic events are well reproduced by calculations with the PYTHIA 8 and EPOS LHC models.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in pp collisions at $\sqrt{s}$ = 5.02 TeV.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV.
Differential two-particle normalized cumulants ($R_2$) and transverse momentum correlations ($P_2$) are measured as a function of the relative pseudorapidity and azimuthal angle difference $( \Delta \eta, \Delta \varphi )$ of charged particle pairs in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of $|\eta| < 0.8$ and the transverse momentum range 0.2 $< \textit{p}_{\mathrm T} < $ 2.0 $\mathrm{GeV}/\textit{c}$ in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p-Pb and Pb-Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the $R_2$ and $P_2$ measured in pp collisions exhibit features qualitatively similar to those observed in p-Pb and Pb-Pb collisions. The $\Delta\eta$ and $\Delta\varphi$ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p-Pb and Pb-Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the $R_2^{\rm CD}$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb-Pb collisions. These results, which are sensitive to the interplay between the underlying event and mini-jets in pp collisions, establish a baseline for heavy-ion collisions.
Correlation functions $R_2^{\rm US}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
Correlation functions $R_2^{\rm LS}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
Correlation functions $P_2^{\rm US}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
The ALICE Collaboration reports measurements of the large relative transverse momentum ($k_{\text{T}}$) component of jet substructure in pp and Pb$-$Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s_{\text{NN}}}=5.02$ TeV. Enhancement in the yield of such large-$k_{\text{T}}$ emissions in head-on Pb$-$Pb collisions is predicted to arise from partonic scattering with quasi-particles of the quark-gluon plasma. The analysis utilizes charged-particle jets reconstructed by the anti-$k_{\text{T}}$ algorithm with resolution parameter $R=0.2$ in the transverse-momentum interval $60 < p_{\text{T,ch jet}} < 80$ GeV/$c$. The soft drop and dynamical grooming algorithms are used to identify high transverse momentum splittings in the jet shower. Comparison of measurements in Pb$-$Pb and pp collisions shows medium-induced narrowing, corresponding to yield suppression of high-$k_{\text{T}}$ splittings, in contrast to the expectation of yield enhancement due to quasi-particle scattering. The measurements are compared to theoretical model calculations incorporating jet modification due to jet-medium interactions ("jet quenching"), both with and without quasi-particle scattering effects. These measurements provide new insight into the underlying mechanisms and theoretical modeling of jet quenching.
Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Dynamical grooming $a = 1.0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.
Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in 30--50% Pb-Pb collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Dynamical grooming $a = 1.0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold,bkg,non_closure"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.
Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in 0--10% Pb-Pb collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Dynamical grooming $a = 1.0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold,bkg,non_closure"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.
The ALICE Collaboration at the CERN LHC has measured the inclusive production cross section of isolated photons at midrapidity as a function of the photon transverse momentum ($p_{\rm T}^{\gamma}$), in Pb$-$Pb collisions in different centrality intervals, and in pp collisions, at centre-of-momentum energy per nucleon pair of $\sqrt{s_{\rm NN}}=5.02$ TeV. The photon transverse momentum range is between 10-14 and 40-140 GeV/$c$, depending on the collision system and on the Pb$-$Pb centrality class. The result extends to lower $p_{\rm T}^{\gamma}$ than previously published results by the ATLAS and CMS experiments at the same collision energy. The covered pseudorapidity range is $|\eta^{\gamma}| <0.67$. The isolation selection is based on a charged particle isolation momentum threshold $p_{\rm T}^{\rm iso,~ch} = 1.5$ GeV/$c$ within a cone of radii $R=0.2$ and $0.4$. The nuclear modification factor is calculated and found to be consistent with unity in all centrality classes, and also consistent with the HG-PYTHIA model, which describes the event selection and geometry biases that affect the centrality determination in peripheral Pb$-$Pb collisions. The measurement is compared to next-to-leading order perturbative QCD calculations and to the measurements of isolated photons and Z$^0$ bosons from the CMS experiment, which are all found to be in agreement.
Isolated-photon differential cross section measured in pp and Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$ for five Pb$-$Pb centrality classes for $R=0.2$. Note that the Pb$-$Pb data in the first five columns is scaled by $\langle N_{\mathrm{coll}} \rangle$, unlike in the figure in the paper where the theory was scaled by $\langle N_{\mathrm{coll}} \rangle$. Last two columns correspond to theory NLO pQCD calculations with JETPHOX, for pp (PDF) and Pb$-$Pb (nPDF) collisions calculated for the 0$-$100% centrality class. Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided. The data normalisation uncertainties are provided in the paper.
Isolated-photon differential cross section measured in pp and Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$ for five Pb$-$Pb centrality classes for $R=0.4$. Note that the Pb$-$Pb data in the first five columns is scaled by $\langle N_{\mathrm{coll}} \rangle$, unlike in the figure in the paper where the theory was scaled by $\langle N_{\mathrm{coll}} \rangle$. Last two columns correspond to theory NLO pQCD calculations with JETPHOX, for pp (PDF) and Pb$-$Pb (nPDF) collisions calculated for the 0$-$100% centrality class. Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided. The data normalisation uncertainties are provided in the paper.
Ratio of isolated-photon cross section measured with $R=0.4$ over $R=0.2$ for Pb$-$Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$. Each column for each Pb$-$Pb collisions centrality class and for pp collisions. The last two columns for the NLO pQCD JETPHOX calculations for pp (PDF) and Pb$-$Pb (nPDF) collisions. Data statistical and systematic uncertainties are provided. The theory statiscal (Monte Carlo approach) and PDF uncertainties are provided.
In ultra-relativistic heavy ion collisions at the LHC, each nucleus acts a sources of high-energy real photons that can scatter off the opposing nucleus in ultra-peripheral photonuclear ($\gamma+A$) collisions. Hard scattering processes initiated by the photons in such collisions provide a novel method for probing nuclear parton distributions in a kinematic region not easily accessible to other measurements. ATLAS has measured production of dijet and multi-jet final states in ultra-peripheral Pb+Pb collisions at $\sqrt{s_{\text{NN}}} = 5.02$ TeV using a data set recorded in 2018 with an integrated luminosity of 1.72 $\text{nb}^{-1}$. Photonuclear final states are selected by requiring a rapidity gap in the photon direction; this selects events where one of the outgoing nuclei remains intact. Jets are reconstructed using the anti-$k_\text{t}$ algorithm with radius parameter, $R = 0.4$. Triple-differential cross-sections, unfolded for detector response, are measured and presented using two sets of kinematic variables. The first set consists of the total transverse momentum ($H_\text{T}$),rapidity, and mass of the jet system. The second set uses $H_\text{T}$ and particle-level nuclear and photon parton momentum fractions, $x_\text{A}$ and $z_{\gamma}$, respectively. The results are compared with leading-order (LO) perturbative QCD calculations of photonuclear jet production cross-sections, where all LO predictions using existing fits fall below the data in the shadowing region. More detailed theoretical comparisons will allow these results to strongly constrain nuclear parton distributions, and these data provide results from the LHC directly comparable to early physics results at the planned Electron-Ion Collider.
The fraction of photonuclear jet events passing the fiducial requirements in which the photon-emitting nucleus does not break up as a function of \zg. The systematic uncertainties are not symmetrized, and correlations in uncertainties are neglected for both the total systematic uncertainty and statistical uncertainty.
Fully unfolded triple-differential cross-sections as a function of $H_\text{T}$, $y_\text{jets}$, and $m_\text{jets}$. Systematic uncertainties are decomposed into symmetrized nuisance parameters, where parameters labelled "Corr" are fully correlated bin-to-bin, while parameters labelled "Uncorr" should be treated as un-correlated bin-to-bin. These cross-sections are not corrected for the effects of additional nuclear break-up. Values for the total fiducial cross-section in each bin are reported with full statistical and systematic uncertainties. Fractions of the total bin volume occupied by the fiducial region, fractions of the total cross-section in that bin satisfying fiducial requirements, and mean bin values for each axis variable are derived from Pythia 8 Monte Carlo and reported as well. For more details on these quantities, see Appendix B.
Fully unfolded triple-differential cross-sections as a function of $H_\text{T}$, $x_\text{A}$, and $z_{\gamma}$. Systematic uncertainties are decomposed into symmetrized nuisance parameters, where parameters labelled "Corr" are fully correlated bin-to-bin, while parameters labelled "Uncorr" should be treated as un-correlated bin-to-bin. These cross-sections are not corrected for the effects of additional nuclear break-up. Values for the total fiducial cross-section in each bin are reported with full statistical and systematic uncertainties. Fractions of the total bin volume occupied by the fiducial region, fractions of the total cross-section in that bin satisfying fiducial requirements, and mean bin values for each axis variable are derived from Pythia 8 Monte Carlo and reported as well. For more details on these quantities, see Appendix B.