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| CMS-EXO-12-054 ; CERN-PH-EP-2015-297 | ||
| Search for dark matter and unparticles produced in association with a Z boson in proton-proton collisions at $ \sqrt{s} = $ 8 TeV | ||
| CMS Collaboration | ||
| 30 November 2015 | ||
| Phys. Rev. D 93 (2016) 052011 [Erratum] | ||
| Abstract: A search for evidence of particle dark matter (DM) and unparticle production at the LHC has been performed using events containing two charged leptons, consistent with the decay of a Z boson, and large missing transverse momentum. This study is based on data collected with the CMS detector corresponding to an integrated luminosity of 19.7 fb$^{-1}$ of pp collisions at the LHC at a center-of-mass energy of 8 TeV. No significant excess of events is observed above the number expected from the standard model contributions. The results are interpreted in terms of 90% confidence level limits on the DM-nucleon scattering cross section, as a function of the DM particle mass, for both spin-dependent and spin-independent scenarios. Limits are set on the effective cutoff scale $\Lambda$, and on the annihilation rate for DM particles, assuming that their branching fraction to quarks is 100%. Additionally, the most stringent 95% confidence level limits to date on the unparticle model parameters are obtained. | ||
| Links: e-print arXiv:1511.09375 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1-a:
The principal Feynman diagrams for the production of DM pairs in association with a Z boson. In (b) and (c) diagrams an additional quark is produced. The hatched circles indicate the interaction modeled with an effective field theory. |
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Figure 1-b:
The principal Feynman diagrams for the production of DM pairs in association with a Z boson. In (b) and (c) diagrams an additional quark is produced. The hatched circles indicate the interaction modeled with an effective field theory. |
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Figure 1-c:
The principal Feynman diagrams for the production of DM pairs in association with a Z boson. In (b) and (c) diagrams an additional quark is produced. The hatched circles indicate the interaction modeled with an effective field theory. |
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Figure 2-a:
Feynman diagrams for unparticle production in association with a Z boson. The hatched circles indicate the interaction modeled with an effective field theory. |
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Figure 2-b:
Feynman diagrams for unparticle production in association with a Z boson. The hatched circles indicate the interaction modeled with an effective field theory. |
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Figure 3-a:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for DM (a) and unparticle (b) scenarios. The DM curves are shown for different $m_\chi $ with vector (D5), axial-vector (D8), and tensor (D9) coupling for Dirac fermions, and vector (C3) coupling for complex scalar particles. The unparticle curves have the scalar unparticle coupling $\lambda $ between unparticle and SM fields set to 1, with the scaling dimension $d_\mathcal {U}$ ranging from 1.5 to 2.1. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid curve. |
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Figure 3-b:
The distribution in ${E_{\mathrm {T}}^{\text {miss}}}$ at the generator level, for DM (a) and unparticle (b) scenarios. The DM curves are shown for different $m_\chi $ with vector (D5), axial-vector (D8), and tensor (D9) coupling for Dirac fermions, and vector (C3) coupling for complex scalar particles. The unparticle curves have the scalar unparticle coupling $\lambda $ between unparticle and SM fields set to 1, with the scaling dimension $d_\mathcal {U}$ ranging from 1.5 to 2.1. The SM background $ {\mathrm{ Z } } {\mathrm{ Z } } \to \ell ^{-}\ell ^{+}\nu \bar{\nu} $ is shown as a red solid curve. |
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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 }^+ $ (a) and $ {\mathrm{ Z } } \to \mu^+ \mu^- $ (b) channels. Expected signal distributions are shown for Dirac fermions with vector or tensor couplings and for unparticles. The total statistical uncertainty in the overall background is shown as a hatched region. The horizontal bars on the data points indicate the bin width. Overflow events are included in the rightmost bins. |
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Figure 4-b:
The distribution of ${E_{\mathrm {T}}^{\text {miss}}}$ after preselection for the $ {\mathrm{ Z } } \to \mathrm{ e }^- \mathrm{ e }^+ $ (a) and $ {\mathrm{ Z } } \to \mu^+ \mu^- $ (b) channels. Expected signal distributions are shown for Dirac fermions with vector or tensor couplings and for unparticles. The total statistical uncertainty in the overall background is shown as a hatched region. The horizontal bars on the data points indicate the bin width. Overflow events are included in the rightmost bins. |
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Figure 5-a:
Distributions of the transverse mass for the final selection in the $\mathrm{ e }^- \mathrm{ e }^+ $ (a) and $\mu^+ \mu^- $ (b) channels. Examples of expected signal distributions are shown for DM particle production and unparticle production. The total statistical and systematic uncertainty in the overall background is shown as a hatched region. Overflow events are included in the rightmost bins. |
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Figure 5-b:
Distributions of the transverse mass for the final selection in the $\mathrm{ e }^- \mathrm{ e }^+ $ (a) and $\mu^+ \mu^- $ (b) channels. Examples of expected signal distributions are shown for DM particle production and unparticle production. The total statistical and systematic uncertainty in the overall background is shown as a hatched region. Overflow events are included in the rightmost bins. |
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Figure 6-a:
Expected and observed 90% CL lower limits on $\Lambda $ as a function of DM particle mass $m_{\chi }$ for the operators D5 (a), D8 (b), D9 (c), and C3 (d). The pink shaded area is shown in each plot to indicate the lower bound $\Lambda > m_{\chi }/2\pi $ on the validity of the effective field theory DM model. The cyan long-dashed line calculated by MadDM1.0 [82] reflects the relic density of cold, nonbaryonic DM: $\Omega h^2= $ 0.1198 $\pm$ 0.0026 measured by the Planck telescope [81]. Monojet results from CMS [14] are shown for comparison. Truncated limits with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with red dot long-dashed lines. The blue double-dot and triple-dot dashed lines indicate the contours of $R_{\Lambda }=80%$ for all operators with couplings $\sqrt {g_\mathrm{ q } g_\chi }=\pi $ and $4\pi $. |
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Figure 6-b:
Expected and observed 90% CL lower limits on $\Lambda $ as a function of DM particle mass $m_{\chi }$ for the operators D5 (a), D8 (b), D9 (c), and C3 (d). The pink shaded area is shown in each plot to indicate the lower bound $\Lambda > m_{\chi }/2\pi $ on the validity of the effective field theory DM model. The cyan long-dashed line calculated by MadDM1.0 [82] reflects the relic density of cold, nonbaryonic DM: $\Omega h^2= $ 0.1198 $\pm$ 0.0026 measured by the Planck telescope [81]. Monojet results from CMS [14] are shown for comparison. Truncated limits with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with red dot long-dashed lines. The blue double-dot and triple-dot dashed lines indicate the contours of $R_{\Lambda }=80%$ for all operators with couplings $\sqrt {g_\mathrm{ q } g_\chi }=\pi $ and $4\pi $. |
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Figure 6-c:
Expected and observed 90% CL lower limits on $\Lambda $ as a function of DM particle mass $m_{\chi }$ for the operators D5 (a), D8 (b), D9 (c), and C3 (d). The pink shaded area is shown in each plot to indicate the lower bound $\Lambda > m_{\chi }/2\pi $ on the validity of the effective field theory DM model. The cyan long-dashed line calculated by MadDM1.0 [82] reflects the relic density of cold, nonbaryonic DM: $\Omega h^2= $ 0.1198 $\pm$ 0.0026 measured by the Planck telescope [81]. Monojet results from CMS [14] are shown for comparison. Truncated limits with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with red dot long-dashed lines. The blue double-dot and triple-dot dashed lines indicate the contours of $R_{\Lambda }=80%$ for all operators with couplings $\sqrt {g_\mathrm{ q } g_\chi }=\pi $ and $4\pi $. |
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Figure 6-d:
Expected and observed 90% CL lower limits on $\Lambda $ as a function of DM particle mass $m_{\chi }$ for the operators D5 (a), D8 (b), D9 (c), and C3 (d). The pink shaded area is shown in each plot to indicate the lower bound $\Lambda > m_{\chi }/2\pi $ on the validity of the effective field theory DM model. The cyan long-dashed line calculated by MadDM1.0 [82] reflects the relic density of cold, nonbaryonic DM: $\Omega h^2= $ 0.1198 $\pm$ 0.0026 measured by the Planck telescope [81]. Monojet results from CMS [14] are shown for comparison. Truncated limits with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with red dot long-dashed lines. The blue double-dot and triple-dot dashed lines indicate the contours of $R_{\Lambda }=80%$ for all operators with couplings $\sqrt {g_\mathrm{ q } g_\chi }=\pi $ and $4\pi $. |
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Figure 7-a:
The 90%CL upper limits on the DM-nucleon cross section as a function of the DM particle mass. a: spin-dependent limits for axial-vector (D8) and tensor (D9) coupling of Dirac fermion DM candidates, together with direct search experimental results from the PICO [101], XENON100 [102], and IceCube [7] collaborations. b: spin-independent limits for vector coupling of complex scalar (C3) and Dirac fermion (D5) DM candidates, together with CDMSlite [8], LUX [11], as well as Higgs-portal scalar DM results from CMS [96] with central (solid), minimum (dashed) and maximum (dot dashed) values of Higgs-nucleon couplings. Collider results from CMS monojet [14] and monophoton [16] searches, interpreted in both spin-dependent and spin-independent scenarios, are shown for comparison. The truncated limits for D5, D8, D9, and C3 with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with dashed lines in same shade as the untruncated ones. |
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Figure 7-b:
The 90%CL upper limits on the DM-nucleon cross section as a function of the DM particle mass. a: spin-dependent limits for axial-vector (D8) and tensor (D9) coupling of Dirac fermion DM candidates, together with direct search experimental results from the PICO [101], XENON100 [102], and IceCube [7] collaborations. b: spin-independent limits for vector coupling of complex scalar (C3) and Dirac fermion (D5) DM candidates, together with CDMSlite [8], LUX [11], as well as Higgs-portal scalar DM results from CMS [96] with central (solid), minimum (dashed) and maximum (dot dashed) values of Higgs-nucleon couplings. Collider results from CMS monojet [14] and monophoton [16] searches, interpreted in both spin-dependent and spin-independent scenarios, are shown for comparison. The truncated limits for D5, D8, D9, and C3 with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with dashed lines in same shade as the untruncated ones. |
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Figure 8:
The 95%CL upper limits on the DM annihilation rate $< \sigma v> $ for $\chi \overline {\chi } \to \mathrm{ q } \mathrm{ \bar{q} } $ as a function of the DM particle mass for vector (D5) and axial-vector (D8) couplings of Dirac fermion DM. A 100% branching fraction of DM annihilating to quarks is assumed. Indirect search experimental results from H.E.S.S [103] and Fermi-LAT [104] are also plotted. The value required for DM particles to account for the relic abundance is labeled ``Thermal relic value'' and is shown as a red dotted line. The truncated limits for D5 and D8 with $\sqrt {g_\mathrm{ q } g_\chi }= $ 1 are presented with dashed lines in same shade as the untruncated ones. |
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Figure 9-a:
Left: 95% CL upper limits on the coupling $\lambda $ between the unparticle and SM fields with fixed effective cutoff scales $\Lambda _\mathcal {U}= $ 10 and 100 TeV . The plot inserted provides an expanded view of the limits at low scaling dimension. Right: 95% CL lower limits on unparticle effective cutoff scale $\Lambda _\mathcal {U}$ with a fixed coupling $\lambda = $ 1 . The results from CMS monojet [14] and reinterpretation of LEP searches [37] are also shown for comparison. The excluded region is indicated by the shading. |
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Figure 9-b:
Left: 95% CL upper limits on the coupling $\lambda $ between the unparticle and SM fields with fixed effective cutoff scales $\Lambda _\mathcal {U}= $ 10 and 100 TeV . The plot inserted provides an expanded view of the limits at low scaling dimension. Right: 95% CL lower limits on unparticle effective cutoff scale $\Lambda _\mathcal {U}$ with a fixed coupling $\lambda = $ 1 . The results from CMS monojet [14] and reinterpretation of LEP searches [37] are also shown for comparison. The excluded region is indicated by the shading. |
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Figure 10:
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. |
| 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 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 yield or acceptance. The symbol -- indicates that the systematic uncertainty is not applicable. |
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Table 3:
Signal predictions, background estimates, and observed number of events. The DM signal yields are given for masses $m_\chi =$ 10, 200, and 500 GeV and cutoff scales $\Lambda = $ 0.37 , 0.53, 0.48, and 1.4 TeV. The yields from an unparticle signal are presented with a scaling dimension $d_\mathcal {U}= $ 1.6 and a renormalization scale $\Lambda _\mathcal {U}= $ 33 TeV. The corresponding statistical and systematic uncertainties are shown, in that order. |
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Table 4:
Expected and observed 90% CL upper limits on the DM-nucleon cross section $\sigma _{\chi N}$ and effective cutoff scale $\Lambda $ for operator D5. |
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Table 5:
Expected and observed 90% CL upper limits on the DM-nucleon cross section $\sigma _{\chi N}$ and effective cutoff scale $\Lambda $ for operator D8. |
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Table 6:
Expected and observed 90% CL upper limits on the DM-nucleon cross section $\sigma _{\chi N}$ and effective cutoff scale $\Lambda $ for operator D9. |
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Table 7:
Expected and observed 90% CL upper limits on the DM-nucleon cross section $\sigma _{\chi N}$ and effective cutoff scale $\Lambda $ for operator C3. |
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Table 8:
Expected and observed 95% CL upper limits on the coupling $\lambda $ between unparticles and the SM fields, for values of $d_\mathcal {U}$ in the range from 1.01 to 2.20 and a fixed effective cutoff scale $\Lambda _\mathcal {U}= $ 10 TeV. |
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Table 9:
Expected and observed 95% CL upper limits on the coupling $\lambda $ between unparticles and the SM fields, for values of $d_\mathcal {U}$ in the range from 1.01 to 2.20 and a fixed effective cutoff scale $\Lambda _\mathcal {U}= $ 100 TeV. |
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Table 10:
Expected and observed 95% CL lower limits on the effective cutoff scale $\Lambda _\mathcal {U}$ for values of $d_\mathcal {U}$ in the range from 1.60 to 2.20 and a fixed coupling $\lambda = $ 1 . |
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Table 11:
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. The ${\pm }1\sigma $ and ${\pm }2\sigma $ excursions from expected limits are also given. |
| Summary |
| A search for evidence for particle dark matter and unparticle production at the LHC has been performed in events containing two charged leptons, consistent with the decay of a Z boson, and large missing transverse momentum. The study is based on a data set corresponding to an integrated luminosity of 19.7 fb$^{-1}$ of pp collisions collected by the CMS detector at a center-of-mass energy of 8 TeV. The results are consistent with the expected standard model contributions. These results are interpreted in two scenarios for physics beyond the standard model: dark matter and unparticles. Model-independent 95% confidence level upper limits are also set on contributions to the visible Z+$E_{\mathrm{T}}^\text{miss}$ cross section from sources beyond the standard model. Upper limits at 90% confidence level are set on the DM-nucleon scattering cross sections as a function of DM particle mass for both spin-dependent and spin-independent cases. Limits are also set on the DM annihilation rate assuming a branching fraction of 100% for annihilation to quarks, and on the effective cutoff scale. In addition, the most stringent limits to date at 95% confidence level on the coupling between unparticles and the standard model fields as well as the effective cutoff scale as a function of the unparticle scaling dimension are obtained in this analysis. |
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