CMS-PAS-TOP-23-002

CMS-PAS-TOP-23-002
Inclusive and differential measurements of the $\mathrm{t\bar{t}}\gamma$ cross section and the $\mathrm{t\bar{t}}\gamma / \mathrm{t\bar{t}}$ ratio in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
21 March 2025

Abstract: Inclusive and differential measurements of the cross section of top quark pair ( $\mathrm{t\bar{t}}$ ) production in association with a photon ( $\gamma$ ) are performed as a function of lepton, photon, top quark, and $\mathrm{t\bar{t}}$ kinematic observables, using 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}=$ 13 TeV. Events containing two leptons, electrons or muons, and a photon in the final state are used. The fiducial cross section of $\mathrm{t\bar{t}}\gamma$ is measured to be 134 $\pm$ 8 fb, in a phase space selecting events with a high momentum, isolated photon. The fiducial cross section of $\mathrm{t\bar{t}}\gamma$ is also measured considering only events where the photon is emitted from the initial state quarks or the off-shell top quarks, in which case the result is 54 $\pm$ 5 fb. Differential measurements at the particle and parton level are performed in the fiducial and in an extended phase space, respectively. Additionally, ratios between the inclusive and differential cross sections of $\mathrm{t\bar{t}}\gamma$ and $\mathrm{t\bar{t}}$ production, as well as the top quark charge asymmetry in $\mathrm{t\bar{t}}\gamma$ events, are measured. The inclusive ratio is measured to be 0.0125 $\pm$ 0.0005, in the extended phase space. The top quark charge asymmetry is measured to be $-$ 0.012 $\pm$ 0.042. All results are found to be consistent with the standard model predictions.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Example Feynman diagrams for the production of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , where both top quarks decay dileptonically.
png pdf	Figure 1-a: Example Feynman diagrams for the production of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , where both top quarks decay dileptonically.
png pdf	Figure 1-b: Example Feynman diagrams for the production of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , where both top quarks decay dileptonically.
png pdf	Figure 1-c: Example Feynman diagrams for the production of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , where both top quarks decay dileptonically.
png pdf	Figure 2: Distributions after the event selection for: the $p_{\mathrm{T}}$ of the photon (upper left), the $p_{\mathrm{T}}$ of the lepton with the highest transverse momentum (upper right), the number of jets (lower left), and the $\Delta R_{\gamma,\mathrm{t}}$ (lower right). The data and their statistical uncertainties are indicated by bullets and error bars. The expectation for the ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process after the fit is shown in red and dark orange, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 2-a: Distributions after the event selection for: the $p_{\mathrm{T}}$ of the photon (upper left), the $p_{\mathrm{T}}$ of the lepton with the highest transverse momentum (upper right), the number of jets (lower left), and the $\Delta R_{\gamma,\mathrm{t}}$ (lower right). The data and their statistical uncertainties are indicated by bullets and error bars. The expectation for the ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process after the fit is shown in red and dark orange, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 2-b: Distributions after the event selection for: the $p_{\mathrm{T}}$ of the photon (upper left), the $p_{\mathrm{T}}$ of the lepton with the highest transverse momentum (upper right), the number of jets (lower left), and the $\Delta R_{\gamma,\mathrm{t}}$ (lower right). The data and their statistical uncertainties are indicated by bullets and error bars. The expectation for the ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process after the fit is shown in red and dark orange, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 2-c: Distributions after the event selection for: the $p_{\mathrm{T}}$ of the photon (upper left), the $p_{\mathrm{T}}$ of the lepton with the highest transverse momentum (upper right), the number of jets (lower left), and the $\Delta R_{\gamma,\mathrm{t}}$ (lower right). The data and their statistical uncertainties are indicated by bullets and error bars. The expectation for the ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process after the fit is shown in red and dark orange, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 2-d: Distributions after the event selection for: the $p_{\mathrm{T}}$ of the photon (upper left), the $p_{\mathrm{T}}$ of the lepton with the highest transverse momentum (upper right), the number of jets (lower left), and the $\Delta R_{\gamma,\mathrm{t}}$ (lower right). The data and their statistical uncertainties are indicated by bullets and error bars. The expectation for the ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process after the fit is shown in red and dark orange, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 3: The $p_{\mathrm{T}}$ distribution of the leading reconstructed top quark (upper left), the reconstructed $\mathrm{t} \overline{\mathrm{t}}$ invariant mass (upper right), and the difference in absolute rapidity between the top quark and antiquark (lower) in data and simulation, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 3-a: The $p_{\mathrm{T}}$ distribution of the leading reconstructed top quark (upper left), the reconstructed $\mathrm{t} \overline{\mathrm{t}}$ invariant mass (upper right), and the difference in absolute rapidity between the top quark and antiquark (lower) in data and simulation, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 3-b: The $p_{\mathrm{T}}$ distribution of the leading reconstructed top quark (upper left), the reconstructed $\mathrm{t} \overline{\mathrm{t}}$ invariant mass (upper right), and the difference in absolute rapidity between the top quark and antiquark (lower) in data and simulation, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 3-c: The $p_{\mathrm{T}}$ distribution of the leading reconstructed top quark (upper left), the reconstructed $\mathrm{t} \overline{\mathrm{t}}$ invariant mass (upper right), and the difference in absolute rapidity between the top quark and antiquark (lower) in data and simulation, after the fit to the production component of ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ , described in Section 9.2. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 4: Distributions of the invariant mass of the two lepton (left) and two lepton + photon (right) system, after requiring that the events the full event selection excluding the selections on these variables, before any fit (with the signal cross section taken from the predictions). The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the total uncertainty in the expectation.
png pdf	Figure 4-a: Distributions of the invariant mass of the two lepton (left) and two lepton + photon (right) system, after requiring that the events the full event selection excluding the selections on these variables, before any fit (with the signal cross section taken from the predictions). The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the total uncertainty in the expectation.
png pdf	Figure 4-b: Distributions of the invariant mass of the two lepton (left) and two lepton + photon (right) system, after requiring that the events the full event selection excluding the selections on these variables, before any fit (with the signal cross section taken from the predictions). The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the total uncertainty in the expectation.
png pdf	Figure 5: Schematic representation of the regions used to estimate the contribution from events with a nonprompt photon in the SR. The green (light red) areas represent the fraction of events with a nonprompt (genuine) photon in each region. The area shaded in grey represents a gap between the regions, and events falling in that gap are excluded. The numbers in black on the axes represent the selections applied to separate the regions for events with a photon reconstructed in the ECAL barrel, while those in pink represent the selections applied to events with a photon reconstructed in the endcaps.
png pdf	Figure 6: Absolute (left) and normalized (right) differential distributions of the leading top quark $p_{\mathrm{T}}$ (upper) and $\Delta R_{\gamma,{\mathrm{t}\overline{\mathrm{t}}} }$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 6-a: Absolute (left) and normalized (right) differential distributions of the leading top quark $p_{\mathrm{T}}$ (upper) and $\Delta R_{\gamma,{\mathrm{t}\overline{\mathrm{t}}} }$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 6-b: Absolute (left) and normalized (right) differential distributions of the leading top quark $p_{\mathrm{T}}$ (upper) and $\Delta R_{\gamma,{\mathrm{t}\overline{\mathrm{t}}} }$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 6-c: Absolute (left) and normalized (right) differential distributions of the leading top quark $p_{\mathrm{T}}$ (upper) and $\Delta R_{\gamma,{\mathrm{t}\overline{\mathrm{t}}} }$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 6-d: Absolute (left) and normalized (right) differential distributions of the leading top quark $p_{\mathrm{T}}$ (upper) and $\Delta R_{\gamma,{\mathrm{t}\overline{\mathrm{t}}} }$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 7: Absolute (left) and normalized (right) differential distributions (expected) of the $\Delta R (\gamma,\text{clos. top})$ (upper) and $m({\mathrm{t}\overline{\mathrm{t}}} )$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 7-a: Absolute (left) and normalized (right) differential distributions (expected) of the $\Delta R (\gamma,\text{clos. top})$ (upper) and $m({\mathrm{t}\overline{\mathrm{t}}} )$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 7-b: Absolute (left) and normalized (right) differential distributions (expected) of the $\Delta R (\gamma,\text{clos. top})$ (upper) and $m({\mathrm{t}\overline{\mathrm{t}}} )$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 7-c: Absolute (left) and normalized (right) differential distributions (expected) of the $\Delta R (\gamma,\text{clos. top})$ (upper) and $m({\mathrm{t}\overline{\mathrm{t}}} )$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 7-d: Absolute (left) and normalized (right) differential distributions (expected) of the $\Delta R (\gamma,\text{clos. top})$ (upper) and $m({\mathrm{t}\overline{\mathrm{t}}} )$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 8: Absolute (left) and normalized (right) differential distributions of the leading lepton $p_{\mathrm{T}}$ (upper) and photon $p_{\mathrm{T}}$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 8-a: Absolute (left) and normalized (right) differential distributions of the leading lepton $p_{\mathrm{T}}$ (upper) and photon $p_{\mathrm{T}}$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 8-b: Absolute (left) and normalized (right) differential distributions of the leading lepton $p_{\mathrm{T}}$ (upper) and photon $p_{\mathrm{T}}$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 8-c: Absolute (left) and normalized (right) differential distributions of the leading lepton $p_{\mathrm{T}}$ (upper) and photon $p_{\mathrm{T}}$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 8-d: Absolute (left) and normalized (right) differential distributions of the leading lepton $p_{\mathrm{T}}$ (upper) and photon $p_{\mathrm{T}}$ (lower). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 9: Absolute (left) and normalized (right) differential distributions of the $\Delta\phi$ between the leptons. The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 9-a: Absolute (left) and normalized (right) differential distributions of the $\Delta\phi$ between the leptons. The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 9-b: Absolute (left) and normalized (right) differential distributions of the $\Delta\phi$ between the leptons. The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 10: Distribution of the $p_{\mathrm{T}}$ of the leading lepton for the " ${\mathrm{t}\overline{\mathrm{t}}},0 \gamma$ " region (left) and the " ${\mathrm{t}\overline{\mathrm{t}}},1 \gamma$ " signal region (centre), and the number of jets for the ${\mathrm{Z}}{\gamma}{+}$ jets CR after the fit. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 10-a: Distribution of the $p_{\mathrm{T}}$ of the leading lepton for the " ${\mathrm{t}\overline{\mathrm{t}}},0 \gamma$ " region (left) and the " ${\mathrm{t}\overline{\mathrm{t}}},1 \gamma$ " signal region (centre), and the number of jets for the ${\mathrm{Z}}{\gamma}{+}$ jets CR after the fit. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 10-b: Distribution of the $p_{\mathrm{T}}$ of the leading lepton for the " ${\mathrm{t}\overline{\mathrm{t}}},0 \gamma$ " region (left) and the " ${\mathrm{t}\overline{\mathrm{t}}},1 \gamma$ " signal region (centre), and the number of jets for the ${\mathrm{Z}}{\gamma}{+}$ jets CR after the fit. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 10-c: Distribution of the $p_{\mathrm{T}}$ of the leading lepton for the " ${\mathrm{t}\overline{\mathrm{t}}},0 \gamma$ " region (left) and the " ${\mathrm{t}\overline{\mathrm{t}}},1 \gamma$ " signal region (centre), and the number of jets for the ${\mathrm{Z}}{\gamma}{+}$ jets CR after the fit. The hatched area indicates the total uncertainty in the expectation. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the sum of the prefit predictions (blue line).
png pdf	Figure 11: Absolute differential distributions of the $R_{\gamma}$ as a function of the leading lepton $p_{\mathrm{T}}$ (left) and the leading top quark $p_{\mathrm{T}}$ (right). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 11-a: Absolute differential distributions of the $R_{\gamma}$ as a function of the leading lepton $p_{\mathrm{T}}$ (left) and the leading top quark $p_{\mathrm{T}}$ (right). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.
png pdf	Figure 11-b: Absolute differential distributions of the $R_{\gamma}$ as a function of the leading lepton $p_{\mathrm{T}}$ (left) and the leading top quark $p_{\mathrm{T}}$ (right). The blue lines show the theoretical predictions, and the lighter blue shaded areas represent the theoretical uncertainties in the predictions. The theoretical uncertainties include the choice of renormalization and factorization scale and PDFs, including $\alpha_S$ variations. The black points represent the measured values, with the total uncertainty, while the red error bar shows the results considering only the statistical uncertainty.

Tables
png pdf	Table 1: Summary of the systematic uncertainty sources in the differential ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ cross section and ${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ / $\mathrm{t} \overline{\mathrm{t}}$ ratio measurements. The first column lists the source of the uncertainty, while the second (third) column indicates the treatment of correlations of the uncertainties between different data-taking periods (processes), where $\checkmark$ means fully correlated, $\sim$ means partially correlated (i.e., contains sub-sources that are either fully correlated or uncorrelated), $\times$ means uncorrelated, and $\text{---}$ means not applicable.
png pdf	Table 2: Definition of objects and event selection used to define the fiducial phase space.

Summary

A comprehensive study of the top quark pair (

$\mathrm{t} \overline{\mathrm{t}}$ ) production in association with a photon (

$\gamma$ ) at the LHC is presented, through inclusive and differential measurements of different properties on the data collected by the CMS experiment in 2016-2018 at a centre-of-mass energy

$\sqrt{s}=$ 13 TeV. The inclusive and differential measurements are performed in the dilepton decay channels, in a fiducial region at particle level including events with photon

$p_{\mathrm{T}} >$ 20 GeV. The inclusive fiducial cross section for

${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ with a photon radiated at any stage of the process is 134

$\pm{7}$ (syst)

$\pm{3}$ (stat)

$\text{fb}$ , while the cross section for events with a photon radiated at the production stage of the process is

$\text{54} \pm{4}$ (syst)

$\pm{2}$ (stat)

$\text{fb}$ . The measured cross sections agree with the predictions from simulation for the combined

${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ process and for

${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ with photons from the production stage, however they underestimate the data for

${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ with photons from the decay part of the process. The cross section is also measured in bins of seven observables related to the kinematic properties and topology of the photon, the leptons, and the reconstructed top quarks in the event. The predictions from simulation accurately describe the shape of the measured cross sections. The

${\mathrm{t}\overline{\mathrm{t}}} {\gamma} / {\mathrm{t}\overline{\mathrm{t}}}$ ratio is measured for the first time, inclusively and differentially. The inclusive ratio is found to be

$R=0.0125\pm{0.0005}$ (syst)

$\pm{0.0002}$ (stat), in agreement with the nominal predictions from simulation. The differential ratios are well described by the predictions, within the total uncertainties. A study of the top quark charge asymmetry is also reported, and an asymmetry of

$A_{C} =$ (

$-$ 1.2

$\pm$ 4.2 )% was observed, consistent with both the standard model prediction at next-to-leading order in QCD and with the no-asymmetry scenario, showing statistical limitations for the measurement of this observable in

${\mathrm{t}\overline{\mathrm{t}}} {\gamma}$ events from the available data.

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