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CMS-PAS-SUS-23-012
Search for dark matter produced in association with a Higgs boson decaying to a $ \tau $ lepton pair at $ \sqrt{s}= $ 13 TeV
Abstract: A search for dark matter particles produced in association with a Higgs boson decaying into a pair of $ \tau $ leptons is performed using data collected in proton-proton collisions with the CMS detector at a center-of-mass energy of 13 TeV. The analysis is based on a data set corresponding to an integrated luminosity of 101 fb$ ^{-1} $ collected in 2017--2018 with the CMS detector. No significant excess over the expected standard model background is observed. This result is interpreted within the framework of two benchmark simplified models: the baryonic-Z' and 2HDM+a models. Upper limits at the 95% confidence level are set on the product of the production cross section and branching fraction in the two simplified models. For the baryonic-Z' model, a statistical combination is made with an earlier search based on a data set of 36 fb$ ^{-1} $ collected in 2016. In this model, Z' masses up to 1050 GeV are excluded for a dark matter particle mass of 1 GeV. In the 2HDM+a model, heavy pseudoscalar masses between 400 and 700 GeV are excluded for a light pseudoscalar mass of 100 GeV.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Representative Feynman diagrams for leading order (LO) DM associated production with a Higgs boson in the 2HDM+a (left) and baryonic-Z' (right) models.

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Figure 1-a:
Representative Feynman diagrams for leading order (LO) DM associated production with a Higgs boson in the 2HDM+a (left) and baryonic-Z' (right) models.

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Figure 1-b:
Representative Feynman diagrams for leading order (LO) DM associated production with a Higgs boson in the 2HDM+a (left) and baryonic-Z' (right) models.

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Figure 2:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-a:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-b:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-c:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-d:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-e:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 2-f:
Distributions of the total transverse mass $ M_\mathrm{T}^{\text{tot}} $ in the SR, comparing observed data with the SM prediction in the $ \mathrm{e}\tau_{\mathrm{h}} $ (upper), $ \mu\tau_{\mathrm{h}} $ (center), and $ \tau_{\mathrm{h}}\!\tau_{\mathrm{h}} $ (lower) final states in 2017 (left) and 2018 (right) after the simultaneous maximum likelihood fit. Representative signal distributions are shown for the 2HDM+a (dashed red curve) and baryonic-Z' (dashed black curve) models. The data points are shown with their statistical uncertainties, and the last bin includes overflow. The ``Other MC'' background contribution includes events from ggh, ggZ, VBF, Wh, Zh, and electroweak vector boson production. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.

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Figure 3:
Upper left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{a}} $ scan using $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Upper right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{A}} $ using $ m_{\mathrm{a}} $ = 150 GeV, $ \sin\theta $ = 0.35, and $ \tan\beta $ = 1. Lower left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \sin\theta $ using $ m_{\mathrm{a}} $ = 200 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Lower right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \tan\beta $ using $ m_{\mathrm{a}} $ = 150 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \sin\theta $ = 0.35, and $ m_{\chi} $ = 10 GeV. The interpolation between the points in the 1-d scan is linear.

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Figure 3-a:
Upper left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{a}} $ scan using $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Upper right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{A}} $ using $ m_{\mathrm{a}} $ = 150 GeV, $ \sin\theta $ = 0.35, and $ \tan\beta $ = 1. Lower left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \sin\theta $ using $ m_{\mathrm{a}} $ = 200 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Lower right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \tan\beta $ using $ m_{\mathrm{a}} $ = 150 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \sin\theta $ = 0.35, and $ m_{\chi} $ = 10 GeV. The interpolation between the points in the 1-d scan is linear.

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Figure 3-b:
Upper left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{a}} $ scan using $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Upper right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{A}} $ using $ m_{\mathrm{a}} $ = 150 GeV, $ \sin\theta $ = 0.35, and $ \tan\beta $ = 1. Lower left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \sin\theta $ using $ m_{\mathrm{a}} $ = 200 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Lower right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \tan\beta $ using $ m_{\mathrm{a}} $ = 150 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \sin\theta $ = 0.35, and $ m_{\chi} $ = 10 GeV. The interpolation between the points in the 1-d scan is linear.

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Figure 3-c:
Upper left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{a}} $ scan using $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Upper right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{A}} $ using $ m_{\mathrm{a}} $ = 150 GeV, $ \sin\theta $ = 0.35, and $ \tan\beta $ = 1. Lower left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \sin\theta $ using $ m_{\mathrm{a}} $ = 200 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Lower right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \tan\beta $ using $ m_{\mathrm{a}} $ = 150 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \sin\theta $ = 0.35, and $ m_{\chi} $ = 10 GeV. The interpolation between the points in the 1-d scan is linear.

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Figure 3-d:
Upper left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{a}} $ scan using $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Upper right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{A}} $ using $ m_{\mathrm{a}} $ = 150 GeV, $ \sin\theta $ = 0.35, and $ \tan\beta $ = 1. Lower left: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \sin\theta $ using $ m_{\mathrm{a}} $ = 200 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \tan\beta $ = 1, and $ m_{\chi} $ = 10 GeV. Lower right: 95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ \tan\beta $ using $ m_{\mathrm{a}} $ = 150 GeV, $ m_{\mathrm{A}} $ = 600 GeV, $ \sin\theta $ = 0.35, and $ m_{\chi} $ = 10 GeV. The interpolation between the points in the 1-d scan is linear.

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Figure 4:
95% CL upper limit on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ in the $ m_{\mathrm{a}} $--$ m_{\mathrm{A}} $ plane. The regions inside the red and black curves correspond to the observed and expected exclusions at 95% CL, respectively.

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Figure 5:
Observed and expected 95% CL upper limits on the signal strength modifier $ \mu=\sigma/\sigma_{theory} $ as a function of $ m_{\mathrm{Z}^{'}} $, using $ m_{\chi} $ = 1 GeV.
Tables

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Table 1:
Target $ \tau_\mathrm{h} $ identification efficiencies for the different working points defined for the three different discriminators [30] that are used in the analysis. These identification efficiencies are evaluated for the genuine $ \tau_\mathrm{h} $ with the $ \mathrm{H}\to\tau\tau $ event sample for $ \tau_\mathrm{h} $ with $ p_{\mathrm{T}} \in $[30, 70] GeV.

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Table 2:
Offline selection requirement applied to e, $ \mu $ and $ \tau_\mathrm{h} $ candidates used for the selection of $ \tau $ pairs. The expressions first and second lepton refer to the label of the final state in the first column for both years. The $ p_{\mathrm{T}} $ requirements are given in GeV.

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Table 3:
Sources of systematic uncertainties.
Summary
A search for dark matter produced in association with a Higgs boson decaying to a pair of $ \tau $ leptons has been performed. A data set of proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 101 fb$ ^{-1} $ is analyzed, and for the baryonic-Z' model, the analysis results are combined with those of an earlier search using an independent data set collected at the same center-of-mass energy, corresponding to an integrated luminosity of 36 fb$ ^{-1} $ [5]. The data are found to be in good agreement with the fit results, with no evidence for a significant signal contribution. This result is interpreted within the framework of two benchmark simplified models: the baryonic-Z' model, where a high mass resonance (Z') decays into a dark matter particle $ \chi $ and a standard model Higgs boson h, and the 2HDM+a model, where a heavy pseudoscalar couples to a Higgs boson and a ligher pseudoscalar decaying to dark matter particles. Upper limits at the 95% confidence level are set on the product of the production cross section and branching fraction for the baryonic-Z' and 2HDM+a models. For the baryonic-Z' model,Z' masses up to 1050 GeV are excluded for a dark matter particle mass of 1 GeV using 137 fb$ ^{-1} $ of proton-proton data. In the 2HDM+a model, heavy pseudoscalar masses between 400 and 700 GeV are excluded for 101 fb$ ^{-1} $ of proton-proton data for a light pseudoscalar mass around 100 GeV.
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Compact Muon Solenoid
LHC, CERN