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| CMS-EXO-14-004 ; CERN-EP-2016-025 | ||
| Search for dark matter particles in proton-proton collisions at $\sqrt{s} =$ 8 TeV using the razor variables | ||
| CMS Collaboration | ||
| 29 March 2016 | ||
| JHEP 12 (2016) 088 | ||
| Abstract: A search for dark matter particles directly produced in proton-proton collisions recorded by the CMS experiment at the LHC is presented. The data correspond to an integrated luminosity of 18.8 fb$^{-1}$, at a center-of-mass energy of 8 TeV. The event selection requires at least two jets and no isolated leptons. The razor variables are used to quantify the transverse momentum balance in the jet momenta. The study is performed separately for events with and without jets originating from b quarks. The observed yields are consistent with the expected backgrounds and, depending on the nature of the production mechanism, dark matter production at the LHC is excluded at 90% confidence level for a mediator mass scale $\Lambda$ below 1 TeV. The use of razor variables yields results that complement those previously published. | ||
| Links: e-print arXiv:1603.08914 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1-a:
Feynman diagrams for the pair production of DM particles corresponding to an effective field theory using a vector or axial-vector operator. |
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Figure 1-b:
Feynman diagrams for the pair production of DM particles corresponding to an effective field theory using a scalar operator. |
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Figure 2:
Comparison of observed yields in the 1$\mu $ control region and the data-driven background estimate derived from on the 2$\mu $ control region data in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The bottom panel in each plot shows the ratio between the two distributions. The observed bin-by-bin deviation from unity is interpreted as an estimate of the systematic uncertainty associated to the background estimation methodology for the 0$\mu $ search region. The dark and light bands represent the statistical and the total uncertainties in the estimates, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 2-a:
Comparison of observed yields in the 1$\mu $ control region and the data-driven background estimate derived from on the 2$\mu $ control region data in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The bottom panel in each plot shows the ratio between the two distributions. The observed bin-by-bin deviation from unity is interpreted as an estimate of the systematic uncertainty associated to the background estimation methodology for the 0$\mu $ search region. The dark and light bands represent the statistical and the total uncertainties in the estimates, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 2-b:
Comparison of observed yields in the 1$\mu $ control region and the data-driven background estimate derived from on the 2$\mu $ control region data in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The bottom panel in each plot shows the ratio between the two distributions. The observed bin-by-bin deviation from unity is interpreted as an estimate of the systematic uncertainty associated to the background estimation methodology for the 0$\mu $ search region. The dark and light bands represent the statistical and the total uncertainties in the estimates, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 2-c:
Comparison of observed yields in the 1$\mu $ control region and the data-driven background estimate derived from on the 2$\mu $ control region data in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The bottom panel in each plot shows the ratio between the two distributions. The observed bin-by-bin deviation from unity is interpreted as an estimate of the systematic uncertainty associated to the background estimation methodology for the 0$\mu $ search region. The dark and light bands represent the statistical and the total uncertainties in the estimates, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 2-d:
Comparison of observed yields in the 1$\mu $ control region and the data-driven background estimate derived from on the 2$\mu $ control region data in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The bottom panel in each plot shows the ratio between the two distributions. The observed bin-by-bin deviation from unity is interpreted as an estimate of the systematic uncertainty associated to the background estimation methodology for the 0$\mu $ search region. The dark and light bands represent the statistical and the total uncertainties in the estimates, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 3:
Comparison of the observed yield and the prediction from simulation as a function of $ {R} ^2$ in the 2$\mu $b control region. The uncertainties in the data and the simulated sample are represented by the vertical bars and the shaded bands, respectively. The horizontal bars indicate the variable bin widths. |
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Figure 4:
Comparison of the observed yield in the zero b-tag control region and the background estimates in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The contribution of individual background processes is shown by the filled histograms. The bottom panels show the ratio between the observed yields and the total background estimate. The systematic uncertainty in the ratio includes the systematic uncertainty in the background estimate. For reference, the distributions from two benchmark signal models are also shown, corresponding to the pair production of DM particles of mass 1 GeV in the EFT approach with vector coupling to u or d quarks. The horizontal bars indicate the variable bin widths. |
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Figure 4-a:
Comparison of the observed yield in the zero b-tag control region and the background estimates in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The contribution of individual background processes is shown by the filled histograms. The bottom panels show the ratio between the observed yields and the total background estimate. The systematic uncertainty in the ratio includes the systematic uncertainty in the background estimate. For reference, the distributions from two benchmark signal models are also shown, corresponding to the pair production of DM particles of mass 1 GeV in the EFT approach with vector coupling to u or d quarks. The horizontal bars indicate the variable bin widths. |
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Figure 4-b:
Comparison of the observed yield in the zero b-tag control region and the background estimates in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The contribution of individual background processes is shown by the filled histograms. The bottom panels show the ratio between the observed yields and the total background estimate. The systematic uncertainty in the ratio includes the systematic uncertainty in the background estimate. For reference, the distributions from two benchmark signal models are also shown, corresponding to the pair production of DM particles of mass 1 GeV in the EFT approach with vector coupling to u or d quarks. The horizontal bars indicate the variable bin widths. |
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Figure 4-c:
Comparison of the observed yield in the zero b-tag control region and the background estimates in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The contribution of individual background processes is shown by the filled histograms. The bottom panels show the ratio between the observed yields and the total background estimate. The systematic uncertainty in the ratio includes the systematic uncertainty in the background estimate. For reference, the distributions from two benchmark signal models are also shown, corresponding to the pair production of DM particles of mass 1 GeV in the EFT approach with vector coupling to u or d quarks. The horizontal bars indicate the variable bin widths. |
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Figure 4-d:
Comparison of the observed yield in the zero b-tag control region and the background estimates in the four $ {M_R} $ categories: VL (top left), L (top right), H (bottom left), and VH (bottom right). The contribution of individual background processes is shown by the filled histograms. The bottom panels show the ratio between the observed yields and the total background estimate. The systematic uncertainty in the ratio includes the systematic uncertainty in the background estimate. For reference, the distributions from two benchmark signal models are also shown, corresponding to the pair production of DM particles of mass 1 GeV in the EFT approach with vector coupling to u or d quarks. The horizontal bars indicate the variable bin widths. |
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Figure 5:
Comparison of the observed yield and the prediction from simulation in the $\mathrm{ Z } (\mu \mu )$b control sample (left) and of the observed yield in the $1\mu $b control sample and the background estimates from the 2$\mu $b and $\mathrm{ Z } (\mu \mu )$b control samples (right), shown as a function of $ {R} ^2$. The bottom panel of each figure shows the ratio between the data and the estimates. The shaded bands represent the statistical uncertainty in the left plot, and the total uncertainty in the right plot. The horizontal bars indicate the variable bin widths. |
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Figure 5-a:
Comparison of the observed yield and the prediction from simulation in the $\mathrm{ Z } (\mu \mu )$b control sample (left) and of the observed yield in the $1\mu $b control sample and the background estimates from the 2$\mu $b and $\mathrm{ Z } (\mu \mu )$b control samples (right), shown as a function of $ {R} ^2$. The bottom panel of each figure shows the ratio between the data and the estimates. The shaded bands represent the statistical uncertainty in the left plot, and the total uncertainty in the right plot. The horizontal bars indicate the variable bin widths. |
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Figure 5-b:
Comparison of the observed yield and the prediction from simulation in the $\mathrm{ Z } (\mu \mu )$b control sample (left) and of the observed yield in the $1\mu $b control sample and the background estimates from the 2$\mu $b and $\mathrm{ Z } (\mu \mu )$b control samples (right), shown as a function of $ {R} ^2$. The bottom panel of each figure shows the ratio between the data and the estimates. The shaded bands represent the statistical uncertainty in the left plot, and the total uncertainty in the right plot. The horizontal bars indicate the variable bin widths. |
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Figure 6:
Comparison of observed event yields and background estimates as a function of $ {R} ^2$, for the one (left) and two (right) b-tag search regions. The shaded bands represent the total uncertainty in the estimate. The horizontal bars indicate the variable bin widths. |
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Figure 6-a:
Comparison of observed event yields and background estimates as a function of $ {R} ^2$, for the one (left) and two (right) b-tag search regions. The shaded bands represent the total uncertainty in the estimate. The horizontal bars indicate the variable bin widths. |
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Figure 6-b:
Comparison of observed event yields and background estimates as a function of $ {R} ^2$, for the one (left) and two (right) b-tag search regions. The shaded bands represent the total uncertainty in the estimate. The horizontal bars indicate the variable bin widths. |
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Figure 7:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. The validity of the EFT is quantified by $R_\Lambda = $ 80% contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
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Figure 7-a:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. The validity of the EFT is quantified by $R_\Lambda = $ 80% contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
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Figure 7-b:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. The validity of the EFT is quantified by $R_\Lambda = $ 80% contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
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Figure 8:
Upper limit at 90% CL on the DM-nucleon scattering cross section $\sigma _{N\chi }$ as a function of the DM mass $M_\chi $ in the case of spin-dependent axial-vector (left) and spin-independent vector (right) currents. A selection of representative direct detection experimental bounds are also shown. |
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Figure 8-a:
Upper limit at 90% CL on the DM-nucleon scattering cross section $\sigma _{N\chi }$ as a function of the DM mass $M_\chi $ in the case of spin-dependent axial-vector (left) and spin-independent vector (right) currents. A selection of representative direct detection experimental bounds are also shown. |
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Figure 8-b:
Upper limit at 90% CL on the DM-nucleon scattering cross section $\sigma _{N\chi }$ as a function of the DM mass $M_\chi $ in the case of spin-dependent axial-vector (left) and spin-independent vector (right) currents. A selection of representative direct detection experimental bounds are also shown. |
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Figure 9:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. A selection of direct detection experimental bounds are also shown. |
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Figure 9-a:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. A selection of direct detection experimental bounds are also shown. |
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Figure 9-b:
Lower limit at 90% CL on the cutoff scale $\Lambda $ as a function of the DM mass $M_\chi $ in the case of axial-vector (left) and vector (right) currents. A selection of direct detection experimental bounds are also shown. |
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Figure 10:
Lower limit at 90% CL on the cutoff scale $\Lambda $ for the scalar operator $\hat{\mathcal {O}}_{S}$ as a function of the DM mass $M_{\chi }$. The validity of the EFT is quantified by $R_\Lambda = $ 80% (left) and $R_\Lambda = $ 25% (right) contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
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Figure 10-a:
Lower limit at 90% CL on the cutoff scale $\Lambda $ for the scalar operator $\hat{\mathcal {O}}_{S}$ as a function of the DM mass $M_{\chi }$. The validity of the EFT is quantified by $R_\Lambda = $ 80% (left) and $R_\Lambda = $ 25% (right) contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
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Figure 10-b:
Lower limit at 90% CL on the cutoff scale $\Lambda $ for the scalar operator $\hat{\mathcal {O}}_{S}$ as a function of the DM mass $M_{\chi }$. The validity of the EFT is quantified by $R_\Lambda = $ 80% (left) and $R_\Lambda = $ 25% (right) contours, corresponding to different values of the effective coupling $g_\text {eff}$. For completeness, regions forbidden by the EFT validity condition $\Lambda > 2M_\chi /g_\text {eff}$ are shown for two choices of the effective coupling: $g_\text {eff} = $ 1 (light gray) and $g_\text {eff}= 4\pi $ (dark gray). |
| Tables | |
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Table 1:
Measured trigger efficiency for different $ {M_R} $ regions. The selection $ {R} ^2 > $ 0.35 is applied. The uncertainty shown represents the statistical uncertainty in the measured efficiency. |
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Table 2:
Analysis regions for events with zero identified b-tagged jets. The definition of these regions is based on the muon multiplicity, the output of the CSV b-tagging algorithm, and the value of $ {M_R} $. For all the regions, $ {R} ^2> $ 0.5 is required. |
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Table 3:
Analysis regions for events with identified b-tagged jets. The definition of these regions is based on the muon multiplicity, the output of the CSV b-tagging algorithm, and the value of $ {M_R} $. For all the regions, $ {R} ^2> $ 0.5 is required. |
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Table 4:
Comparison of the observed yield in the 1$\mu $ control region in each $ {M_R} $ category and the corresponding data-driven background estimate obtained by extrapolating from the 2$\mu $ control region. The uncertainty in the estimates takes into account both the statistical and systematic components. The contribution of each individual background process is also shown, as estimated from simulated samples, as well as the total MC predicted yield. |
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Table 5:
Comparison of the observed yield for the 2$\mu $ control region in each $ {M_R} $ category and the corresponding prediction from background simulation. The quoted uncertainty in the prediction reflects only the size of the simulated sample. The contribution of each individual background process is also shown, as estimated from simulated samples. |
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Table 6:
Observed yield and predicted background from simulated samples in the 2$\mu $b control region. The quoted uncertainty in the prediction only reflects the size of the simulated sample. The contribution of each individual background process is also shown, as estimated from simulated samples. |
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Table 7:
Comparison of the observed yields for for the zero b-tag search region in each $ {M_R} $ category and the corresponding background estimates. The uncertainty in the background estimate takes into account both the statistical and systematic components. The contribution of each individual background process is also shown, as estimated from simulated samples, as well as the total MC predicted yield. |
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Table 8:
Comparison of the observed yields in the $\mathrm{ Z } (\mu \mu )$b and $1\mu $b samples, the corresponding predictions from background simulation, and (for $1\mu $b only) the cross-check background estimate. The contribution of each individual background process is also shown, as estimated from simulated samples. |
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Table 9:
Comparison of the observed yield for events in the one and two b-tag search regions and the corresponding background estimates. The uncertainty in the estimates takes into account both the statistical and systematic components. The contribution of each individual background process is also shown, as estimated from simulated samples, as well as the total MC predicted yield. |
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Table 10:
Systematic uncertainties associated with the description of the DM signal. The values indicated represent the typical size. The dependence of these systematic uncertainties on the $ {R} ^2$ and $ {M_R} $ values is taken into account in the determination of the results. |
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Table 11:
The 90% CL limits on DM production in the case of axial-vector couplings. Here, $\sigma ^{u}_\mathrm {UL}$ and $\sigma ^{d}_\mathrm {UL}$ are the observed upper limits on the production cross section for u and d quarks, respectively; $\Lambda _\mathrm {LL}$ is the observed cutoff energy scale lower limit; and $\sigma _{N\chi }$ is the observed DM-nucleon scattering cross section upper limit. |
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Table 12:
The 90% CL limits on DM production in the case of vector couplings. Here, $\sigma ^{u}_\mathrm {UL}$ and $\sigma ^{d}_\mathrm {UL}$ are the observed upper limits on the production cross section for u and d quarks, respectively; $\Lambda _\mathrm {LL}$ is the observed cutoff energy scale lower limit; and $\sigma _{N\chi }$ is the observed DM-nucleon scattering cross section upper limit. |
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Table 13:
The 90% CL limits on DM production in the case of scalar couplings. Here, $\sigma ^\text {obs}_\mathrm {UL}$ is the observed upper limit on the production cross section, $\Lambda ^\text {obs}_\mathrm {LL}$ and $\Lambda ^\text {exp}_\mathrm {LL}$ are the observed and expected cutoff energy scale lower limit, respectively. |
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Table 14:
Background estimates and observed yield for each $ {R} ^2$ bin in the VL $ {M_R} $ category. |
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Table 15:
Background estimates and observed yield for each $ {R} ^2$ bin in the L $ {M_R} $ category. |
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Table 16:
Background estimates and observed yield for each $ {R} ^2$ bin in the H $ {M_R} $ category. |
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Table 17:
Background estimates and observed yield for each $ {R} ^2$ bin in the VH $ {M_R} $ category. |
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Table 18:
Background estimates and observed yield for each bin in the 0$\mu $b signal region. |
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Table 19:
Background estimates and observed yield for each bin in the 0$\mu $bb signal region. |
| Summary |
|
A search for dark matter has been performed studying proton-proton collisions collected with the CMS detector at the LHC at a center-of-mass energy of 8 TeV. The data correspond to an integrated luminosity of 18.8 fb$^{-1}$, collected with a dedicated high-rate trigger in 2012, made possible by the creation of parked data, and processed during the LHC shutdown in 2013. Events with at least two jets are analyzed by studying the distribution in the ($M_R$, $R^2$) plane, in an event topology complementary to that of monojet searches. Events with one or two muons are used in conjunction with simulated samples, to predict the expected background from standard model processes, mainly Z+jets and W+jets. The analysis is performed on events both with and without b-tagged jets, originating from the hadronization of a bottom quark, where in the latter case the dominant background comes from $\mathrm{ t \bar{t} } $. No significant excess is observed. The results are presented as exclusion limits on dark matter production at 90% confidence level for models based on effective operators and for different assumptions on the interaction between the dark matter particles and the colliding partons. Dark matter production at the LHC is excluded for a mediator mass scale $\Lambda$ below 1 TeV in the case of a vector or axial vector operator. While the sensitivity achieved is similar to those of previously published searches, this analysis complements those results since the use of razor variables provides more inclusive selection criteria and since the exploitation of parked data allows events with small values of $M_R$ to be included. |
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