Measurements of production cross sections of the Higgs boson in the four-lepton final state in proton-proton collisions at s = 13 TeV

Abstract

Production cross sections of the Higgs boson are measured in the $H\to ZZ\to 4\ell$ ( $\ell =e,{\mu }_{}^{}$ ) decay channel. A data sample of proton-proton collisions at a center-of-mass energy of 13 $\text{TeV}$ , collected by the CMS detector at the LHC and corresponding to an integrated luminosity of 137 ${\text{fb}}^{-1}$ is used. The signal strength modifier $\mu$ , defined as the ratio of the Higgs boson production rate in the $4\ell$ channel to the standard model (SM) expectation, is measured to be $\mu =0.94\pm 0.07{\text{(stat)}}_{-0.08}^{+0.09}\text{(syst)}$ at a fixed value of $m_H=125.38\text{GeV}$ . The signal strength modifiers for the individual Higgs boson production modes are also reported. The inclusive fiducial cross section for the $H\to 4\ell$ process is measured to be $2.{84}_{-0.22}^{+0.23}{\text{(stat)}}_{-0.21}^{+0.26}\text{(syst)}\text{fb}$ , which is compatible with the SM prediction of $2.84\pm 0.15\text{fb}$ for the same fiducial region. Differential cross sections as a function of the transverse momentum and rapidity of the Higgs boson, the number of associated jets, and the transverse momentum of the leading associated jet are measured. A new set of cross section measurements in mutually exclusive categories targeted to identify production mechanisms and kinematical features of the events is presented. The results are in agreement with the SM predictions.

Fig. 1

Binning of the gluon fusion production process, the electroweak production process (combines $\mathrm{VBF}$ and ${\mathrm{V}}_{}^{}\mathrm{H}$ with hadronic ${\mathrm{V}}_{}^{}$ decay), the ${\mathrm{V}}_{}^{}\mathrm{H}$ production process with leptonic ${\mathrm{V}}_{}^{}$ decay (combining $\mathrm{W}\mathrm{H}$, $\mathrm{Z}\mathrm{H}$, and gluon fusion $\mathrm{Z}\mathrm{H}$ production), and the ${\mathrm{t}}_{}^{}{\overline{{\mathrm{t}}_{}^{}}}_{}^{}\mathrm{H}$ production process in the merged stage 1.2 of the STXS framework used in the $\mathrm{H}\to \mathrm{Z}\mathrm{Z}\to 4\ell$ analysis

Fig. 2

The shape of the parametric signal model for each year of simulated data, and for the sum of all years together. The black points represent weighted simulation events of the $\mathrm{g}\mathrm{g}\mathrm{H}$ production mechanism for $m_{\mathrm{H}}=125\text{GeV}$ and the blue line the corresponding model. Also shown is the ${\sigma }_{\text{CB}}$ value (half the width of the narrowest interval containing 68% of the invariant mass distribution) in the gray shaded area. The contribution of the signal model from each year of data-taking is illustrated with the dotted lines. The models are shown for the $4\mathrm{e}$ (upper) and $4{\mathrm{\mu }}_{}^{}$ (lower) final states in the untagged event category

Fig. 3

The impact of the dominant systematic uncertainties (in percent) on the inclusive signal strength $\mu$ and stage 0 production mode cross section described in Sect. 10. Impacts from different NPs are combined assuming no correlation. Only dominant experimental sources are presented: integrated luminosity uncertainty (Lumi.), lepton reconstruction and selection efficiency, scale and resolution (Leptons), jet energy scale and resolution (Jet), ${\mathrm{b}}_{}^{}$-tagging efficiency (B-tag), and reducible background estimation uncertainty (Red. bkg). Only dominant theoretical sources are presented: $\mathrm{g}\mathrm{g}\mathrm{H}$, $\mathrm{VBF}$, and ${\mathrm{V}}_{}^{}\mathrm{H}$ cross section theoretical uncertainty scheme (THU), renormalization and factorization scale (QCD), choice of the PDF set (PDF), the branching fraction of $\mathrm{H}\to 4\ell$ ($\mathcal{B}$), modeling of hadronization and the underlying event (Hadr), and background modeling (Bkg. mod.). The THU uncertainty is not considered in the stage 0 cross section measurements. The uncertainties are rounded to the nearest 0.5%

Fig. 4

Four-lepton mass distribution, $m_{4\ell }$, up to $500\text{GeV}$ with $4\text{GeV}$ bin size (upper) and in the low-mass range with $2\text{GeV}$ bin size (lower). Points with error bars represent the data and stacked histograms represent the expected distributions for the signal and background processes. The SM Higgs boson signal with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, the $\mathrm{Z}\mathrm{Z}$ and rare electroweak backgrounds are normalized to the SM expectation, the $\mathrm{Z}$+X background to the estimation from data

Fig. 5

Four-lepton mass distribution in three final states: $4\mathrm{e}$ upper), $4{\mathrm{\mu }}_{}^{}$ (center), and $2\mathrm{e}2{\mathrm{\mu }}_{}^{}$ (lower). Points with error bars represent the data and stacked histograms represent the expected distributions for the signal and background processes. The SM Higgs boson signal with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, the $\mathrm{Z}\mathrm{Z}$ and rare electroweak backgrounds are normalized to the SM expectation, the $\mathrm{Z}$+X background to the estimation from data

Fig. 6

Distributions of the expected and observed number of events for the reconstructed event categories in the mass region $105<m_{4\ell }<140\text{GeV}$. Points with error bars represent the data and stacked histograms represent the expected numbers of the signal and background events. The yields of the different H boson production mechanisms with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, and those of the $\mathrm{Z}\mathrm{Z}$ and rare electroweak backgrounds are normalized to the SM expectations, while the $\mathrm{Z}$+X background yield is normalized to the estimate from the data

Fig. 7

Distribution of the ${\mathrm{Z}}_1$ (upper left) and ${\mathrm{Z}}_2$ (upper right) reconstructed masses in the $118<m_{4\ell }<130\text{GeV}$ mass region and their 2D distribution (lower) in the $105<m_{4\ell }<140\text{GeV}$ mass region. The stacked histograms and the red and blue scales represent expected distributions of the signal and background processes and the points represent the data. The yields of the different H boson production mechanisms with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, and those of the $\mathrm{Z}\mathrm{Z}$ and rare electroweak backgrounds are normalized to the SM expectations, while the $\mathrm{Z}$+X background yield is normalized to the estimate from the data

Fig. 8

Distribution of categorization discriminants in the mass region $118<m_{4\ell }<130\text{GeV}$: ${\mathcal{D}}_{\text{2jet}}^{\mathrm{VBF}}$ (upper), ${\mathcal{D}}_{\text{1jet}}^{\mathrm{VBF}}$ (center), ${\mathcal{D}}_{\text{2jet}}^{{\mathrm{V}}_{}^{}\mathrm{H}}$ (lower) = max(${\mathcal{D}}_{\text{2jet}}^{\mathrm{W}\mathrm{H}}$,${\mathcal{D}}_{\text{2jet}}^{\mathrm{Z}\mathrm{H}}$). Points with error bars represent the data and stacked histograms represent expected distributions of the signal and background processes. The SM Higgs boson signal with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, and the $\mathrm{Z}\mathrm{Z}$ backgrounds and rare electroweak backgrounds are normalized to the SM expectation, the $\mathrm{Z}$+X background to the estimation from data. The vertical dashed lines denote the working points used in the event categorization. The SM H boson signal is separated into two components: the production mode which is targeted by the specific discriminant, and other production modes, where the gluon fusion process dominates.

Fig. 9

Distribution of three different kinematic discriminants versus $m_{4\ell }$: ${\mathcal{D}}_{\text{bkg}}^{\text{kin}}$ (upper), ${\mathcal{D}}_{\text{bkg}}^{\mathrm{VBF}+\text{dec}}$ (middle) and ${\mathcal{D}}_{\text{bkg}}^{{\mathrm{V}}_{}^{}\mathrm{H}+\text{dec}}$ (lower) shown in the mass region $105<m_{4\ell }<140\text{GeV}$. The blue scale represents the expected total number of $\mathrm{Z}\mathrm{Z}$, rare electroweak, and $\mathrm{Z}$+X background events. The red scale represents the number of expected SM H boson signal events for $m_{\mathrm{H}}=125\text{GeV}$. The points show the data from the categories listed in the legend

Fig. 10

Distribution of kinematic discriminants in the mass region $118<m_{4\ell }<130\text{GeV}$: (uppper) ${\mathcal{D}}_{\text{bkg}}^{\text{kin}}$ , (center) ${\mathcal{D}}_{\text{bkg}}^{\mathrm{VBF}+\text{dec}}$, (lower) ${\mathcal{D}}_{\text{bkg}}^{{\mathrm{V}}_{}^{}\mathrm{H}+\text{dec}}$. Points with error bars represent the data and stacked histograms represent expected distributions of the signal and background processes. The yields of the different H boson production mechanisms with $m_{\mathrm{H}}=125\text{GeV}$, denoted as $\mathrm{H}(125)$, and those of the $\mathrm{Z}\mathrm{Z}$ and rare electroweak backgrounds are normalized to the SM expectations, while the $\mathrm{Z}$+X background yield is normalized to the estimate from the data. In the center and lower figures the SM H boson signal is separated into two components: the production mode which is targeted by the specific discriminant, and other production modes, where the gluon fusion process dominates

Fig. 11

(Upper) The observed and expected profile likelihood scans of the inclusive signal strength modifier. The scans are shown both with (solid line) and without (dashed line) systematic uncertainties. (Lower) Results of likelihood scans for the signal strength modifiers corresponding to the five main SM H boson production mechanisms, compared to the SM prediction shown as a vertical dashed line. The thick black lines indicate the one standard deviation confidence intervals including both statistical and systematic sources. The thick red lines indicate the statistical uncertainties corresponding to the one standard deviation confidence intervals

Fig. 12

Result of the 2D likelihood scan for the ${\mu }_{\mathrm{f}}\equiv {\mu }_{\mathrm{g}\mathrm{g}\mathrm{H},{\mathrm{t}}_{}^{}{\overline{{\mathrm{t}}_{}^{}}}_{}^{}\mathrm{H},{\mathrm{b}}_{}^{}{\overline{{\mathrm{b}}_{}^{}}}_{}^{}\mathrm{H},{\mathrm{t}}_{}^{}\mathrm{H}}$ and ${\mu }_{{\mathrm{V}}_{}^{}}\equiv {\mu }_{\mathrm{VBF},{\mathrm{V}}_{}^{}\mathrm{H}}$ signal strength modifiers. The solid and dashed contours show the 68 and 95% $\text{CL}$ regions, respectively. The cross indicates the best fit value, and the diamond represents the expected value for the SM Higgs boson

Fig. 13

The measured product of cross section times branching fraction for $\mathrm{H}\to \mathrm{Z}\mathrm{Z}$ decay ${(\sigma \mathcal{B})}_{\text{obs}}$ and the SM predictions ${(\sigma \mathcal{B})}_{\mathrm{SM}}$ for the stage 0 STXS production bins and the inclusive measurement at $m_{\mathrm{H}}=125.38\text{GeV}$. Points with error bars represent measured values and black dashed lines with gray uncertainty bands represent the SM predictions. In the bottom panel ratios of the measured cross sections and the SM predictions are shown along with the uncertainties for each of the bins and the inclusive measurement

Fig. 14

The measured cross sections ${(\sigma \mathcal{B})}_{\text{obs}}$ and the SM predictions ${(\sigma \mathcal{B})}_{\mathrm{SM}}$ for $\mathrm{H}\to \mathrm{Z}\mathrm{Z}$ decay and the merged stage 1.2 STXS production bins at $m_{\mathrm{H}}=125.38\text{GeV}$. Points with error bars represent measured values and black dashed lines with gray uncertainty bands represent the SM predictions. In the bottom panel ratios of the measured cross sections and the SM predictions are shown with corresponding uncertainties for each of the bins

Fig. 15

Correlation matrices between the measured cross sections for the stage 0 (upper) and the merged stage 1.2 (lower) for $\mathrm{H}\to \mathrm{Z}\mathrm{Z}$ decay

Fig. 16

The measured inclusive fiducial cross section in different final states (upper) and integrated as a function of $\sqrt{s}$ (lower). The acceptance is calculated using powheg at $\sqrt{s}=13\text{TeV}$ and HRes [107, 109] at $\sqrt{s}=$ 7 and 8$\text{TeV}$, and the total gluon fusion cross section and uncertainty are taken from Ref. [58]. The fiducial volume for $\sqrt{s}=6$–$9\text{TeV}$ uses the lepton isolation definition from Ref. [25] and the SM predictions and measurements are calculated at $m_{\mathrm{H}}=125.0\text{GeV}$, while for $\sqrt{s}=12$–$14\text{TeV}$ the definition described in the text is used and SM predictions and measurements are calculated at $m_{\mathrm{H}}=125.38\text{GeV}$

Fig. 17

Differential cross sections as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper) and $|y^{\mathrm{H}}|$ (lower). The acceptance and theoretical uncertainties in the differential bins are calculated using powheg. The sub-dominant component of the signal ($\mathrm{VBF}+{\mathrm{V}}_{}^{}\mathrm{H}+{\mathrm{t}}_{}^{}{\overline{{\mathrm{t}}_{}^{}}}_{}^{}\mathrm{H}$) is denoted as XH

Fig. 18

Differential cross sections as a function of the number of associated jets (upper), and $p_{\mathrm{T}}$ of the leading jet (lower). The acceptance and theoretical uncertainties in the differential bins are calculated using powheg. The sub-dominant component of the signal ($\mathrm{VBF}+{\mathrm{V}}_{}^{}\mathrm{H}+{\mathrm{t}}_{}^{}{\overline{{\mathrm{t}}_{}^{}}}_{}^{}\mathrm{H}$) is denoted as XH