CERN Accelerating science

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: : Diagrams representing different types of leading-order contributions to dijet production in high-energy photon-nucleus collisions. Diagram (a) represents the direct contribution in which the photon itself participates in the hard scattering. Diagram (b) represents the ``resolved'' contribution in which a virtual excitation of the photon, into a state involving at least a $q\bar{q}$ pair and possibly multiple gluons, participates in the hard scattering. The black circles represent hadronic processes where hard partons are contributed from the initial state. Additional hadronic particle production occurs in the final state resulting from the breakup of the struck nucleus ($X$, $X_1$) or the resolved photon remnant ($X_2$).

The photon flux generated coherently by a single nucleus in EPA with a hard cut-off at the nuclear radius (red dashed), compared to a photon flux fully corrected using the \textsc{Starlight} \cite{Klein:2016yzr} event generator (solid black). The ratio shown in the bottom panel is used to correct the \pythia MC sample used in this analysis.

Distribution of energies measured in the ATLAS ZDCs expressed in terms of the ratio of the measured energy to the beam energy, $E_\mathrm{beam} = 2510$ \GeV. The energies are measured in the calorimeter opposite the \zn side in events satisfying all photonuclear dijet event selections except the \xn energy requirement which selects events to the right of the dotted line.

Diagram illustrating how the various rapidity gap quantities are computed in a typical event with photonuclear jet production. Tracks and clusters are indicated by black points while the jets are shown with blue circles. The lack of neutrons in the positive $\eta$ direction defines that as the photon-going direction. The \edgeGapGam\ and \edgeGapA\ are indicated by the green and red solid shaded areas, respectively. The regions contributing to the \sumGapGam\ are shown with the hatched green shading, with the solid grey shaded region indicating a $\Delta \eta$ that is smaller than 0.5 and excluded from the \sumGapGam\ calculation. All hatched regions contribute to \sumGap.

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: : The (a) mean and (b) standard deviation of jet response distributions as a function of \pTtruth\ for different $|\etaTruth|$ intervals. The red and blue dashed lines in (a) mark the $0.5\%$ and $1\%$ levels of closure, respectively.

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: : (a) The distribution of charged track multiplicity, \Nch, versus the sum of gaps in the photon-going direction, \sumGapGam. (b) The distribution of \Nch for events passing and failing the $\sumGapGam > 2.5$ requirement. The distributions are obtained by applying all event selections detailed in Table~\ref{tbl:select} except the requirement on \sumGapGam.

Template fits of the \sumGapGam\ distributions for several bins in \zg, with nominal analysis selections applied. The \pythia Direct and Resolved MC samples provide the two contributions to the signal, and the hadronic background template is derived from a fitted combination of MC simulation and \pp data. The bottom panel shows the ratio of the template fit results to the data in open markers and the ratio to each template component as the hatched bands. The orange dashed line denotes the nominal gap selection.

Template fits of the \edgeGapA\ distributions for several bins in \zg, with nominal analysis selections applied. The \pythia MC sample corresponds to photonuclear MC, the $\gamma + IP$ sample corresponds to the coherent photo-diffractive MC, and the Reverse \gamA\ MC sample corresponds to \gamA\ MC with its coordinate system inverted. The bottom panel shows the ratio of the template fit results to the data in open markers and the ratio to each template component as the hatched bands. The orange dashed line denotes the nominal gap selection.

Residual background fractions for several different possible gap selections, extracted from template fits of the \sumGapGam and \edgeGapA distributions. The red markers indicate the nominal selections which are applied in this measurement, and the other markers show variations demonstrating the sensitivity of the background rate to the choice of selection. Error bars represent statistical uncertainties only.

The fraction of events resulting from direct photon processes, extracted from template fits of the \sumGapGam distributions, compared to the results from \pythia using CJKL photon PDFs. Several different intervals in $H_\text{T}$ are shown. Error bars represent statistical uncertainties only.

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: : Comparison of data and MC distributions for UPC \gamAjets production, within the fiducial acceptance, for (a) the jet multiplicity and (b) the $\Delta\phi$ of the leading dijet pair. The distributions are shown for reconstructed jet kinematics after applying all event selections and efficiency corrections. The bottom panels show the ratios of the data and MC distributions. The error bars in both panels show statistical uncertainties only.

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: : Comparison of data and MC distributions for UPC \gamAjets production, within the fiducial acceptance, for (a) \yjets and (b) \HT. The distributions are shown for reconstructed jet kinematics after applying all event selections and efficiency corrections. The bottom panels show the ratios of the data and MC distributions. The error bars in both panels show statistical uncertainties only.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

Two-dimensional measured differential distributions of \Ncorr for \gamAjets production in \PbPb\ UPC interactions obtained by integrating the three-dimensional cross-sections obtained from Eqs.~(\ref{eq:diffcsJetKin}) and (\ref{eq:diffcsPartKin}) over the acceptance of the third variable. The left column shows results using \kinsetjet and the right column results using \kinsetpart. These results are not unfolded for detector response.

A breakdown of the different systematic uncertainty contributions as a function of \xA, for a selection of bins in \HT, summed over \zg.

The fraction of photonuclear jet events passing the fiducial requirements in which the photon-emitting nucleus does not break up as a function \zg. The systematic uncertainties are shown as shaded blue bands, and the error bars are statistical uncertainties. A quadratic fit in $\ln(\zg)$ is shown in red. These results indicate a strong dependence of the breakup rate on \zg and an overall high rate of breakup due to additional Coulomb interactions, reaching $70\%$ at high \zg. Results are compared to theoretical calculations from Ref. \cite{Eskola:2024fhf}.

The impact of nPDF modifications on the photo-nuclear jet cross-section, represented by the ratio of the cross-section calculated with modified nPDFs ($\sigma_\text{mod}$) to the cross-section for un-modified free nucleon PDFs ($\sigma_\text{free}$). These effects are shown for nCTEQ15 WZ+SIH (squares) and nNNPDF 3.0 (diamonds) fits, where ratios are taken with respect to CT18 and NNPDF 3.1, respectively. Results are integrated over the \zg range $3.7\times10^{-4} < \zg < 0.027$, and each panel shows a separate range in \HT. The total uncertainty on this measurement in each bin is compared to the size of these modifications, where the light red bands show the total scale uncertainty, the grey bands are the quadrature sum of the residual systematic uncertainty, and the yellow bands show the statistical uncertainty.

Triple-differential cross-sections, \sigtridiffJetKin, as a function of \yjets, in four \mjets intervals with \mjets increasing from the top left to the bottom right. The cross-sections are shown for the selected intervals in \mjets and integrated over the \HT acceptance. For each plot, systematic uncertainties are shown in the upper panel as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup fraction. The bottom panels show the ratio between the theory prediction and the data. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiffJetKin, as a function of \yjets, in four \mjets intervals with \mjets increasing from the top left to the bottom right. The cross-sections are shown for the selected intervals in \mjets and integrated over the \HT acceptance. For each plot, systematic uncertainties are shown in the upper panel as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup fraction. The bottom panels show the ratio between the theory prediction and the data. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiffJetKin, as a function of \yjets, in four \mjets intervals with \mjets increasing from the top left to the bottom right. The cross-sections are shown for the selected intervals in \mjets and integrated over the \HT acceptance. For each plot, systematic uncertainties are shown in the upper panel as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup fraction. The bottom panels show the ratio between the theory prediction and the data. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiffJetKin, as a function of \yjets, in four \mjets intervals with \mjets increasing from the top left to the bottom right. The cross-sections are shown for the selected intervals in \mjets and integrated over the \HT acceptance. For each plot, systematic uncertainties are shown in the upper panel as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup fraction. The bottom panels show the ratio between the theory prediction and the data. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiffJetKin, as a function of \mjets, in several \yjets intervals. The cross-sections are integrated over the \HT acceptance. Systematic uncertainties are shown in the upper panel as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup fraction. The bottom panels show the ratio between the theory prediction and the data for a selection of the \yjets intervals. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\xA$ for different bins of $\HT$ for events with emitted photon energies in the kinematic range $0.0023 < \zg < 0.0043$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\xA$ for different bins of $\HT$ for events with emitted photon energies in the kinematic range $0.0079 < \zg < 0.015$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\xA$ for different bins of $\HT$ for events with emitted photon energies in the kinematic range $3.7\times10^{-4} < \zg < 0.027$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\HT$ for different bins of $\xA$ for events with emitted photon energies in the kinematic range $3.7\times10^{-4} < \zg < 0.027$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \xA. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of \zg for different bins of \HT for events with struck parton energies in the kinematic range $0.010 < \xA < 0.166$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of intervals in \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Ratios of the triple-differential cross-sections, \sigtridiff, to theoretical preductions using several nPDF models as a function of \xA for different bins of \HT for events with struck parton energies in the kinematic range $3.7\times10^{-4} < \zg < 0.027$. Theoretical comparisons for the cross-sections are computed using \pythia with a photon flux from \textsc{Starlight}, and a \zg-dependent data-driven breakup correction. Four different theoretical comparisons are shown corresponding to the nCTEQ 15 WZ+SIH, nNNPDF 3.0, EPPS21, and TUJU21 nPDF fits. The light red bands are the quadrature sum of scale uncertainties on the ratio, while the gray band shows the residual systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

In-situ correction to the absolute JES as a function of \pTjet derived from data and MC evaluation of the $Z$+jet balance in low-$\mu$ ($\mu \sim 2$) \pp collisions at 13~\TeV. The binned results are smoothed with a Gaussian kernel smoothing procedure, the result of which is shown as a black line. The red line shows the result from high-$\mu$ \pp collisions.

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: : A summary of all sources of JES systematic uncertainties as a function of $\eta^*$ for (a) $\pTjet = 20$~\GeV and (b) $\pTjet = 35$~\GeV.

Correction factors to the jet energy scale, derived in low-$\mu$ ($\mu \sim 2$) 13~\TeV\pp collisions, used to translate the JES to jets in photonuclear \PbPb events. The $\eta$-dependence of the correction is largely driven by the structure of the ATLAS calorimeter.

The fraction of each bin volume that is included in the geometric acceptance region for the hard-scattering kinematic variables. Re-computed bin means for each bin are shown as markers. Only bins that pass a minimum threshold on the fiducial and geometric acceptance are shown, and the means are only shown for bins with $f_\text{vol} > 50\%$.

The fraction of each bin volume that is included in the geometric acceptance region for the jet system kinematic variables. Re-computed bin means for each bin are shown as markers. Only bins that pass a minimum threshold on the fiducial and geometric acceptance are shown, and the means are only shown for bins with $f_\text{vol} > 50\%$.

Triple-differential cross-sections, \sigtridiff, as a function of $\xA$ for different bins of $\HT$ for events with emitted photon energies in the kinematic range $0.0043 < \zg < 0.0079$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\xA$ for different bins of $\HT$ for events with emitted photon energies in the kinematic range $0.015 < \zg < 0.027$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \HT. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\HT$ for different bins of $\xA$ for events with emitted photon energies in the kinematic range $0.0023 < \zg < 0.0043$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \xA. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\HT$ for different bins of $\xA$ for events with emitted photon energies in the kinematic range $0.0043 < \zg < 0.079$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \xA. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\HT$ for different bins of $\xA$ for events with emitted photon energies in the kinematic range $0.0079 < \zg < 0.015$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \xA. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.

Triple-differential cross-sections, \sigtridiff, as a function of $\HT$ for different bins of $\xA$ for events with emitted photon energies in the kinematic range $0.015 < \zg < 0.027$. In the upper panel, systematic uncertainties are shown as shaded boxes, while statistical uncertainties shown as vertical lines are usually smaller than the size of the markers. A theoretical comparison is shown to cross-sections computed using \pythia with nCTEQ15 WZ+SIH PDFs, a photon flux from \textsc{Starlight}, and a \zg-dependent breakup fraction. The bottom panels show the ratio between the theory prediction and data for a representative subset of the bins of \xA. The light red bands in the ratio panels are the quadrature sum of scale uncertainties on the cross-section, while the gray band shows the remaining systematic uncertainty. The yellow band shows the point-to-point statistical uncertainty.