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Assorted diagrams that give rise to a $t \bar t + E_{T, \rm miss}$ (left), $Z+ E_{T, \rm miss}$ (middle) and $h + E_{T, \rm miss}$~(right) signal in the simplified pseudoscalar model considered in our work. The exchanged spin-0 particles are of scalar ($H$) or pseudoscalar ($a, A$) type. Further Feynman graphs that contribute to the different mono-$X$ channels can be found in Figures~\ref{fig:jDMDM} to \ref{fig:WDMDM}.

Branching ratios of the lighter pseudoscalar $a$ as a function of its mass for two different choices of $\sin \theta$ and $m_\chi$ as indicated in the headline of the plots. The other relevant parameters have been set to $\tan \beta = 1$, $M_H = M_A = M_{H^\pm} = 750 \, {\rm GeV}$ and $y_\chi = 1$. Notice that for this specific $\tan \beta$ value the branching ratios of the pseudoscalar~$a$ do not depend on the choice of Yukawa sector.

Branching ratios of the lighter pseudoscalar $a$ as a function of its mass for two different choices of $\sin \theta$ and $m_\chi$ as indicated in the headline of the plots. The other relevant parameters have been set to $\tan \beta = 1$, $M_H = M_A = M_{H^\pm} = 750 \, {\rm GeV}$ and $y_\chi = 1$. Notice that for this specific $\tan \beta$ value the branching ratios of the pseudoscalar~$a$ do not depend on the choice of Yukawa sector.

Branching ratios of the lighter scalar $h$ as a function of the pseudoscalar mass $M_a$ for two different choices of $m_\chi$ as indicated in the headline of the plots. The other relevant parameters have been set to $\tan \beta = 1$, $M_H = M_A = M_{H^\pm} = 750 \, {\rm GeV}$, $\sin \theta = 1/\sqrt{2}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$ and~$y_\chi = 1$.

Branching ratios of the lighter scalar $h$ as a function of the pseudoscalar mass $M_a$ for two different choices of $m_\chi$ as indicated in the headline of the plots. The other relevant parameters have been set to $\tan \beta = 1$, $M_H = M_A = M_{H^\pm} = 750 \, {\rm GeV}$, $\sin \theta = 1/\sqrt{2}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$ and~$y_\chi = 1$.

Branching ratios of the heavier scalar $H$ as a function of $M_a$ for two different choices of $\sin \theta$ and $M_{H}$ as indicated in the headline of the plots. The other used input parameters are $\tan \beta = 1$, $M_A = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P2} = 0$ and $\lambda_{P1} = 1$.

Branching ratios of the heavier scalar $H$ as a function of $M_a$ for two different choices of $\sin \theta$ and $M_{H}$ as indicated in the headline of the plots. The other used input parameters are $\tan \beta = 1$, $M_A = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P2} = 0$ and $\lambda_{P1} = 1$.

Branching ratios of the heavier pseudoscalar $A$ as a function of $M_a$ for two different choices of $M_A$ and $\sin \theta$ as indicated in the headline of the plots. The other parameter choices are $\tan \beta = 1$, $M_H = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$, $y_\chi = 1$ and $m_\chi= 1 \, {\rm GeV}$.

Branching ratios of the heavier pseudoscalar $A$ as a function of $M_a$ for two different choices of $M_A$ and $\sin \theta$ as indicated in the headline of the plots. The other parameter choices are $\tan \beta = 1$, $M_H = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$, $y_\chi = 1$ and $m_\chi= 1 \, {\rm GeV}$.

Branching ratios of the charged scalar $H^+$ as a function of $M_a$ for two different sets of input parameters as indicated in the headline of the plots. In the left (right) panel in addition $\tan \beta = 1$ and $M_A = M_{H^\pm} = 750 \, {\rm GeV}$ ($M_H = M_{H^\pm} = 750 \, {\rm GeV}$) is used.

Branching ratios of the charged scalar $H^+$ as a function of $M_a$ for two different sets of input parameters as indicated in the headline of the plots. In the left (right) panel in addition $\tan \beta = 1$ and $M_A = M_{H^\pm} = 750 \, {\rm GeV}$ ($M_H = M_{H^\pm} = 750 \, {\rm GeV}$) is used.

Examples of diagrams that give rise to a $j +E_{T,\rm miss}$ signature through the exchange of a lighter pseudoscalar $a$. Graphs involving a heavier pseudoscalar $A$ also contribute to the signal in the pseudoscalar extensions of the THDM but are not shown explicitly.

Two possible diagrams that give rise to a $t \bar t +E_{T,\rm miss}$ signal. Graphs with both an exchange of an $a$ and $A$ contribute in the THDM plus pseudoscalar extensions but only the former are displayed.

Representative Feynman diagrams that lead to a $Z +E_{T,\rm miss}$ signal in the pseudoscalar extensions of the THDM. In the case of triangle diagram (left) only the shown graph contributes, while in the case of the box diagram (right) instead of an $a$ also an~$A$ exchange is possible.

Sample diagrams in the THDM with an extra pseudoscalar that induce a $h +E_{T,\rm miss}$ signal in the alignment/decoupling limit. Graphs in which the role of $a$ and $A$ is interchanged can also provide a relevant contribution.

Examples of diagrams that lead to a $W +E_{T,\rm miss}$ signature through the exchange of a charged Higgs $H^\pm$ and a lighter pseudoscalar $a$ in the THDM plus pseudoscalar extension.

Predictions for the mono-jet ($t \bar t + E_{T, \rm miss}$) cross section as a function of $M_a$ for three different values of $M_A$. In the left (right) plot $\sin \theta = 1/\sqrt{2}$ ($\sin \theta = 1/2$) is used and the other relevant parameters are $\tan \beta = 1$, $M_H = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$, $y_\chi = 1$ and $m_\chi = 1 \, {\rm GeV}$. The shown results correspond to~13~TeV $pp$ collisions and employ minimal sets of cuts as explained in the main text.

Predictions for the mono-jet ($t \bar t + E_{T, \rm miss}$) cross section as a function of $M_a$ for three different values of $M_A$. In the left (right) plot $\sin \theta = 1/\sqrt{2}$ ($\sin \theta = 1/2$) is used and the other relevant parameters are $\tan \beta = 1$, $M_H = M_{H^\pm} = 750 \, {\rm GeV}$, $\lambda_3 = \lambda_{P1} = \lambda_{P2} = 0$, $y_\chi = 1$ and $m_\chi = 1 \, {\rm GeV}$. The shown results correspond to~13~TeV $pp$ collisions and employ minimal sets of cuts as explained in the main text.

Summary plots showing all relevant constraints in the $M_a$--$\hspace{0.5mm} \tan \beta$ plane for four benchmark scenarios. The colour shaded regions correspond to the parameter space excluded by the different $E_{T, \rm miss}$ searches, while the constraints arising from di-top resonance searches and flavour physics are indicated by the dashed and dotted black lines, respectively. Parameters choices below the black lines are excluded. All exclusions are 95\%~CL bounds. See text for further details.

Summary plots showing all relevant constraints in the $M_a$--$\hspace{0.5mm} \tan \beta$ plane for four benchmark scenarios. The colour shaded regions correspond to the parameter space excluded by the different $E_{T, \rm miss}$ searches, while the constraints arising from di-top resonance searches and flavour physics are indicated by the dashed and dotted black lines, respectively. Parameters choices below the black lines are excluded. All exclusions are 95\%~CL bounds. See text for further details.

Summary plots showing all relevant constraints in the $M_a$--$\hspace{0.5mm} \tan \beta$ plane for four benchmark scenarios. The colour shaded regions correspond to the parameter space excluded by the different $E_{T, \rm miss}$ searches, while the constraints arising from di-top resonance searches and flavour physics are indicated by the dashed and dotted black lines, respectively. Parameters choices below the black lines are excluded. All exclusions are 95\%~CL bounds. See text for further details.

Summary plots showing all relevant constraints in the $M_a$--$\hspace{0.5mm} \tan \beta$ plane for four benchmark scenarios. The colour shaded regions correspond to the parameter space excluded by the different $E_{T, \rm miss}$ searches, while the constraints arising from di-top resonance searches and flavour physics are indicated by the dashed and dotted black lines, respectively. Parameters choices below the black lines are excluded. All exclusions are 95\%~CL bounds. See text for further details.

95\%~CL exclusion contours for our four benchmark scenarios following from hypothetical $Z + E_{T, \rm miss}$~(blue regions) and $h + E_{T, \rm miss}$~(orange regions) searches at 13~TeV LHC energies. The solid, dashed and dotted curves correspond to integrated luminosities of $40 \, {\rm fb}^{-1}$, $100 \, {\rm fb}^{-1}$ and $300 \, {\rm fb}^{-1}$, respectively.

95\%~CL exclusion contours for our four benchmark scenarios following from hypothetical $Z + E_{T, \rm miss}$~(blue regions) and $h + E_{T, \rm miss}$~(orange regions) searches at 13~TeV LHC energies. The solid, dashed and dotted curves correspond to integrated luminosities of $40 \, {\rm fb}^{-1}$, $100 \, {\rm fb}^{-1}$ and $300 \, {\rm fb}^{-1}$, respectively.

95\%~CL exclusion contours for our four benchmark scenarios following from hypothetical $Z + E_{T, \rm miss}$~(blue regions) and $h + E_{T, \rm miss}$~(orange regions) searches at 13~TeV LHC energies. The solid, dashed and dotted curves correspond to integrated luminosities of $40 \, {\rm fb}^{-1}$, $100 \, {\rm fb}^{-1}$ and $300 \, {\rm fb}^{-1}$, respectively.

95\%~CL exclusion contours for our four benchmark scenarios following from hypothetical $Z + E_{T, \rm miss}$~(blue regions) and $h + E_{T, \rm miss}$~(orange regions) searches at 13~TeV LHC energies. The solid, dashed and dotted curves correspond to integrated luminosities of $40 \, {\rm fb}^{-1}$, $100 \, {\rm fb}^{-1}$ and $300 \, {\rm fb}^{-1}$, respectively.

95\%~CL exclusion contours in our third and fourth benchmark scenario that follow from a hypothetical $h + E_{T, \rm miss}$~(orange regions) search with $300 \, {\rm fb}^{-1}$ of 13~TeV data. The solid lines correspond to the limits obtained from $gg$ production alone, while the dashed curves include both the $gg$ and $b \bar b$ initiated channel.

95\%~CL exclusion contours in our third and fourth benchmark scenario that follow from a hypothetical $h + E_{T, \rm miss}$~(orange regions) search with $300 \, {\rm fb}^{-1}$ of 13~TeV data. The solid lines correspond to the limits obtained from $gg$ production alone, while the dashed curves include both the $gg$ and $b \bar b$ initiated channel.