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| CMS-EXO-16-010 ; CERN-EP-2016-309 | ||
| Search for dark matter and unparticles in events with a Z boson and missing transverse momentum in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 8 January 2017 | ||
| JHEP 03 (2017) 061 [Erratum] | ||
| Abstract: A search for dark matter and unparticle production at the LHC has been performed using events containing two charged leptons (electrons or muons), consistent with the decay of a Z boson, and large missing transverse momentum. This study is based on data collected with the CMS detector in 2015, corresponding to an integrated luminosity of 2.3 fb$^{-1}$ of proton-proton collisions at the LHC, at a center-of-mass energy of 13 TeV. No excess over the standard model expectation is observed. Compared to previous searches in this topology, which exclusively relied on effective field theories, the results are interpreted in terms of a simplified model of dark matter production for both vector and axial vector couplings between a mediator and dark matter particles. The first study of this class of models using CMS data at $\sqrt{s}=$ 13 TeV is presented. Additionally, effective field theories of dark matter and unparticle production are used to interpret the data. | ||
| Links: e-print arXiv:1701.02042 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Leading order Feynman diagrams for production of DM pairs ($\chi \overline {\chi }$) in association with a Z boson. Left: the simplified model containing a spin-1 mediator A. The constant $g_\mathrm{ q } $ ($g_\chi $) is the coupling strength between A and quarks (DM). |
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Figure 1-a:
Leading order Feynman diagram for production of DM pairs ($\chi \overline {\chi }$) in association with a Z boson: the simplified model containing a spin-1 mediator A. The constant $g_\mathrm{ q } $ ($g_\chi $) is the coupling strength between A and quarks (DM). |
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Figure 1-b:
Leading order Feynman diagram for production of DM pairs ($\chi \overline {\chi }$) in association with a Z boson: an EFT benchmark with a DM pair coupling to gauge bosons via dimension-7 operators. |
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Figure 2:
Leading order Feynman diagram for unparticle (denoted by U) production in association with a Z boson. The hatched circle indicates the interaction modeled with an EFT operator. |
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Figure 3:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for the simplified DM model with vector mediator (upper left), EFT DM model (upper right), and unparticle scenarios (lower panel). The y-axis corresponds to the integrated cross section per bin divided by the total cross section and bin width. The DM curves are shown for different values of the vector mediator mass $M_\text {med}$ in the upper left panel and for different values of the DM mass $m_\chi $ in the upper right panel. The unparticle curves have the scalar unparticle coupling $\lambda $ between unparticle and SM fields set to 1. They are shown for several values of the scaling dimension $d_{\textsf {U}}$ ranging from 1.06 to 2.20, spanning the region of sensitivity of this analysis. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid histogram. The rightmost bins include overflow. |
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Figure 3-a:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for the simplified DM model with vector mediator. The y-axis corresponds to the integrated cross section per bin divided by the total cross section and bin width. The DM curves are shown for different values of the vector mediator mass $M_\text {med}$. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid histogram. The rightmost bins include overflow. |
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Figure 3-b:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for the EFT DM model. The y-axis corresponds to the integrated cross section per bin divided by the total cross section and bin width. The DM curves are shown for different values of the DM mass $m_\chi $. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid histogram. The rightmost bins include overflow. |
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Figure 3-c:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for the unparticle scenario. The y-axis corresponds to the integrated cross section per bin divided by the total cross section and bin width. The unparticle curves have the scalar unparticle coupling $\lambda $ between unparticle and SM fields set to 1. They are shown for several values of the scaling dimension $d_{\textsf {U}}$ ranging from 1.06 to 2.20, spanning the region of sensitivity of this analysis. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid histogram. The rightmost bins include overflow. |
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Figure 4:
The distribution of $ {E_{\mathrm {T}}^{\text {miss}}} $ after preselection for the $ {\mathrm{ Z } } \to \mathrm{ e }^{+} \mathrm{ e }^{-} $ (left) and $ {\mathrm{ Z } } \to \mu^+ \mu^- $ (right) channels. Representative expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT scenario of DM production, and unparticles. The SM expectation is based on simulation only. The total statistical uncertainty in the overall background prediction is shown as a hatched region. Overflow events are included in the rightmost bins. The upper error bars on data points are shown for bins with zero entries (Garwood procedure) in the region up to the last non-zero entry. In the lower panels, the ratio between data and predicted background is shown. |
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Figure 4-a:
The distribution of $ {E_{\mathrm {T}}^{\text {miss}}} $ after preselection for the $ {\mathrm{ Z } } \to \mathrm{ e }^{+} \mathrm{ e }^{-} $ channel. Representative expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT scenario of DM production, and unparticles. The SM expectation is based on simulation only. The total statistical uncertainty in the overall background prediction is shown as a hatched region. Overflow events are included in the rightmost bin. The upper error bars on data points are shown for bins with zero entries (Garwood procedure) in the region up to the last non-zero entry. In the lower panel, the ratio between data and predicted background is shown. |
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Figure 4-b:
The distribution of $ {E_{\mathrm {T}}^{\text {miss}}} $ after preselection for the $ {\mathrm{ Z } } \to \mu^+ \mu^- $ channel. Representative expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT scenario of DM production, and unparticles. The SM expectation is based on simulation only. The total statistical uncertainty in the overall background prediction is shown as a hatched region. Overflow events are included in the rightmost bin. The upper error bars on data points are shown for bins with zero entries (Garwood procedure) in the region up to the last non-zero entry. In the lower panel, the ratio between data and predicted background is shown. |
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Figure 5:
Distributions of $ {E_{\mathrm {T}}^{\text {miss}}} $ for the final selection in the $\mathrm{ e }^{+} \mathrm{ e }^{-} $ (left) and $\mu^+ \mu^- $ (right) channels. Expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT DM production benchmark, and unparticle model. The total uncertainty (stat.$\oplus $sys.) in the overall background is shown as a hatched region. Overflow events are included in the rightmost bins. In the lower panels, the ratio between data and predicted background is shown. |
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Figure 5-a:
Distributions of $ {E_{\mathrm {T}}^{\text {miss}}} $ for the final selection in the $\mathrm{ e }^{+} \mathrm{ e }^{-} $ channel. Expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT DM production benchmark, and unparticle model. The total uncertainty (stat.$\oplus $sys.) in the overall background is shown as a hatched region. Overflow events are included in the rightmost bin. In the lower panel, the ratio between data and predicted background is shown. |
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Figure 5-b:
Distributions of $ {E_{\mathrm {T}}^{\text {miss}}} $ for the final selection in the $\mu^+ \mu^- $ channel. Expected signal distributions are shown for the simplified model of DM production with vector couplings, the EFT DM production benchmark, and unparticle model. The total uncertainty (stat.$\oplus $sys.) in the overall background is shown as a hatched region. Overflow events are included in the rightmost bin. In the lower panel, the ratio between data and predicted background is shown. |
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Figure 6:
The 95%CL observed limits on the signal strength $\sigma _\text {obs}/\sigma _{\rm theo}$ in both vector (left) and axial-vector (right) mediator scenarios, for mediator-quark coupling constant values $g_{\mathrm{ q } } = $ 0.25 (upper) and 1 (lower). In all cases, the DM-mediator coupling $g_{\chi }$ is set to one. The expected exclusion curves for unity signal strength are shown as a reference, with black dashed lines indicating the expected $\pm$1 s.d. interval due to experimental uncertainties. The red dashed lines show the influence of theory-related signal normalization uncertainties on the observed limits, which are estimated to be 15%. The solid line labeled ``$\Omega _c\times h^2 = $ 0.12" identifies the parameter region where no additional new physics beyond the simplified model is necessary to reproduce the observed DM relic abundance in the universe [34,74,73,1,72]. |
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Figure 6-a:
The 95%CL observed limits on the signal strength $\sigma _\text {obs}/\sigma _{\rm theo}$ in the vector mediator scenario, for mediator-quark coupling constant values $g_{\mathrm{ q } } = $ 0.25. The DM-mediator coupling $g_{\chi }$ is set to one. The expected exclusion curves for unity signal strength are shown as a reference, with black dashed lines indicating the expected $\pm$1 s.d. interval due to experimental uncertainties. The red dashed lines show the influence of theory-related signal normalization uncertainties on the observed limits, which are estimated to be 15%. The solid line labeled ``$\Omega _c\times h^2 = $ 0.12" identifies the parameter region where no additional new physics beyond the simplified model is necessary to reproduce the observed DM relic abundance in the universe [34,74,73,1,72]. |
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Figure 6-b:
The 95%CL observed limits on the signal strength $\sigma _\text {obs}/\sigma _{\rm theo}$ in the axial-vector mediator scenario, for mediator-quark coupling constant values $g_{\mathrm{ q } } = $ 0.25. The DM-mediator coupling $g_{\chi }$ is set to one. The expected exclusion curves for unity signal strength are shown as a reference, with black dashed lines indicating the expected $\pm$1 s.d. interval due to experimental uncertainties. The red dashed lines show the influence of theory-related signal normalization uncertainties on the observed limits, which are estimated to be 15%. The solid line labeled ``$\Omega _c\times h^2 = $ 0.12" identifies the parameter region where no additional new physics beyond the simplified model is necessary to reproduce the observed DM relic abundance in the universe [34,74,73,1,72]. |
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Figure 6-c:
The 95%CL observed limits on the signal strength $\sigma _\text {obs}/\sigma _{\rm theo}$ in the vector mediator scenario, for mediator-quark coupling constant values $g_{\mathrm{ q } } = $ 1. The DM-mediator coupling $g_{\chi }$ is set to one. The expected exclusion curves for unity signal strength are shown as a reference, with black dashed lines indicating the expected $\pm$1 s.d. interval due to experimental uncertainties. The red dashed lines show the influence of theory-related signal normalization uncertainties on the observed limits, which are estimated to be 15%. The solid line labeled ``$\Omega _c\times h^2 = $ 0.12" identifies the parameter region where no additional new physics beyond the simplified model is necessary to reproduce the observed DM relic abundance in the universe [34,74,73,1,72]. |
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Figure 6-d:
The 95%CL observed limits on the signal strength $\sigma _\text {obs}/\sigma _{\rm theo}$ in the axial-vector mediator scenario, for mediator-quark coupling constant values $g_{\mathrm{ q } } = $ 1. The DM-mediator coupling $g_{\chi }$ is set to one. The expected exclusion curves for unity signal strength are shown as a reference, with black dashed lines indicating the expected $\pm$1 s.d. interval due to experimental uncertainties. The red dashed lines show the influence of theory-related signal normalization uncertainties on the observed limits, which are estimated to be 15%. The solid line labeled ``$\Omega _c\times h^2 = $ 0.12" identifies the parameter region where no additional new physics beyond the simplified model is necessary to reproduce the observed DM relic abundance in the universe [34,74,73,1,72]. |
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Figure 7:
Observed 90% CL limits on the DM-nucleon scattering cross sections in both spin-independent (left) and spin-dependent (right) cases, assuming a mediator-quark coupling constant $g_{\mathrm{ q } } = $ 0.25 and mediator-DM coupling constant $g_{\chi } = $ 1. The line shading indicates the excluded region. Limits from the LUX [75], CDMSLite [76], PandaX-II [77], and CRESST-II [78] experiments are shown for the spin-independent case. Limits from the Super-Kamiokande [79], PICO-2L [80], PICO-60 [81], and IceCube [82] experiments are shown for the spin-dependent case. |
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Figure 7-a:
Observed 90% CL limits on the DM-nucleon scattering cross sections in the spin-independent case, assuming a mediator-quark coupling constant $g_{\mathrm{ q } } = $ 0.25 and mediator-DM coupling constant $g_{\chi } = $ 1. The line shading indicates the excluded region. Limits from the LUX [75], CDMSLite [76], PandaX-II [77], and CRESST-II [78] experiments are shown for the spin-independent case. Limits from the Super-Kamiokande [79], PICO-2L [80], PICO-60 [81], and IceCube [82] experiments are shown for the spin-dependent case. |
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Figure 7-b:
Observed 90% CL limits on the DM-nucleon scattering cross sections in the spin-dependent case, assuming a mediator-quark coupling constant $g_{\mathrm{ q } } = $ 0.25 and mediator-DM coupling constant $g_{\chi } = $ 1. The line shading indicates the excluded region. Limits from the LUX [75], CDMSLite [76], PandaX-II [77], and CRESST-II [78] experiments are shown for the spin-independent case. Limits from the Super-Kamiokande [79], PICO-2L [80], PICO-60 [81], and IceCube [82] experiments are shown for the spin-dependent case. |
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Figure 8:
The 95%CL expected and observed limits on the cutoff scale $\Lambda $ of the EFT benchmark of DM production as a function of DM particle mass $m_\chi $. |
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Figure 9:
The 95%CL observed limits on the cutoff scale $\Lambda $ (left) and signal strength $\sigma ^\text {obs}/\sigma ^\text {th}$ (right) as a function of coupling $c_1$ and DM mass $m_\chi $. The expected exclusion curves for unit signal strength are shown as a reference. The gray shaded area bounded by gray dashed lines indicates the expected $\pm$1 s.d. interval due to experimental uncertainties. |
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Figure 9-a:
The 95%CL observed limits on the cutoff scale $\Lambda $ as a function of coupling $c_1$ and DM mass $m_\chi $. The expected exclusion curves for unit signal strength are shown as a reference. The gray shaded area bounded by gray dashed lines indicates the expected $\pm$1 s.d. interval due to experimental uncertainties. |
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Figure 9-b:
The 95%CL observed limits on the signal strength $\sigma ^\text {obs}/\sigma ^\text {th}$ as a function of coupling $c_1$ and DM mass $m_\chi $. The expected exclusion curves for unit signal strength are shown as a reference. The gray shaded area bounded by gray dashed lines indicates the expected $\pm$1 s.d. interval due to experimental uncertainties. |
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Figure 10:
The 95% CL lower limits on the effective unparticle cutoff scale $\Lambda_{\textsf {U}}$ for a fixed coupling $\lambda =1$. The results from the CMS monojet [15] and mono-Z [17] searches, as well as a reinterpretation of LEP and CDF searches [83] are shown for comparison. The LEP results assume a coupling of unparticles to Z bosons and photons. The CDF (CMS) monojet result is based on a gluon-unparticle coupling operator (gluon- and quark-unparticle coupling operators). The inset compares the expected and observed limits for the CMS mono-Z analyses at $\sqrt {s}=$ 8 and 13 TeV. Note that the cutoff scales $\Lambda_{\textsf {U}}$ for different operators do not have to be identical. Consequently, the comparison shown here with the results other than the CMS 8 TeV mono-Z analysis is only qualitative. |
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Figure 11:
The model-independent upper limits at 95% CL on the visible cross section ($\sigma A \epsilon $) for BSM production of events, as a function of $ {E_{\mathrm {T}}^{\text {miss}}} $ threshold. The values plotted correspond to those given in Table 4. |
| Tables | |
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Table 1:
Summary of selections used in the analysis. |
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Table 2:
Summary of systematic uncertainties. Each background uncertainty represents the variation of the relative yields of the particular background components. The signal uncertainties represent the relative variations in the signal acceptance, and the ranges quoted cover both signals of DM and unparticles with different DM masses or scaling dimensions. For shape uncertainties, the numbers correspond to the overall effect of the shape variation on the yield or acceptance. The symbol `` -- '' indicates that the systematic uncertainty is not applicable. The impact of each group of systematic uncertainties is calculated by performing a maximum likelihood fit to obtain the signal strength with each parameter separately varied by its uncertainty. The number given in the impact column is the relative change of the expected best fit signal strength that is introduced by the variation for the simplified model signal scenario with a vector mediator of mass 200 GeV, DM of mass 50 GeV, and coupling $g_{\mathrm{ q } }=$ 1.0. |
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Table 3:
Signal predictions and background estimates for the final selection with $ {E_{\mathrm {T}}^{\text {miss}}} > $ 80 GeV. The DM signal yields from the simplified model are given for mass $m_\chi = $ 50 GeV and a mediator mass $M_\text {med} = $ 200 GeV for both the vector and axial-vector coupling scenarios. For the EFT benchmark with DM pair coupling to gauge bosons, the signal yields are given for $m_\chi = $ 1 GeV, cutoff scale $\Lambda = $ 300 GeV, and the coupling $c_1= $ 1. Yields for the unparticle model are shown for scaling dimension $d_\mathsf {U}= $ 1.05, and cutoff scale $\Lambda = $ 15 TeV. The corresponding statistical and systematic uncertainties are shown, in that order. |
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Table 4:
Total SM background predictions for the numbers of events passing the selection requirements, for different $ {E_{\mathrm {T}}^{\text {miss}}} $ thresholds, compared with the observed numbers of events. The listed uncertainties include both statistical and systematic components. The 95% CL observed and expected upper limits for the contribution of events from BSM sources are also shown. In addition, the ${\pm }$1 s.d. and ${\pm }$2 s.d. excursions from expected limits are given. |
| Summary |
| A search for physics beyond the standard model has been performed in events with a Z boson and missing transverse momentum, using a data set corresponding to an integrated luminosity of 2.3 fb$^{-1}$ of pp collisions at a center-of-mass energy of 13 TeV. The observed data are consistent with the expected standard model processes. The results are analyzed to obtain limits in three different scenarios of physics beyond the standard model. In a simplified model of DM production via a vector or axial vector mediator, 95% confidence level limits are obtained on the masses of the DM particles and the mediator. Limits on the DM-nucleon scattering cross section are set at 90% confidence level in spin-dependent and spin-independent coupling scenarios. In an effective field theory approach, limits are set on the DM coupling parameters to $U(1)$ and $SU(2)$ gauge fields and on the scale of new physics. For an unparticle model, 95% confidence level limits are obtained on the effective cutoff scale as a function of the scaling dimension. In addition, model-independent limits on the contribution to the visible Z+$E_{\mathrm{T}}^{\text{miss}}$ cross section from non-standard-model sources are presented as a function of the minimum requirement on $E_{\mathrm{T}}^{\text{miss}}$. These results are the first in this signal topology to be interpreted in terms of a simplified model. Furthermore, the limits on unparticle production are the first of their kind to be presented at $ \sqrt{s} = $ 13 TeV. |
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