t-channel dark matter models – a whitepaper
- Arina, Chiara et al
- arXiv:2504.10597CERN-LPCC-2025-001IRMP-CP3-25-07TTK-25-07
 | Exclusion limits at 95\% confidence level from the reinterpretation of several Run~2 ATLAS and CMS searches~\cite{ATLAS:2021kxv, ATLAS:2020xgt, ATLAS:2019vcq, CMS:2019zmd, CMS:2021far}. The results are shown for the \lstinline{S3M_uR} (left) and \lstinline{S3M_dR} (right) real dark matter scenarios described in section~\ref{sec:model_minimal}, considering two configurations: $\lambda = 3.5$ (top row) and $\Gamma_Y / M_Y = 0.05$ (bottom row). For scenarios with $\lambda = 3.5$, dotted grey lines represent isolines of constant $\Gamma_Y / M_Y$ value. Conversely, for scenarios with $\Gamma_Y / M_Y = 0.05$, these lines correspond to isolines of fixed $\lambda$ value. Individual contributions to the bounds are displayed for processes $XX$ (red), $XY$ (green), and $YY$ (dark blue), with the $YY$ process further decomposed into its purely QCD part ($YY_{\rm QCD}$, teal) and its $t$-channel part ($YY_t$, turquoise). The yellow gradient highlights regimes where either the perturbative approach becomes increasingly invalid due to large coupling values or the narrow-width approximation loses validity due to a large mediator width-to-mass ratio. |
 | Exclusion limits at 95\% confidence level from the reinterpretation of several Run~2 ATLAS and CMS searches~\cite{ATLAS:2021kxv, ATLAS:2020xgt, ATLAS:2019vcq, CMS:2019zmd, CMS:2021far}. The results are shown for the \lstinline{S3M_uR} (left) and \lstinline{S3M_dR} (right) real dark matter scenarios described in section~\ref{sec:model_minimal}, considering two configurations: $\lambda = 3.5$ (top row) and $\Gamma_Y / M_Y = 0.05$ (bottom row). For scenarios with $\lambda = 3.5$, dotted grey lines represent isolines of constant $\Gamma_Y / M_Y$ value. Conversely, for scenarios with $\Gamma_Y / M_Y = 0.05$, these lines correspond to isolines of fixed $\lambda$ value. Individual contributions to the bounds are displayed for processes $XX$ (red), $XY$ (green), and $YY$ (dark blue), with the $YY$ process further decomposed into its purely QCD part ($YY_{\rm QCD}$, teal) and its $t$-channel part ($YY_t$, turquoise). The yellow gradient highlights regimes where either the perturbative approach becomes increasingly invalid due to large coupling values or the narrow-width approximation loses validity due to a large mediator width-to-mass ratio. |
 | Exclusion limits at 95\% confidence level from the reinterpretation of several Run~2 ATLAS and CMS searches~\cite{ATLAS:2021kxv, ATLAS:2020xgt, ATLAS:2019vcq, CMS:2019zmd, CMS:2021far}. The results are shown for the \lstinline{S3M_uR} (left) and \lstinline{S3M_dR} (right) real dark matter scenarios described in section~\ref{sec:model_minimal}, considering two configurations: $\lambda = 3.5$ (top row) and $\Gamma_Y / M_Y = 0.05$ (bottom row). For scenarios with $\lambda = 3.5$, dotted grey lines represent isolines of constant $\Gamma_Y / M_Y$ value. Conversely, for scenarios with $\Gamma_Y / M_Y = 0.05$, these lines correspond to isolines of fixed $\lambda$ value. Individual contributions to the bounds are displayed for processes $XX$ (red), $XY$ (green), and $YY$ (dark blue), with the $YY$ process further decomposed into its purely QCD part ($YY_{\rm QCD}$, teal) and its $t$-channel part ($YY_t$, turquoise). The yellow gradient highlights regimes where either the perturbative approach becomes increasingly invalid due to large coupling values or the narrow-width approximation loses validity due to a large mediator width-to-mass ratio. |
 | Exclusion limits at 95\% confidence level from the reinterpretation of several Run~2 ATLAS and CMS searches~\cite{ATLAS:2021kxv, ATLAS:2020xgt, ATLAS:2019vcq, CMS:2019zmd, CMS:2021far}. The results are shown for the \lstinline{S3M_uR} (left) and \lstinline{S3M_dR} (right) real dark matter scenarios described in section~\ref{sec:model_minimal}, considering two configurations: $\lambda = 3.5$ (top row) and $\Gamma_Y / M_Y = 0.05$ (bottom row). For scenarios with $\lambda = 3.5$, dotted grey lines represent isolines of constant $\Gamma_Y / M_Y$ value. Conversely, for scenarios with $\Gamma_Y / M_Y = 0.05$, these lines correspond to isolines of fixed $\lambda$ value. Individual contributions to the bounds are displayed for processes $XX$ (red), $XY$ (green), and $YY$ (dark blue), with the $YY$ process further decomposed into its purely QCD part ($YY_{\rm QCD}$, teal) and its $t$-channel part ($YY_t$, turquoise). The yellow gradient highlights regimes where either the perturbative approach becomes increasingly invalid due to large coupling values or the narrow-width approximation loses validity due to a large mediator width-to-mass ratio. |
 | Search including the most sensitive signal region for the new physics signal originating from the combination of all processes at NLO for \lstinline{S3M_uR} models with a fixed width/mass ratio (left), and \lstinline{S3M_dR} models with a fixed coupling (right). |
 | Search including the most sensitive signal region for the new physics signal originating from the combination of all processes at NLO for \lstinline{S3M_uR} models with a fixed width/mass ratio (left), and \lstinline{S3M_dR} models with a fixed coupling (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_uR} (left) and \lstinline{F3S_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 4.8$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_uR} (left) and \lstinline{F3S_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 4.8$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_uR} (left) and \lstinline{F3S_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 4.8$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_uR} (left) and \lstinline{F3S_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 4.8$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3V_uR} (left) and \lstinline{F3V_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 1$. Moreover, results are given at LO only. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3V_uR} (left) and \lstinline{F3V_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 1$. Moreover, results are given at LO only. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3V_uR} (left) and \lstinline{F3V_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 1$. Moreover, results are given at LO only. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3V_uR} (left) and \lstinline{F3V_dR} (right) real dark matter scenarios. For scenarios with fixed $\lambda$ values, we adopt $\lambda = 1$. Moreover, results are given at LO only. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_cR} (left) and \lstinline{S3M_sR} (right) classes of models. For scenarios with a fixed coupling value, we adopt $\lambda = 2.2$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_cR} (left) and \lstinline{S3M_sR} (right) classes of models. For scenarios with a fixed coupling value, we adopt $\lambda = 2.2$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_cR} (left) and \lstinline{S3M_sR} (right) classes of models. For scenarios with a fixed coupling value, we adopt $\lambda = 2.2$. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_cR} (left) and \lstinline{S3M_sR} (right) classes of models. For scenarios with a fixed coupling value, we adopt $\lambda = 2.2$. |
 | : Search including the most sensitive signal region for the new physics signal emerging from the $YY_{\mathrm{QCD}}$ processes at NLO, for the \lstinline{S3M_cR} (left) and \lstinline{S3M_sR} (right) models with a fixed width-to-mass ratio. The 95\% CL exclusion limit is also reported. |
 | : LO and NLO distributions of the transverse momentum of the leading jet (left) and of the number of leptons (right) for the $YY_{\rm QCD}$ channel. We show the number of events obtained at reconstruction level, after hadronisation, detector simulation and before any selection, and for an integrated luminosity of 300~fb$^{-1}$. The distributions correspond to the \lstinline{S3M_cR} and \lstinline{S3M_sR} scenarios with $M_Y=800$~GeV, $M_X=10$~GeV and $\lambda$ fixed to obtain $\Gamma_Y/M_Y=0.05$. The cross sections reported in the legend are effective to reflect the reduction due to selecting specific final state particles. |
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 | NLO/LO ratios of parton luminosities for the NNPDF40 set of parton densities. We consider first the charm-gluon (top left) and strange-gluon (top right) initial states relevant for the $XY$ process, and next the charm-anticharm (bottom left) and strange-antistrange (bottom right) initial states relevant for the $Y\bar Y_t$ process. Band thickness refers to PDF uncertainties. |
 | NLO/LO ratios of parton luminosities for the NNPDF40 set of parton densities. We consider first the charm-gluon (top left) and strange-gluon (top right) initial states relevant for the $XY$ process, and next the charm-anticharm (bottom left) and strange-antistrange (bottom right) initial states relevant for the $Y\bar Y_t$ process. Band thickness refers to PDF uncertainties. |
 | NLO/LO ratios of parton luminosities for the NNPDF40 set of parton densities. We consider first the charm-gluon (top left) and strange-gluon (top right) initial states relevant for the $XY$ process, and next the charm-anticharm (bottom left) and strange-antistrange (bottom right) initial states relevant for the $Y\bar Y_t$ process. Band thickness refers to PDF uncertainties. |
 | NLO/LO ratios of parton luminosities for the NNPDF40 set of parton densities. We consider first the charm-gluon (top left) and strange-gluon (top right) initial states relevant for the $XY$ process, and next the charm-anticharm (bottom left) and strange-antistrange (bottom right) initial states relevant for the $Y\bar Y_t$ process. Band thickness refers to PDF uncertainties. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3S_cR} (left) and \lstinline{F3S_sR} (right) classes of scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3S_cR} (left) and \lstinline{F3S_sR} (right) classes of scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3S_cR} (left) and \lstinline{F3S_sR} (right) classes of scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3S_cR} (left) and \lstinline{F3S_sR} (right) classes of scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3V_cR} (left) and \lstinline{F3V_sR} (right) scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3V_cR} (left) and \lstinline{F3V_sR} (right) scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3V_cR} (left) and \lstinline{F3V_sR} (right) scenarios. |
 | Same as figure \ref{fig:2ndgenS3M}, but for the \lstinline{F3V_cR} (left) and \lstinline{F3V_sR} (right) scenarios. |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_tR} real dark matter scenarios with $\Gamma_Y/M_Y=0.05$ (left), and for the \lstinline{S3M_bR} scenarios with either $\lambda=2.2$ (central) or $\Gamma_Y/M_Y=0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_tR} real dark matter scenarios with $\Gamma_Y/M_Y=0.05$ (left), and for the \lstinline{S3M_bR} scenarios with either $\lambda=2.2$ (central) or $\Gamma_Y/M_Y=0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{S3M_tR} real dark matter scenarios with $\Gamma_Y/M_Y=0.05$ (left), and for the \lstinline{S3M_bR} scenarios with either $\lambda=2.2$ (central) or $\Gamma_Y/M_Y=0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Same as in figure~\ref{fig:1stgen}, but for the \lstinline{F3S_tR} (top left), \lstinline{F3V_tR} (bottom left) scenarios with a fixed mediator width-to-mass ratio $\Gamma_Y / M_Y = 0.05$, and for the \lstinline{F3S_bR} (top row, central and right panels) and \lstinline{F3V_bR} (bottom row, central and right panels) setups. We either fix the new physics coupling to $\lambda = 3.8$ (top central) or $0.9$ (bottom central), or derive it from $\Gamma_Y / M_Y = 0.05$ (right). |
 | Differential distributions for the missing transverse energy $\met$ in the case of the \lstinline{S3M_uR} (top row) and \lstinline{F3S_uR} (bottom row) scenarios, with mass configurations $\{M_Y,M_X\}=\{3000,10\}$ GeV (left column) and $\{M_Y,M_X\}=\{3000,1500\}$ GeV (right column). The distributions represent the number of signal events expected for an integrated luminosity of 300 fb$^{-1}$ of proton-proton collisions at 13~TeV, and have been obtained using the \lstinline{SFS} detector simulation module included in \lstinline{MadAnalysis 5} with the default ATLAS configuration. The contributions of each channel with a cross section larger than 1~ab at both NLO and LO are shown, together with the resulting combined distribution. |
 | Differential distributions for the missing transverse energy $\met$ in the case of the \lstinline{S3M_uR} (top row) and \lstinline{F3S_uR} (bottom row) scenarios, with mass configurations $\{M_Y,M_X\}=\{3000,10\}$ GeV (left column) and $\{M_Y,M_X\}=\{3000,1500\}$ GeV (right column). The distributions represent the number of signal events expected for an integrated luminosity of 300 fb$^{-1}$ of proton-proton collisions at 13~TeV, and have been obtained using the \lstinline{SFS} detector simulation module included in \lstinline{MadAnalysis 5} with the default ATLAS configuration. The contributions of each channel with a cross section larger than 1~ab at both NLO and LO are shown, together with the resulting combined distribution. |
 | Differential distributions for the missing transverse energy $\met$ in the case of the \lstinline{S3M_uR} (top row) and \lstinline{F3S_uR} (bottom row) scenarios, with mass configurations $\{M_Y,M_X\}=\{3000,10\}$ GeV (left column) and $\{M_Y,M_X\}=\{3000,1500\}$ GeV (right column). The distributions represent the number of signal events expected for an integrated luminosity of 300 fb$^{-1}$ of proton-proton collisions at 13~TeV, and have been obtained using the \lstinline{SFS} detector simulation module included in \lstinline{MadAnalysis 5} with the default ATLAS configuration. The contributions of each channel with a cross section larger than 1~ab at both NLO and LO are shown, together with the resulting combined distribution. |
 | Differential distributions for the missing transverse energy $\met$ in the case of the \lstinline{S3M_uR} (top row) and \lstinline{F3S_uR} (bottom row) scenarios, with mass configurations $\{M_Y,M_X\}=\{3000,10\}$ GeV (left column) and $\{M_Y,M_X\}=\{3000,1500\}$ GeV (right column). The distributions represent the number of signal events expected for an integrated luminosity of 300 fb$^{-1}$ of proton-proton collisions at 13~TeV, and have been obtained using the \lstinline{SFS} detector simulation module included in \lstinline{MadAnalysis 5} with the default ATLAS configuration. The contributions of each channel with a cross section larger than 1~ab at both NLO and LO are shown, together with the resulting combined distribution. |
 | : Same as in figure~\ref{fig:dist_S3M_u} but for the \lstinline{F3S_cR} (left panel) and \lstinline{F3S_sR} (right panel) scenarios, and the mass spectrum $\{M_Y,M_X\}=\{1600,800\}$~GeV. |
 | : Differential distributions for the missing transverse energy $\met$ for different $t$-channel DM scenarios in which the mediator width is less than 10\% of its mass. The coupling $\lambda$ is determined to obtain an NLO total signal cross section of 5 fb after the selection cut $\met>200$ GeV. We either consider NLO and LO predictions for mediator and DM masses fixed to 1600 GeV and 800 GeV respectively (left panel), or we compute NLO predictions for a scenario in which we assume a mediator mass of 1600~GeV, interactions with the up quark only, and DM masses of 10, 800 and 1595~GeV (right panel). In this case, the LO rates are indicated in the figure's legend. |
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 | Current LHC exclusions on the muon-philic benchmark models considered. The exclusion curves correspond to the reinterpretation of the results of the run~2 ATLAS searches from~\cite{ATLAS:2019lff} (blue) and~\cite{ATLAS:2019lng} (orange), as well as from the LHC Run~1 ATLAS results from~\cite{ATLAS:2014zve} (dashed red). The dashed green curve represents the limits from the \href{https://lepsusy.web.cern.ch/lepsusy/www/sleptons_summer04/slep_final.html}{LEP2 SUSY Working Group}. |
 | Current LHC exclusions on the muon-philic benchmark models considered. The exclusion curves correspond to the reinterpretation of the results of the run~2 ATLAS searches from~\cite{ATLAS:2019lff} (blue) and~\cite{ATLAS:2019lng} (orange), as well as from the LHC Run~1 ATLAS results from~\cite{ATLAS:2014zve} (dashed red). The dashed green curve represents the limits from the \href{https://lepsusy.web.cern.ch/lepsusy/www/sleptons_summer04/slep_final.html}{LEP2 SUSY Working Group}. |
 | Expected limits from single-top final states on a model with Dirac flavoured DM coupling to right-handed up-type quarks, shown for the QDF (left) and FFS (right) benchmark scenarios of DM freeze-out. Solid lines indicate the expected reach in the $(M_Y, D_1)$ plane for $tj+\met$ and $t+\met$ analyses, assuming an integrated luminosity of 137\,fb$^{-1}$ at the 14\,TeV LHC. The excluded regions lie to the left of the curves. Dashed lines show the corresponding projections for 300\,fb$^{-1}$, and results for 3000\,fb$^{-1}$ can be found in \cite{Blanke:2020bsf}. The shaded region represents the exclusion derived from a recast of the CMS search~\cite{CMS:2019zmd}, and the orange dash-dotted lines indicate parameter values that yield the correct relic abundance. Figure adapted from \cite{Blanke:2020bsf}. |
 | Expected limits from single-top final states on a model with Dirac flavoured DM coupling to right-handed up-type quarks, shown for the QDF (left) and FFS (right) benchmark scenarios of DM freeze-out. Solid lines indicate the expected reach in the $(M_Y, D_1)$ plane for $tj+\met$ and $t+\met$ analyses, assuming an integrated luminosity of 137\,fb$^{-1}$ at the 14\,TeV LHC. The excluded regions lie to the left of the curves. Dashed lines show the corresponding projections for 300\,fb$^{-1}$, and results for 3000\,fb$^{-1}$ can be found in \cite{Blanke:2020bsf}. The shaded region represents the exclusion derived from a recast of the CMS search~\cite{CMS:2019zmd}, and the orange dash-dotted lines indicate parameter values that yield the correct relic abundance. Figure adapted from \cite{Blanke:2020bsf}. |
 | Representative Feynman diagrams illustrating the production of two dark matter particles in association with a single top quark. Adapted from \cite{Blanke:2020bsf}. |
 | Predictions for the single-top charge asymmetry $a_{tj}$ in a model of Majorana flavoured DM coupling to the three flavours of right-handed up-type quarks. We present predictions for $a_{tj}$ (colour-coded) at the 14\,TeV LHC, compared with current constraints from tops$+\met$ (light grey) and jets$+\met$ (dark grey) searches, for $D_2 = 0$, $M_Y = 1200$\,GeV, and $M_X = 400$\,GeV (left); we also show the correlations between predictions for $a_{tj}$ and the total single-top cross section $\sigma_\text{tot}$ as defined in the denominator of \eqref{eq:atj}, for viable scenarios featuring canonical DM freeze-out (green) and conversion-driven freeze-out (blue). Here, $D_i$ represent the DM coupling strengths to the $i^\mathrm{th}$ generation, and the figures have been adapted from \cite{Acaroglu:2023phy}. |
 | Predictions for the single-top charge asymmetry $a_{tj}$ in a model of Majorana flavoured DM coupling to the three flavours of right-handed up-type quarks. We present predictions for $a_{tj}$ (colour-coded) at the 14\,TeV LHC, compared with current constraints from tops$+\met$ (light grey) and jets$+\met$ (dark grey) searches, for $D_2 = 0$, $M_Y = 1200$\,GeV, and $M_X = 400$\,GeV (left); we also show the correlations between predictions for $a_{tj}$ and the total single-top cross section $\sigma_\text{tot}$ as defined in the denominator of \eqref{eq:atj}, for viable scenarios featuring canonical DM freeze-out (green) and conversion-driven freeze-out (blue). Here, $D_i$ represent the DM coupling strengths to the $i^\mathrm{th}$ generation, and the figures have been adapted from \cite{Acaroglu:2023phy}. |
 | Exclusion limits at 95\% confidence level (CL) for the composite DM model with partial compositeness considered. Results are shown in the $(M_Y, M_X)$ plane, where $M_Y$ is the common mediator mass, $M_X$ the DM mass, and with fixed new physics couplings of $1$. The left panel displays the region yielding the correct DM relic abundance (green), and exclusions from LHC new physics searches (blue, solid) and SM measurements (red, dashed). The right panel shows the most sensitive analysis pool at each grid point, to which we superimpose 95\% observed (solid), 68\% CL observed (dashed), and 95\% CL expected (dotted) exclusions. Analysis pools include $\ell^+\ell^-\gamma$ (light brown), $\met+$jets (green), hadronic $t\bar{t}$ (dark brown), and $\ell+\met+$jet measurements, with the black area denoting the unconstrained region. |
 | Exclusion limits at 95\% confidence level (CL) for the composite DM model with partial compositeness considered. Results are shown in the $(M_Y, M_X)$ plane, where $M_Y$ is the common mediator mass, $M_X$ the DM mass, and with fixed new physics couplings of $1$. The left panel displays the region yielding the correct DM relic abundance (green), and exclusions from LHC new physics searches (blue, solid) and SM measurements (red, dashed). The right panel shows the most sensitive analysis pool at each grid point, to which we superimpose 95\% observed (solid), 68\% CL observed (dashed), and 95\% CL expected (dotted) exclusions. Analysis pools include $\ell^+\ell^-\gamma$ (light brown), $\met+$jets (green), hadronic $t\bar{t}$ (dark brown), and $\ell+\met+$jet measurements, with the black area denoting the unconstrained region. |
 | Representative Feynman diagram for scalar sextet mediator production in association with a $W$ boson in the fDM model, followed by a leptonic $W$ decay and a $\varphi$ decay to same-sign top quarks. |
 | Cross section for scalar mediator production in association with a $W$ boson at the LHC, for the fDM scenario considered. Results are inclusive with respect to the $W$-boson decay, but the mediator $\varphi$ is enforced to decay into a same-sign top pair. Calculation applies to the benchmark scenario defined in~\eqref{eq:lambda_benchmark}, and for a hadronic centre-of-mass energy of $\sqrt{S} = 14$~\text{TeV}. A flat $K$ factor of 1.3 is included to estimate the NLO yields~\cite{Han:2009ya}. |
 | Distribution in the leading fat jet transverse momentum $p_T(J_1)$ (left), and in the invariant mass $m_{J_1J_2}$ of the pair of leading fat jets (right), for a signal scenario with $M_{\varphi}=1.3$~TeV (\ie\ $\varphi_Y \to tt$ production in association with a $W^{\pm}$ boson, followed by a leptonic $W$-boson decay and hadronic top decays), and the two components of the irreducible SM background. |
 | Distribution in the leading fat jet transverse momentum $p_T(J_1)$ (left), and in the invariant mass $m_{J_1J_2}$ of the pair of leading fat jets (right), for a signal scenario with $M_{\varphi}=1.3$~TeV (\ie\ $\varphi_Y \to tt$ production in association with a $W^{\pm}$ boson, followed by a leptonic $W$-boson decay and hadronic top decays), and the two components of the irreducible SM background. |
 | Projected LHC sensitivity $\mathcal{S}$ (left) to the considered fDM colour-sextet scalar signal and associated exclusion (right), following the search strategy proposed. Our sensitivity predictions are given as a function of the HL-LHC integrated luminosity, the exclusion ones for $\mathcal{L} = 3\,\text{ab}^{-1}$, and we take $\mathcal{S} = 2$ as an estimate of the 95\%~CL exclusion threshold. |
 | Projected LHC sensitivity $\mathcal{S}$ (left) to the considered fDM colour-sextet scalar signal and associated exclusion (right), following the search strategy proposed. Our sensitivity predictions are given as a function of the HL-LHC integrated luminosity, the exclusion ones for $\mathcal{L} = 3\,\text{ab}^{-1}$, and we take $\mathcal{S} = 2$ as an estimate of the 95\%~CL exclusion threshold. |
 | Feynman diagram representative of LHC processes relevant for an FPVDM scenario with top-partners (left), and regions of the parameter space excluded by the results of the LHC at the 95\% confidence level (right). We consider exclusion limits projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV, and $g_D = 0.3$. Cross section isolines for $hV^\prime$ and $V^\prime V^\prime$ production processes are also displayed, together with the regions related to non-perturbativity and large kinetic mixing (hatched areas). The blue regions correspond to non-physical scenarios where $t_D$ is heavier than $T$ or lighter than the top quark. |
 | Feynman diagram representative of LHC processes relevant for an FPVDM scenario with top-partners (left), and regions of the parameter space excluded by the results of the LHC at the 95\% confidence level (right). We consider exclusion limits projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV, and $g_D = 0.3$. Cross section isolines for $hV^\prime$ and $V^\prime V^\prime$ production processes are also displayed, together with the regions related to non-perturbativity and large kinetic mixing (hatched areas). The blue regions correspond to non-physical scenarios where $t_D$ is heavier than $T$ or lighter than the top quark. |
 | Feynman diagram representative of LHC processes relevant for an FPVDM scenario with top-partners (left), and regions of the parameter space excluded by the results of the LHC at the 95\% confidence level (right). We consider exclusion limits projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV, and $g_D = 0.3$. Cross section isolines for $hV^\prime$ and $V^\prime V^\prime$ production processes are also displayed, together with the regions related to non-perturbativity and large kinetic mixing (hatched areas). The blue regions correspond to non-physical scenarios where $t_D$ is heavier than $T$ or lighter than the top quark. |
 | Feynman diagram representative of LHC processes relevant for an FPVDM scenario with top-partners (left), and regions of the parameter space excluded by the results of the LHC at the 95\% confidence level (right). We consider exclusion limits projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV, and $g_D = 0.3$. Cross section isolines for $hV^\prime$ and $V^\prime V^\prime$ production processes are also displayed, together with the regions related to non-perturbativity and large kinetic mixing (hatched areas). The blue regions correspond to non-physical scenarios where $t_D$ is heavier than $T$ or lighter than the top quark. |
 | Representative Feynman diagram of a multi-fermion final state achievable with the FPVDM scenario. |
 | Schematic representation of the coverage of LLP searches in the parameter space defined by the LLP proper lifetime and the associated spectrum mass splitting. Regions corresponding to various cosmological DM production scenarios are also indicated. |
 | Constraints on $t$-channel DM models featuring quark-philic mediators in the freeze-in/superWIMP (non-thermalised) DM production regime, adapted from~\cite{Decant:2021mhj, Belanger:2018sti}. In the left panel, we display the viable region of the parameter space (\ie\ with $\Omega h^2 = 0.12$) of a scenario with a top-philic scalar mediator and a Majorana DM state. Shaded regions indicate exclusions from DV (violet, \cite{ATLAS:2017tny}) and HSCP (blue, \cite{ATLAS:2019gqq}) searches, as well as from structure formation (purple) and BBN (red) (see details in section~\ref{sec:cosmology}). In the right panel, we consider instead a model where a fermionic mediator couples to first-generation quarks and scalar DM, and display again the constraints originating from DV (blue, \cite{ATLAS:2017tny}) and HSCP (purple, \cite{CMS:2016ybj}) searches. In addition, the grey region represents setups with a hot DM candidate. |
 | Constraints on $t$-channel DM models featuring quark-philic mediators in the freeze-in/superWIMP (non-thermalised) DM production regime, adapted from~\cite{Decant:2021mhj, Belanger:2018sti}. In the left panel, we display the viable region of the parameter space (\ie\ with $\Omega h^2 = 0.12$) of a scenario with a top-philic scalar mediator and a Majorana DM state. Shaded regions indicate exclusions from DV (violet, \cite{ATLAS:2017tny}) and HSCP (blue, \cite{ATLAS:2019gqq}) searches, as well as from structure formation (purple) and BBN (red) (see details in section~\ref{sec:cosmology}). In the right panel, we consider instead a model where a fermionic mediator couples to first-generation quarks and scalar DM, and display again the constraints originating from DV (blue, \cite{ATLAS:2017tny}) and HSCP (purple, \cite{CMS:2016ybj}) searches. In addition, the grey region represents setups with a hot DM candidate. |
 | Isolines of constant relic density $\Omega h^2 = 0.12$ for different choices of the DM mass in a leptophilic Majorana DM model with a scalar mediator coupling to right-handed muons. We show constraints stemming from HSCP searches (red, \cite{ATLAS:2019gqq}), ATLAS and CMS displaced lepton searches (green, \cite{ATLAS:2020wjh, CMS:2021kdm}) and disappearing track searches (yellow, \cite{CMS:2020atg}). The plot is adapted from~\cite{Calibbi:2021fld, Junius:2022vzl}. |
 | Isolines of constant reheating temperature $T_\text{rh}$ expressed in the $(M_Y, c\tau)$ plane, for scenarios accounting for the observed DM relic abundance and a DM mass of 12~keV for a muon-philic Majorana DM model (left), and 10~keV for a top-philic model with scalar DM (right). In the left panel, adapted from~\cite{Becker:2023tvd}, we study the impact of the reheating potential $V(\Phi) \sim \Phi^k$, and consider $T_\text{rh} = 20\,\text{GeV}$ (blue), $100\,\text{GeV}$ (black) and $10^4\,\text{GeV}$ (red, with details of reheating being no longer relevant for the considered mediator masses). Solid lines apply to $k = 2$, while dashed and dot-dashed lines illustrate fermionic and bosonic reheating scenarios for $k = 4$ potentials respectively. Various constraints from LLP searches are additionally shown as grey-shaded regions. In the right panel, adapted from~\cite{Calibbi:2021fld}, we consider $k=2$, vary $T_\text{rh}$, and show collider constraints from DJ (blue, \cite{CMS:2019qjk}), DV (green, \cite{ATLAS:2017tny, ATLAS:2020xyo}) and DL (dark green, \cite{ATLAS:2020wjh}) searches. |
 | Isolines of constant reheating temperature $T_\text{rh}$ expressed in the $(M_Y, c\tau)$ plane, for scenarios accounting for the observed DM relic abundance and a DM mass of 12~keV for a muon-philic Majorana DM model (left), and 10~keV for a top-philic model with scalar DM (right). In the left panel, adapted from~\cite{Becker:2023tvd}, we study the impact of the reheating potential $V(\Phi) \sim \Phi^k$, and consider $T_\text{rh} = 20\,\text{GeV}$ (blue), $100\,\text{GeV}$ (black) and $10^4\,\text{GeV}$ (red, with details of reheating being no longer relevant for the considered mediator masses). Solid lines apply to $k = 2$, while dashed and dot-dashed lines illustrate fermionic and bosonic reheating scenarios for $k = 4$ potentials respectively. Various constraints from LLP searches are additionally shown as grey-shaded regions. In the right panel, adapted from~\cite{Calibbi:2021fld}, we consider $k=2$, vary $T_\text{rh}$, and show collider constraints from DJ (blue, \cite{CMS:2019qjk}), DV (green, \cite{ATLAS:2017tny, ATLAS:2020xyo}) and DL (dark green, \cite{ATLAS:2020wjh}) searches. |
 | Representation of a typical cosmologically viable parameter space for $t$-channel DM scenarios featuring a bottom-philic scalar mediator~\cite{Garny:2021qsr}, adapted from~\cite{Heisig:2024xbh}. The black line separates the WIMP and CDFO regimes, where in the latter the mediator decay length is displayed via the colour code. We recall that in the WIMP regime decays are prompt. |
 | LHC constraints on the parameter space of a scenario featuring a bottom-philic mediator and DM production in the CDFO regime~\cite{Heisig:2024xbh}. We display constraints from LHC searches for disappearing tracks (green, \cite{CMS:2020atg}), displaced vertices (red, \cite{ATLAS:2017tny}) and monojet searches (blue, \cite{CMS:2021far}). |
 | LHC constraints on the parameter space of a scenario featuring a muon-philic Majorana DM state and a scalar mediator, where the observed relic density is achieved within the CDFO regime~\cite{Junius:2019dci}. The blue contours correspond to isolines of correct relic abundance for different values of the mass splitting $\Delta m$, and we display constraints from LHC searches for HSCP (red, \cite{CMS:2016ybj, CMS:2015lsu}), and disappearing tracks (purple and green, \cite{CMS:2018rea, ATLAS:2017oal}). For this illustrative case a quartic coupling of $\lambda_H=0.1$ has been assumed between the scalar mediator and the SM Higgs boson. |
 | Constraints on CDFO flavoured DM scenarios, shown as a function of the proper lifetime and mass of the mediator (left, adapted from~\cite{Heisig:2024mwr}) and the heavier dark states (right, adapted from~\cite{Acaroglu:2023phy}). In the left panel, the blue and red lines represent slices in the parameter space of a leptophilic two-flavour model that simultaneously account for the observed DM abundance and successful leptogenesis (excluding the regions shown with faint colours). The solid shaded areas indicate current LHC constraints, while the transparent light blue areas illustrate projected sensitivities from dedicated searches. In the right panel, cosmologically viable points are shown for a three-flavour quark-philic model. The green and blue points represent the decay lengths of the heavier DM multiplet states $X_2$ and $X_1$, respectively, as functions of the mass of the heaviest state $X_1$. |
 | Constraints on CDFO flavoured DM scenarios, shown as a function of the proper lifetime and mass of the mediator (left, adapted from~\cite{Heisig:2024mwr}) and the heavier dark states (right, adapted from~\cite{Acaroglu:2023phy}). In the left panel, the blue and red lines represent slices in the parameter space of a leptophilic two-flavour model that simultaneously account for the observed DM abundance and successful leptogenesis (excluding the regions shown with faint colours). The solid shaded areas indicate current LHC constraints, while the transparent light blue areas illustrate projected sensitivities from dedicated searches. In the right panel, cosmologically viable points are shown for a three-flavour quark-philic model. The green and blue points represent the decay lengths of the heavier DM multiplet states $X_2$ and $X_1$, respectively, as functions of the mass of the heaviest state $X_1$. |
 | In the left panel, we show the two-dimensional distribution in the number of displaced vertices as a function of their invariant mass $m_\text{DV}$ and their number of tracks $n_\text{trk}$, for a quark-philic CDFO benchmark scenario with $M_{Y} = 481$~GeV, $\Delta m = 31$~GeV and $\lambda = 3.9 \times 10^{-7}$~\cite{Heisig:2024xbh}. In the right panel, we examine how the parameter space region excluded by the ATLAS DV search depends on the specific requirements on the displaced vertices, as detailed in the text. |
 | In the left panel, we show the two-dimensional distribution in the number of displaced vertices as a function of their invariant mass $m_\text{DV}$ and their number of tracks $n_\text{trk}$, for a quark-philic CDFO benchmark scenario with $M_{Y} = 481$~GeV, $\Delta m = 31$~GeV and $\lambda = 3.9 \times 10^{-7}$~\cite{Heisig:2024xbh}. In the right panel, we examine how the parameter space region excluded by the ATLAS DV search depends on the specific requirements on the displaced vertices, as detailed in the text. |
 | Kinematic properties of an LLP signal relevant to design new LLP searches at the 13.6\,TeV LHC, emerging from a typical quark-philic CDFO scenario. We consider the distribution in the charged $R$-hadron decay length (upper left) for a benchmark with $c \tau \simeq 1$~cm (blue) and $30$~cm (orange), the $p_T$ distributions of prompt (blue) and displaced (orange) jets with $p_T(j) > 25$~GeV and $|\eta(j)| < 5$ (upper right) as well as the associated prompt (blue) and displaced (orange) jet multiplicity spectrum (lower left), and the $\met$ distribution (lower right). |
 | Kinematic properties of an LLP signal relevant to design new LLP searches at the 13.6\,TeV LHC, emerging from a typical quark-philic CDFO scenario. We consider the distribution in the charged $R$-hadron decay length (upper left) for a benchmark with $c \tau \simeq 1$~cm (blue) and $30$~cm (orange), the $p_T$ distributions of prompt (blue) and displaced (orange) jets with $p_T(j) > 25$~GeV and $|\eta(j)| < 5$ (upper right) as well as the associated prompt (blue) and displaced (orange) jet multiplicity spectrum (lower left), and the $\met$ distribution (lower right). |
 | Kinematic properties of an LLP signal relevant to design new LLP searches at the 13.6\,TeV LHC, emerging from a typical quark-philic CDFO scenario. We consider the distribution in the charged $R$-hadron decay length (upper left) for a benchmark with $c \tau \simeq 1$~cm (blue) and $30$~cm (orange), the $p_T$ distributions of prompt (blue) and displaced (orange) jets with $p_T(j) > 25$~GeV and $|\eta(j)| < 5$ (upper right) as well as the associated prompt (blue) and displaced (orange) jet multiplicity spectrum (lower left), and the $\met$ distribution (lower right). |
 | Kinematic properties of an LLP signal relevant to design new LLP searches at the 13.6\,TeV LHC, emerging from a typical quark-philic CDFO scenario. We consider the distribution in the charged $R$-hadron decay length (upper left) for a benchmark with $c \tau \simeq 1$~cm (blue) and $30$~cm (orange), the $p_T$ distributions of prompt (blue) and displaced (orange) jets with $p_T(j) > 25$~GeV and $|\eta(j)| < 5$ (upper right) as well as the associated prompt (blue) and displaced (orange) jet multiplicity spectrum (lower left), and the $\met$ distribution (lower right). |
 | Schematic plot showing the dependence of the relic density, $\Omega h^2$, on the DM coupling $\lambda$ for a scenario with a relatively small mass splitting between the DM particle $X$ and the $t$-channel mediator $Y$. The blue band indicates the region for which $\Omega h^2=0.12$ and depends on the new physics masses $M_X$ and $M_Y$. The numbers for $\lambda$ indicate rough orders of magnitude, and are model-dependent. The four characteristic production regimes are further discussed in sections~\ref{sec:FO}, \ref{sec:conv}, \ref{sec:FI} and \ref{sec:SW}, respectively, in the order of decreasing coupling strength $\lambda$. This leads to a distinct phenomenology in each case. |
 | Representative LO Feynman diagrams contributing to the DM annihilation cross section $\langle \sigma_\text{eff} v \rangle$. They include $t$-channel DM annihilations (top left), $XY$ co-annihilations (top central and right), and mediator pair-annihilations (bottom row) with the blob accounting for channels yielding SM electroweak bosons or gluons. The final state $q$ represents any quark flavour, and may include a sum over flavours depending on the model. For leptophilic models, $q$ can be replaced by a lepton $\ell$, and for models with self-conjugate DM, additional $YY$ annihilation diagrams must be added. Moreover, in cases where the S-wave contribution to $\langle \sigma_\text{ann} v \rangle (X\bar{X} \to q\bar{q})$ is helicity suppressed, NLO corrections become relevant (see the diagrams in figure~\ref{fig:indirect}). |
 | Diagramatic representation of bound state ($\cal B$) formation of two coloured particles via the emission of a gluon, and of the Sommerfeld Effect relevant for the initial state. Figure adapted from~\cite{Becker:2022iso}. |
 | VIB and loop-induced processes contributing to DM indirect detection through the production of gamma-ray lines and other features in the gamma-ray spectrum. |
 | Illustrative Feynman diagrams contributing to DM-nucleon scattering, where we select as an example the case of fermionic DM. We include all diagrams that account for the scattering off gluons at one-loop and that are always present regardless of the model details (top row), tree-level scattering (relevant if the DM couples to an up or down quark) and the one-loop exchange of a photon, $Z$ boson or Higgs boson (bottom row). |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Constraints on minimal simplified $t$-channel DM models from cosmological and astrophysical observables, as well as from the measured $Z$-boson visible decay width. The coloured region in the $(M_X, M_Y/M_X - 1)$ plane represents scenarios that achieve $\Omega h^2 \simeq 0.12$, with the coupling value $\lambda$ indicated by the grey-scale colour map. The left (right) panels correspond to models with self-conjugate (complex) DM, featuring scalar (top row), fermionic (middle row), and vector (bottom row) DM particles. The hatched regions indicate exclusions from gamma-ray searches (`ID gamma rays', including gamma-line searches from Fermi-LAT~\cite{Fermi-LAT:2015kyq} and HESS~\cite{HESS:2018cbt} from the galactic centre and gamma-ray continuum searches in dSPhs by Fermi-LAT~\cite{Fermi-LAT:2016uux}), cosmic-ray antiproton searches (`ID antiprotons'), DM direct detection via spin-independent and spin-dependent interactions (`DD SI' and `DD SD,' respectively, including limits from LZ~\cite{LZ:2022ufs}, PICO-60~\cite{PICO:2017tgi}, CRESST-III~\cite{CRESST:2019jnq} and DarkSide-50~\cite{DarkSide:2018bpj}), and $Z$-boson visible decays (`Z decay', from~\cite{Zyla:2020zbs}). The blank upper region corresponds to scenarios requiring non-perturbative couplings, while the white region at the bottom represents the CDFO regime (see section~\ref{sec:BMquarkconversiondriven}). This figure is taken from~\cite{Arina:2023msd}, where further details can be found. |
 | Cosmologically viable region of the parameter space of models featuring a DM state coupling to the right-handed top quark $t_R$ (with $\Omega h^2 = 0.12$), and constraints shown as functions of the DM mass $M_X$ and the relative mass splitting $M_Y / M_X - 1$. The left panel corresponds to Majorana DM, while the right panel depicts a scenario with real scalar DM. These plots are based on the results from~\cite{Garny:2018icg} and~\cite{Colucci:2018vxz}, respectively, and the direction detection (DD) constraints on both plots are derived from the XENON1T bounds. The thick black line separates the WIMP region (above) from the CDFO region (see section~\ref{sec:BMquarkconversiondriven}), and the shaded regions denote exclusions due to the various experimental and theoretical constraints discussed in the text. |
 | Cosmologically viable region of the parameter space of models featuring a DM state coupling to the right-handed top quark $t_R$ (with $\Omega h^2 = 0.12$), and constraints shown as functions of the DM mass $M_X$ and the relative mass splitting $M_Y / M_X - 1$. The left panel corresponds to Majorana DM, while the right panel depicts a scenario with real scalar DM. These plots are based on the results from~\cite{Garny:2018icg} and~\cite{Colucci:2018vxz}, respectively, and the direction detection (DD) constraints on both plots are derived from the XENON1T bounds. The thick black line separates the WIMP region (above) from the CDFO region (see section~\ref{sec:BMquarkconversiondriven}), and the shaded regions denote exclusions due to the various experimental and theoretical constraints discussed in the text. |
 | Constraints on a simplified DM model featuring three mass-degenerate mediators universally coupling to a Majorana DM candidate and all generations of SM right-handed up quarks. The blue solid lines are isocontours with fixed $\lambda$, as labelled. The black-shaded region represents parameter values where avoiding DM overproduction would violate perturbative unitarity. The green and magenta areas show exclusions from spin-independent and spin-dependent direct detection experiments, respectively, and the grey-shaded region corresponds to a DM relic density explained through the CDFO mechanism. The results incorporate the effects of bound states, including their excitations, on freeze-out dynamics. This plot is adapted from~\cite{Becker:2022iso}. |
 | Parameter space regions of a bottom-philic Majorana fermion DM model~\cite{Garny:2021qsr} compatible with the observed relic density. The left panel shows the required couplings and the resulting decay length of the mediator, with the CDFO region lying below the thick black line. The results account for Sommerfeld enhancement and excited bound state effects. The right panel highlights the significance of bound state effects in this scenario, showing the CDFO contour’s boundary (solid lines) along with isolines of constant $\lambda$ values in the canonical freeze-out regime (dashed lines). Results including Sommerfeld enhancement and bound state effects are shown in blue, while those without these effects are shown in red. |
 | Parameter space regions of a bottom-philic Majorana fermion DM model~\cite{Garny:2021qsr} compatible with the observed relic density. The left panel shows the required couplings and the resulting decay length of the mediator, with the CDFO region lying below the thick black line. The results account for Sommerfeld enhancement and excited bound state effects. The right panel highlights the significance of bound state effects in this scenario, showing the CDFO contour’s boundary (solid lines) along with isolines of constant $\lambda$ values in the canonical freeze-out regime (dashed lines). Results including Sommerfeld enhancement and bound state effects are shown in blue, while those without these effects are shown in red. |
 | Regions of the top-philic Majorana DM model compatible with DM production through the freeze-in and superWIMP regime, and existing cosmological constraints as studied in~\cite{Decant:2021mhj}. The plot highlights the interplay between these two DM production processes across the parameter space (long dashed lines). Relevant constraints from structure formation (purple) and BBN (red) are also indicated. In addition, isolines of constant $\lambda$ values and of constant mediator decay length are shown in green and grey, respectively. |
 | Viable regions of the parameter space of a simplified \lstinline{S1M_muR} leptophilic DM model where a Majorana DM particle couples to right-handed muons. In the left panel (adapted from \cite{Garny:2015wea}), results assume that the relic abundance is achieved through thermal freeze-out, while the region where the measured abundance could be reproduced within conversion driven freeze out production region is shown in the lower left corner. Projected constraints from indirect and direct detection are shown through the dashed blue and purple areas, while LEP limits are given in green. The figure in the right panel is dedicated to the CDFO regime and is adapted from \cite{Junius:2019dci}. Here, the Higgs-portal coupling is set to $\lambda_H=0.5$, and the blue lines are isolines of constant $\lambda/10^{-6}$ values. |
 | Viable regions of the parameter space of a simplified \lstinline{S1M_muR} leptophilic DM model where a Majorana DM particle couples to right-handed muons. In the left panel (adapted from \cite{Garny:2015wea}), results assume that the relic abundance is achieved through thermal freeze-out, while the region where the measured abundance could be reproduced within conversion driven freeze out production region is shown in the lower left corner. Projected constraints from indirect and direct detection are shown through the dashed blue and purple areas, while LEP limits are given in green. The figure in the right panel is dedicated to the CDFO regime and is adapted from \cite{Junius:2019dci}. Here, the Higgs-portal coupling is set to $\lambda_H=0.5$, and the blue lines are isolines of constant $\lambda/10^{-6}$ values. |
 | Viable regions of the parameter space of flavoured Majorana DM scenarios~\cite{Acaroglu:2023phy} in which the dark matter couples to right-handed up quarks. Constraints from the observed dark matter relic abundance, direct and indirect detection experiments, and flavour data are shown as a function of the DM mass $m_{X_3}$ and the mass splitting between the dark matter and the mediator $\Delta m_{Y3}$. On the left panel, the \mbox{(co-)annihilation} freeze-out regime is considered, with QDF scenarios shown in green, SFF ones in yellow, and generic ones in blue. On the right panel, the CDFO regime is examined instead, with conversions between $X_3/X_2$ (yellow), $X_3/Y$ (blue), and combined $X_3/X_2/Y$ (green). |
 | Viable regions of the parameter space of flavoured Majorana DM scenarios~\cite{Acaroglu:2023phy} in which the dark matter couples to right-handed up quarks. Constraints from the observed dark matter relic abundance, direct and indirect detection experiments, and flavour data are shown as a function of the DM mass $m_{X_3}$ and the mass splitting between the dark matter and the mediator $\Delta m_{Y3}$. On the left panel, the \mbox{(co-)annihilation} freeze-out regime is considered, with QDF scenarios shown in green, SFF ones in yellow, and generic ones in blue. On the right panel, the CDFO regime is examined instead, with conversions between $X_3/X_2$ (yellow), $X_3/Y$ (blue), and combined $X_3/X_2/Y$ (green). |
 | Limits from direct and indirect searches (XENON1T and Fermi-LAT) on a fDM realisation featuring Dirac DM and colour-sextet mediators. Here the scalar is taken to couple to pairs of like-sign up-type quarks, preferentially to the third generation. |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Constraints on the parameter space of a composite $t$-channel DM scenario featuring one DM state $X$, two mediator states $Y$ (that is $\mathbb{Z}_2$ odd) and $Y'$ (that is $\mathbb{Z}_2$-even), and the two new physics couplings $\lambda_t$ and $\lambda'_t$ of the Lagrangian~\eqref{eq:lagtopcompoDM}. Results are given in the $(\lambda_t, \lambda'_t)$ plane, and the value of the masses in GeV, represented through the colour code, are determined so that the relic density matches observations. The top, central and bottom rows respectively address the masses $M_X$, $M_Y$ and $M_{Y'}$, and we consider the mass hierarchies $M_{Y'} |
 | Representative Feynman diagrams for $t$-channel and resonant contributions to DM annihilation and DM-mediator co-annihilation processes (top), and processes relevant for direct detection experiments (bottom). |
 | Representative Feynman diagrams for $t$-channel and resonant contributions to DM annihilation and DM-mediator co-annihilation processes (top), and processes relevant for direct detection experiments (bottom). |
 | Representative Feynman diagrams for $t$-channel and resonant contributions to DM annihilation and DM-mediator co-annihilation processes (top), and processes relevant for direct detection experiments (bottom). |
 | Representative Feynman diagrams for $t$-channel and resonant contributions to DM annihilation and DM-mediator co-annihilation processes (top), and processes relevant for direct detection experiments (bottom). |
 | Representative Feynman diagrams for $t$-channel and resonant contributions to DM annihilation and DM-mediator co-annihilation processes (top), and processes relevant for direct detection experiments (bottom). |
 | Excluded and allowed parameter space regions of the considered FPVDM realisation, as obtained from a full five-dimensional scan of the parameters in \eqref{eq:fpvdm_prm}. Results are projected in the $(m_{V_D}, g_D)$ plane and include scenarios compatible with observations by virtue of $t$-channel annihilations (green), $H$-funnel resonant contributions (cyan) and co-annihilations (blue), as well as under-abundant (grey) and overabundant (red) DM setups. Constraints from indirect and direct detection are additionally displayed through the orange and magenta regions, while white areas represent a non-perturbative regime. |
 | Excluded regions of the considered FPVDM realisation by cosmological observables projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV and $g_D =$ 0.05 (left) or 0.3 (right). Non-perturbative and large kinetic-mixing regions are also shown as hatched areas. |
 | Excluded regions of the considered FPVDM realisation by cosmological observables projected onto the $(m_{t_D}, m_{V_D})$ plane for $m_T = 1600$ GeV, $m_H = 1000$ GeV and $g_D =$ 0.05 (left) or 0.3 (right). Non-perturbative and large kinetic-mixing regions are also shown as hatched areas. |
 | Excluded region at the 95$\%$ CL, displayed in the $(m_{\tilde{t}_1}, m_{\tilde{\chi}^{0}_{1}})$ mass plane for the $p p \to \tilde{t}_1 \tilde{t}_1^* \to (c \tilde{\chi}^{0}_{1}) (\bar{c} \tilde{\chi}^{0}_{1})$ (left) and $p p \to \tilde{t}_1 \tilde{t}_1^* \to ( b f\bar{f}^\prime \tilde{\chi}^{0}_{1}) (\bar{b} f\bar{f}^\prime \tilde{\chi}^{0}_{1})$ (right) processes. The green crosses and red dots respectively correspond to scenarios allowed and excluded when using our implementation of the ATLAS-EXOT-2018-06 analysis in \lstinline{MadAnalysis 5}. The excluded parameter space regions are thus delineated by the green contours, that could be compared to the official ATLAS exclusions (black). |
 | Excluded region at the 95$\%$ CL, displayed in the $(m_{\tilde{t}_1}, m_{\tilde{\chi}^{0}_{1}})$ mass plane for the $p p \to \tilde{t}_1 \tilde{t}_1^* \to (c \tilde{\chi}^{0}_{1}) (\bar{c} \tilde{\chi}^{0}_{1})$ (left) and $p p \to \tilde{t}_1 \tilde{t}_1^* \to ( b f\bar{f}^\prime \tilde{\chi}^{0}_{1}) (\bar{b} f\bar{f}^\prime \tilde{\chi}^{0}_{1})$ (right) processes. The green crosses and red dots respectively correspond to scenarios allowed and excluded when using our implementation of the ATLAS-EXOT-2018-06 analysis in \lstinline{MadAnalysis 5}. The excluded parameter space regions are thus delineated by the green contours, that could be compared to the official ATLAS exclusions (black). |