CMS-HIG-23-014

CMS-HIG-23-014 ; CERN-EP-2025-067
Measurements of inclusive and differential Higgs boson production cross sections at $\sqrt{s} =$ 13.6 TeV in the $\mathrm{H}\to\gamma\gamma$ decay channel
CMS Collaboration
24 April 2025
Submitted to J. High Energy Phys.
Abstract: Inclusive and differential cross sections for Higgs boson production in proton-proton collisions at a centre-of-mass energy of 13.6 TeV are measured using data collected with the CMS detector at the LHC in 2022, corresponding to an integrated luminosity of 34.7 fb $^{-1}$ . Events with the diphoton final state are selected, and the measured inclusive fiducial cross section is $\sigma_{\text{fid}}=$ 74 $\pm$ 11 (stat) $^{+5}_{-4}$ (syst) fb, in agreement with the standard model prediction of 67.8 $\pm$ 3.8 fb. Differential cross sections are measured as functions of several observables: the Higgs boson transverse momentum and rapidity, the number of associated jets, and the transverse momentum of the leading jet in the event. Within the uncertainties, the differential cross sections agree with the standard model predictions.
Links: e-print arXiv:2504.17755 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Normalized distributions of the photon identification BDT scores for prompt (blue) and non-prompt (orange) photons from $\gamma$ + jet simulated events. The shaded region indicates the photons that are rejected by the photon preselection requirement of ${>} -$ 0.9.
png pdf	Figure 2: Data-to-simulation comparison for $\sigma_{E}$ (upper left), $H/E$ (upper right), the photon identification BDT score in EB (lower left) and EE (lower right) for electrons from $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ decays reconstructed as photons. The uncorrected distributions are shown in blue and the corrected distributions from the normalizing flow are shown in green. The error bars in the ratio panels include the statistical uncertainty from the data and the uncertainty from the limited number of simulated events. For the distributions of the photon identification BDT score, the shaded region corresponds to photons with a BDT score ${<}$ 0.25, which are excluded by the selection applied in the cross section measurements. For the $\sigma_{E}$ distribution, the last bin contains the overflow.
png pdf	Figure 2-a: Data-to-simulation comparison for $\sigma_{E}$ (upper left), $H/E$ (upper right), the photon identification BDT score in EB (lower left) and EE (lower right) for electrons from $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ decays reconstructed as photons. The uncorrected distributions are shown in blue and the corrected distributions from the normalizing flow are shown in green. The error bars in the ratio panels include the statistical uncertainty from the data and the uncertainty from the limited number of simulated events. For the distributions of the photon identification BDT score, the shaded region corresponds to photons with a BDT score ${<}$ 0.25, which are excluded by the selection applied in the cross section measurements. For the $\sigma_{E}$ distribution, the last bin contains the overflow.
png pdf	Figure 2-b: Data-to-simulation comparison for $\sigma_{E}$ (upper left), $H/E$ (upper right), the photon identification BDT score in EB (lower left) and EE (lower right) for electrons from $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ decays reconstructed as photons. The uncorrected distributions are shown in blue and the corrected distributions from the normalizing flow are shown in green. The error bars in the ratio panels include the statistical uncertainty from the data and the uncertainty from the limited number of simulated events. For the distributions of the photon identification BDT score, the shaded region corresponds to photons with a BDT score ${<}$ 0.25, which are excluded by the selection applied in the cross section measurements. For the $\sigma_{E}$ distribution, the last bin contains the overflow.
png pdf	Figure 2-c: Data-to-simulation comparison for $\sigma_{E}$ (upper left), $H/E$ (upper right), the photon identification BDT score in EB (lower left) and EE (lower right) for electrons from $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ decays reconstructed as photons. The uncorrected distributions are shown in blue and the corrected distributions from the normalizing flow are shown in green. The error bars in the ratio panels include the statistical uncertainty from the data and the uncertainty from the limited number of simulated events. For the distributions of the photon identification BDT score, the shaded region corresponds to photons with a BDT score ${<}$ 0.25, which are excluded by the selection applied in the cross section measurements. For the $\sigma_{E}$ distribution, the last bin contains the overflow.
png pdf	Figure 2-d: Data-to-simulation comparison for $\sigma_{E}$ (upper left), $H/E$ (upper right), the photon identification BDT score in EB (lower left) and EE (lower right) for electrons from $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ decays reconstructed as photons. The uncorrected distributions are shown in blue and the corrected distributions from the normalizing flow are shown in green. The error bars in the ratio panels include the statistical uncertainty from the data and the uncertainty from the limited number of simulated events. For the distributions of the photon identification BDT score, the shaded region corresponds to photons with a BDT score ${<}$ 0.25, which are excluded by the selection applied in the cross section measurements. For the $\sigma_{E}$ distribution, the last bin contains the overflow.
png pdf	Figure 3: Data-to-simulation comparison of the per-event decorrelated mass-resolution estimator $\sigma_m/m$ using $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ events. Both electrons are reconstructed as photons and categorized either both in the EB (left) or at least one in the EE (right). The uncertainty band in the lower panel represents the systematic uncertainty based on the residual mismodelling of $\sigma_E/E$ (5%). The error bars on the markers in the lower panels include the statistical uncertainty from data and the uncertainty from a limited number of simulated events. The last bin contains the overflow.
png pdf	Figure 3-a: Data-to-simulation comparison of the per-event decorrelated mass-resolution estimator $\sigma_m/m$ using $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ events. Both electrons are reconstructed as photons and categorized either both in the EB (left) or at least one in the EE (right). The uncertainty band in the lower panel represents the systematic uncertainty based on the residual mismodelling of $\sigma_E/E$ (5%). The error bars on the markers in the lower panels include the statistical uncertainty from data and the uncertainty from a limited number of simulated events. The last bin contains the overflow.
png pdf	Figure 3-b: Data-to-simulation comparison of the per-event decorrelated mass-resolution estimator $\sigma_m/m$ using $\mathrm{Z} \to \mathrm{e}\mathrm{e}$ events. Both electrons are reconstructed as photons and categorized either both in the EB (left) or at least one in the EE (right). The uncertainty band in the lower panel represents the systematic uncertainty based on the residual mismodelling of $\sigma_E/E$ (5%). The error bars on the markers in the lower panels include the statistical uncertainty from data and the uncertainty from a limited number of simulated events. The last bin contains the overflow.
png pdf	Figure 4: Combined parametrized signal shapes per category and for the sum of all categories for the measurement of the inclusive cross section. The open squares denote the expectation from the simulation and the blue lines show the parametric models that describe the simulations. The uncertainty bars for the expectation from the simulation due to the limited number of simulated events are smaller than the marker size. The normalization of the histograms corresponds to the expected number of events, taking into account the cross sections of the considered production modes, the efficiency of the selection, and the integrated luminosity of 34.7 fb $^{-1}$ . The effective mass resolution $\sigma_{\text{eff}}$ (defined as half of the width of the smallest interval containing 68.3% of the area of the distribution) for each combined signal model is indicated in the grey area.
png pdf	Figure 4-a: Combined parametrized signal shapes per category and for the sum of all categories for the measurement of the inclusive cross section. The open squares denote the expectation from the simulation and the blue lines show the parametric models that describe the simulations. The uncertainty bars for the expectation from the simulation due to the limited number of simulated events are smaller than the marker size. The normalization of the histograms corresponds to the expected number of events, taking into account the cross sections of the considered production modes, the efficiency of the selection, and the integrated luminosity of 34.7 fb $^{-1}$ . The effective mass resolution $\sigma_{\text{eff}}$ (defined as half of the width of the smallest interval containing 68.3% of the area of the distribution) for each combined signal model is indicated in the grey area.
png pdf	Figure 4-b: Combined parametrized signal shapes per category and for the sum of all categories for the measurement of the inclusive cross section. The open squares denote the expectation from the simulation and the blue lines show the parametric models that describe the simulations. The uncertainty bars for the expectation from the simulation due to the limited number of simulated events are smaller than the marker size. The normalization of the histograms corresponds to the expected number of events, taking into account the cross sections of the considered production modes, the efficiency of the selection, and the integrated luminosity of 34.7 fb $^{-1}$ . The effective mass resolution $\sigma_{\text{eff}}$ (defined as half of the width of the smallest interval containing 68.3% of the area of the distribution) for each combined signal model is indicated in the grey area.
png pdf	Figure 4-c: Combined parametrized signal shapes per category and for the sum of all categories for the measurement of the inclusive cross section. The open squares denote the expectation from the simulation and the blue lines show the parametric models that describe the simulations. The uncertainty bars for the expectation from the simulation due to the limited number of simulated events are smaller than the marker size. The normalization of the histograms corresponds to the expected number of events, taking into account the cross sections of the considered production modes, the efficiency of the selection, and the integrated luminosity of 34.7 fb $^{-1}$ . The effective mass resolution $\sigma_{\text{eff}}$ (defined as half of the width of the smallest interval containing 68.3% of the area of the distribution) for each combined signal model is indicated in the grey area.
png pdf	Figure 4-d: Combined parametrized signal shapes per category and for the sum of all categories for the measurement of the inclusive cross section. The open squares denote the expectation from the simulation and the blue lines show the parametric models that describe the simulations. The uncertainty bars for the expectation from the simulation due to the limited number of simulated events are smaller than the marker size. The normalization of the histograms corresponds to the expected number of events, taking into account the cross sections of the considered production modes, the efficiency of the selection, and the integrated luminosity of 34.7 fb $^{-1}$ . The effective mass resolution $\sigma_{\text{eff}}$ (defined as half of the width of the smallest interval containing 68.3% of the area of the distribution) for each combined signal model is indicated in the grey area.
png pdf	Figure 5: Likelihood scans for the inclusive fiducial cross section measurement. The black line corresponds to considering both the statistical and systematic uncertainties. The blue dash-dotted line corresponds to considering only the statistical uncertainty, including the discrete profiling method for the background modelling uncertainty. The theoretical prediction from MadGraph-5_aMC@NLO, including the NNLOPS reweighting for the ggH component, is shown in red. The shaded theory uncertainty band includes the uncertainties in the renormalization and factorization scales, in the parton distribution functions, in $\alpha_\mathrm{S}$ , in the $\mathcal{B}(\mathrm{H}\to\gamma\gamma)$ , and in the fiducial acceptance.
png pdf	Figure 6: Diphoton invariant mass distribution in the inclusive fiducial measurement, weighted by $S/(S+B)$ for the different mass-resolution categories. The distribution is shown together with the signal $+$ background fit (red line) and the background-only component (dashed line). In the lower panel, the signal component is shown, estimated by subtracting the background component from the signal $+$ background fit. The green (yellow) bands indicate the $\pm1\sigma$ ( $\pm2\sigma$ ) uncertainties in the background component. They are derived from pseudoexperiments using the best-fit background function from the signal+background fit.
png pdf	Figure 7: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{H}}$ (left) and the corresponding correlation matrix (right). The measured cross section in each bin is divided by the corresponding bin width. The coloured lines denote the predictions from different event generation setups, explained in the legend and in the text. The dashed boxes show the uncertainties in theoretical predictions on both the ggH and $\mathrm{x\mathrm{H}}$ components. The $p$ -value is calculated for the nominal SM prediction, which is MadGraph-5_aMC@NLO with NNLOPS (MG5_aMC@NLO + NNLOPS) reweighting. The lower panel in the left plot shows the ratio to the nominal SM prediction. The last bin extends to infinity and the normalization of the bin is indicated in the plot.
png pdf	Figure 7-a: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{H}}$ (left) and the corresponding correlation matrix (right). The measured cross section in each bin is divided by the corresponding bin width. The coloured lines denote the predictions from different event generation setups, explained in the legend and in the text. The dashed boxes show the uncertainties in theoretical predictions on both the ggH and $\mathrm{x\mathrm{H}}$ components. The $p$ -value is calculated for the nominal SM prediction, which is MadGraph-5_aMC@NLO with NNLOPS (MG5_aMC@NLO + NNLOPS) reweighting. The lower panel in the left plot shows the ratio to the nominal SM prediction. The last bin extends to infinity and the normalization of the bin is indicated in the plot.
png pdf	Figure 7-b: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{H}}$ (left) and the corresponding correlation matrix (right). The measured cross section in each bin is divided by the corresponding bin width. The coloured lines denote the predictions from different event generation setups, explained in the legend and in the text. The dashed boxes show the uncertainties in theoretical predictions on both the ggH and $\mathrm{x\mathrm{H}}$ components. The $p$ -value is calculated for the nominal SM prediction, which is MadGraph-5_aMC@NLO with NNLOPS (MG5_aMC@NLO + NNLOPS) reweighting. The lower panel in the left plot shows the ratio to the nominal SM prediction. The last bin extends to infinity and the normalization of the bin is indicated in the plot.
png pdf	Figure 8: Differential fiducial cross sections for $\|y^\mathrm{H}\|$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7. In this case, the last bin does not extend to infinity, but it is limited to 2.5.
png pdf	Figure 8-a: Differential fiducial cross sections for $\|y^\mathrm{H}\|$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7. In this case, the last bin does not extend to infinity, but it is limited to 2.5.
png pdf	Figure 8-b: Differential fiducial cross sections for $\|y^\mathrm{H}\|$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7. In this case, the last bin does not extend to infinity, but it is limited to 2.5.
png pdf	Figure 9: Differential fiducial cross sections for $N_{\text{Jets}}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.
png pdf	Figure 9-a: Differential fiducial cross sections for $N_{\text{Jets}}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.
png pdf	Figure 9-b: Differential fiducial cross sections for $N_{\text{Jets}}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.
png pdf	Figure 10: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{j}_1}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.
png pdf	Figure 10-a: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{j}_1}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.
png pdf	Figure 10-b: Differential fiducial cross sections for $p_{\mathrm{T}}^{\mathrm{j}_1}$ (left) and the corresponding correlation matrix (right). Other details as for the caption of Fig. 7.

Tables
png pdf	Table 1: Bin boundaries for the differential cross section measurement. The first $p_{\mathrm{T}}^{\mathrm{j}_1}$ bin corresponds to events without jets. For the $N_{\text{Jets}}$ binning, the right boundary should be considered as not included in the bin, i.e., [lower, upper).
png pdf	Table 2: Magnitude of the systematic uncertainties (Impact) in the inclusive fiducial cross section measurement. The magnitude of the uncertainty from the photon energy scale and resolution is extracted by performing a fit with the corresponding group of nuisance parameters frozen to their best-fit values. The obtained confidence interval is then subtracted in quadrature from the total confidence interval from the fit where all nuisance parameters are profiled. The magnitudes of the other sources of systematic uncertainty are obtained by varying the corresponding nuisance parameter by one standard deviation, keeping the other nuisance parameters at their best-fit values.

Summary

The fiducial inclusive cross section for Higgs boson production in proton-proton collisions has been measured at a centre-of-mass energy of 13.6 TeV using the

$\mathrm{H}\to\gamma\gamma$ decay channel. The data were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 34.7 fb

$^{-1}$ . A new normalizing-flow-based method is applied to correct the imperfect modelling of reconstructed photon variables in the simulation and to reduce the associated systematic uncertainties. The fiducial phase space is defined at the particle level and requires two isolated photons within the pseudorapidity

$|\eta| <$ 2.5 and not within 1.4442

$< |\eta| <$ 1.5660. These photons must fulfil a requirement on the geometric mean of their transverse momenta scaled by their invariant mass,

$\sqrt{\smash[b]{p_{\mathrm{T}}^{\gamma_1} p_{\mathrm{T}}^{\gamma_2}}} / m_{\gamma\gamma} > 1/$ 3, which improves the perturbative convergence of the theoretical predictions, as well as the requirement

$p_{\mathrm{T}}^{\gamma_2} / m_{\gamma\gamma} > 1/$ 4. The measured inclusive fiducial cross section is

$\sigma_{\text{fid}} =$ 74

$\pm$ 11 (stat)

$^{+5}_{-4}$ (syst) fb and is in agreement with the standard-model (SM) expectation of 67.8

$\pm$ 3.8 fb. Differential cross sections are measured as functions of the Higgs boson transverse momentum, rapidity, the number of associated jets, and the transverse momentum of the leading jet in the event. Within the uncertainties, the differential cross sections agree with the SM predictions.

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