Studies of dark matter lie at the interface of collider physics, astrophysics and cosmology. Constraining models featuring dark matter candidates entails the capability to provide accurate predictions for large sets of observables and compare them to a wide spectrum of data. We present a framework which, starting from a model Lagrangian, allows one to consistently and systematically make predictions, as well as to confront those predictions with a multitude of experimental results. As an application, we consider a class of simplified dark matter models where a scalar mediator couples only to the top quark and a fermionic dark sector (i.e. the simplified top-philic dark matter model). We study in detail the complementarity of relic density, direct/indirect detection and collider searches in constraining the multi-dimensional model parameter space, and efficiently identify regions where individual approaches to dark matter detection provide the most stringent bounds. In the context of collider studies of dark matter, we point out the complementarity of LHC searches in probing different regions of the model parameter space with final states involving top quarks, photons, jets and/or missing energy. Our study of dark matter production at the LHC goes beyond the tree-level approximation and we show examples of how higher-order corrections to dark matter production processes can affect the interpretation of the experimental results.

Article funded by SCOAP3

m_t, \mdm$
decay predominantly into pairs of top quarks and/or dark matter particles, where the
exact details of the partial width values strongly depend on the masses and couplings. The
branching ratio of $\y$ to photons is always
suppressed, as argued above. We present in appendix~\ref{sec:ywidth}
the dependence of the $\Gamma_Y/m_Y$ ratio on the $g_t$ and $g_X$ couplings for
different mass choices and on the $m_Y$ and $m_X$ masses for different coupling choices.
\begin{table}
\centering
\renewcommand{\arraystretch}{2.0}
\begin{tabular}{|l|p{1.30cm}clp{3.3cm}|}
\hline
& & \raisebox{-.4\height}{\includegraphics[height=1cm]{diagrams/id_tt.pdf}} & $\mdm>m_t$ & \\
Cosmology &relic$\qquad~$ indirect& \raisebox{-.4\height}{\includegraphics[height=1cm]{diagrams/id_aa.pdf}} & $\mdm

m_t$, and by annihilation into gluons and to a lesser extent photons for light dark matter particles with $\mdm < m_t$. If the mediator is lighter than the dark matter state, an additional annihilation channel into a pair of mediators can open up. The annihilation mechanisms into top-quarks, gluons/photons and mediators moreover provide an opportunity to indirectly search for dark matter, \eg~in gamma-ray data. The interactions of the dark matter particles with nuclei, relevant for direct detection experiments, proceed via mediator exchanges. The mediator-nucleon coupling is in turn dominated by the scattering off gluons through top-quark loops. Dark matter production at the LHC proceeds either through the production of the mediator in association with top quarks, or from gluon-fusion through top-quark loops. Searches at the LHC can be classified into two categories regarding the nature of the final states that can contain missing transverse energy $\MET$ or not. Searches involving missing energy may include final state systems containing a top-quark pair and probe in this way the associated production of a top-antitop-mediator system where the mediator subsequently decays into a pair of dark matter particles. Alternatively, the mediator can be produced via gluon fusion through top-quark loops, where the probe of the associated events consists of tagging an extra radiated object. This yields the well-known monojet, mono-$Z$ and mono-Higgs signatures. We do not consider the monophoton channel, as photon emission is forbidden at LO in our simplified model by means of charge conjugation invariance. The second search category is related to final states without any missing energy, \ie~when the mediator decays back into Standard Model particles. This includes decays into top-quarks, leading to final states comprised of four top quarks, into a top-quark pair, as well as into a dijet or a diphoton system via a loop-induced decay. This is, however, relevant only for on-shell (or close to on-shell) mediator production. We proceed with a description of the numerical setup for our calculations. In the following sections, we explore the full four-dimensional model parameter space and present results in terms of two-dimensional projections. We perform the four-dimensional sampling using the \MN\ algorithm~\cite{Feroz-ml-2007kg, Feroz-ml-2008xx}, where we assume Jeffeys' prior on all the free parameters in order not to favour a particular mass or coupling scale. The choice of prior ranges for the parameters is summarised in table~\ref{tab:param}, in which we have chosen to limit the coupling values to a maximum of $\pi$ to ensure perturbativity. We implement the relic density constraints into {\sc MultiNest} using a Gaussian likelihood profile, while for the direct detection limits we assume a step likelihood function smoothed with half a Gaussian. In addition, the sampling imposes that the model is consistent with values of $\wy$ such that the mediator $\y$ decays promptly within the LHC detectors. Table~\ref{tab:co} summarises the constraints that we have imposed on the model parameter space. \begin{table} \centering \renewcommand\arraystretch{1.2} \begin{tabular}{|c c|} \hline {\sc MultiNest} parameter & Prior \\ \hline $\log(\mdm/\GeV)$ & $0 \to 3$ \\ $\log(\my/ \GeV)$ & $0 \to 3.7$ \\ $\log(\gx)$ & $-4 \to \log(\pi)$ \\ $\log(\gsm)$ & $-4 \to \log(\pi)$ \\ \hline \end{tabular} \renewcommand\arraystretch{1.0} ]]>

8$\,GeV}~\cite{Akerib-ml-2013tjd} and by CDMSLite for \mbox{1\,GeV$<\mdm<8$\,GeV}~\cite{Agnese-ml-2015nto}. In section~\ref{sec:dm_id}, we focus on indirect detection constraints that are imposed on the basis of the gamma-ray measurements achieved by the Fermi-LAT telescope~\cite{Ackermann-ml-2015zua,Ackermann-ml-2015lka}. Those bounds are however not applied at the level of the likelihood function encoded in our \MN\ routine, and we have chosen instead to reprocess the scan results for those parameter points that are consistent with both the relic density and direct detection considerations. For the purpose of the relic density and direct detection cross section calculations, we utilise both the \MD~\cite{Backovic-ml-2013dpa, Backovic-ml-2015cra} and \MO~\cite{Belanger-ml-2014vza} numerical packages, although we only present the results obtained with \MD. The consistency checks that we have performed with both codes are detailed in appendix~\ref{sec:cc}.} \begin{table} \centering \renewcommand\arraystretch{1.2} {\footnotesize\begin{tabular}{| c c c l |} \hline & Observable & Value/Constraint & Comment\\ \hline \emph{\underline{Measurement}} & $\Omega_{\rm DM} h^2$ & $ 0.1198 \pm 0.0015 $ & Planck 2015~\cite{Planck-ml-2015xua} \\ \hline \emph{\underline{Limits}} & $\wy/\my$ & $ < 0.2 $ & Narrow width approximation\\ & $\wy$ & $ > 10^{-11}$\,GeV & Ensures prompt decay at colliders \\ & $ \sigma_{n}^{\rm SI} $ & $ < \sigma^{\rm SI}_{\rm LUX}$ (90\% CL) & LUX bound~\cite{Akerib-ml-2013tjd} ($m_X > 8$\,GeV)\\ & $ \sigma_{n}^{\rm SI} $ & $ < \sigma^{\rm SI}_{\rm CDMS}$ (95\% CL) & CDMSlite bound~\cite{Agnese-ml-2015nto} ($1 \, {\rm GeV} < m_X < 8\, {\rm GeV}$) \\ \hline \end{tabular}} \renewcommand\arraystretch{1.0} ]]>

m_t,\my$ and $\my < 2m_t$: similarly to the case above, the dominant annihilation mechanism is process (III), as annihilation into top quarks occurs far from the resonant pole and is suppressed kinematically; \item for $ \mdm > m_t,\my$ and $\my > 2m_t$: processes (I) and (III) are competitive and the dominant process among the two is determined by the hierarchy between the $\gsm$ and $\gx$ couplings. \end{itemize} Requiring our simplified top-philic dark matter model to result in a dark matter relic density consistent with the most recent Planck measurements~\cite{Planck-ml-2015xua} implies strong constraints on the viable regions of the parameter space. As an illustration, we consider the region of the parameter space in which $m_t \gtrsim \mdm \gtrsim \my$, where we expect the dominant annihilation mechanism of dark matter to be process (III) and to give rise to a pair of mediators. In this region, the thermally averaged annihilation cross section approximately reads \begin{equation} \langle \sigma v_{\rm rel} \rangle_{\rm ann} \sim \frac{\gx^4} { \mdm^2 } \sim 10^{-9} \GeV^{-2}, \end{equation} so that it is clear that imposing that the relic density predictions agree with Planck data leads to a stringent constraint on the ratio $\gx^2/\mdm$. The argument is more involved in parameter space regions where the total mediator width $\wy$ plays a role, as the relevant quantity involved in the relic density calculation is in general not $\langle \sigma v_{\rm rel} \rangle_{\rm ann} $ but $\int {\rm d}x \langle \sigma v_{\rm rel} \rangle_{\rm ann}(x)$ where $x \equiv \mdm/T$ and $\langle \sigma v_{\rm rel} \rangle_{\rm ann}$ is a non trivial function of $x$. This is especially true, for instance, for the Breit-Wigner-type amplitudes that appear in processes (I) and (II). In order to provide a more detailed quantitative analysis, we have performed a four-dimensional scan the top-philic dark matter model parameter space and examined the effects of imposing relic density constraints on the allowed/ruled out parameter sets. Figure~\ref{fig:scan1maddm} reveals the rich structure of the four-dimensional parameter space allowed by relic density measurements. The bulk of the allowed parameter points lies in the region where $\mdm > \my$, and the annihilation cross section is dominantly driven by process (III). This region of the parameter space has the particularity of not being reachable by traditional monojet, monophoton, mono-$Z$ and mono-Higgs searches at colliders. The decay of the mediator into a pair of dark matter particles is indeed not kinematically allowed, so that any new physics signal will not contain a large amount of missing energy. The model can however be probed at colliders via dijet, diphoton, $t\bar{t}$ (plus jets) and four-top analyses. We elaborate on this point more in section~\ref{sec:nonmet}. The characteristic mediator width $\wy$ in this region tends to be extremely small, with values of at most $10^{-4}$\,GeV as shown in the top left panel of figure~\ref{fig:scan1maddm}. This is expected as the width is mostly controlled by the decays into gluons, and into top quarks in the regions where this decay is kinematically allowed, the decay into a pair of dark matter particles being forbidden. \begin{figure} \centering \includegraphics[width=0.49\textwidth]{Plots/maddm_noDD_mDM_mY0_GammaY_clrbar_topg_Y0even_1.pdf}\hfill \includegraphics[width=0.49\textwidth]{Plots/maddm_noDD_mDM_mY0_gSq_clrbar_topg_Y0even_1.pdf}\\ \includegraphics[width=0.49\textwidth]{Plots/maddm_noDD_mDM_mY0_gSXd_clrbar_topg_Y0even_1.pdf}\hfill \includegraphics[width=0.49\textwidth]{Plots/maddm_noDD_mDM_mY0_topg_Y0even_1_zoomin_largemass.pdf} ]]>

10^{-11}$\,GeV (cf.~table~\ref{tab:co}).]]>

10^{-11}$\,GeV (cf.~table~\ref{tab:co}).]]>

10^{-11}$\,GeV and accommodate the direct detection constraints (cf.~table~\ref{tab:co}).]]>

10^{-11}$\,GeV and accommodate the direct detection constraints (cf.~table~\ref{tab:co}).]]>

150$\,GeV) production for a mediator mass of $m_Y=50$ and 100\,GeV and at a centre-of-mass energy of $\sqrt{s}=8$\,TeV given as a function of the dark matter mass. ]]>

150~{\rm GeV})<0.85$\,fb & CMS~\cite{Khachatryan-ml-2015bbl} & Leptonic $Z$-boson decay\\ $\MET+h$ & $\sigma(\MET>150~{\rm GeV})<3.6$\,fb & ATLAS~\cite{Aad-ml-2015dva} & $h\to b\bar b$ decay\\ \hline $jj$ & $\sigma(m_Y=500~{\rm GeV})<10$\,pb & CMS~\cite{CMS-ml-2015neg} & Only when $m_Y>500$\,GeV\\ $\gamma\gamma$ & $\sigma(m_Y=150~{\rm GeV})<30$\,fb & CMS~\cite{Khachatryan-ml-2015qba} & Only when $m_Y>150$\,GeV\\ $t\bar t$ & $\sigma(m_Y=400~{\rm GeV})<3$\,pb & ATLAS~\cite{Aad-ml-2015fna} & Only when $m_Y>400$\,GeV \\ $t\bar t t\bar t$ & $\sigma<32$\,fb & CMS~\cite{Khachatryan-ml-2014sca} & Upper limit on the SM cross section \\ \hline \end{tabular}} ]]>

2m_t$, the $Y_0\to t\bar t$ decay mode is open, and $t\bar t+\MET$ production turns out to be suppressed by the visible decay channels of the mediator, unless $g_X>g_t$. Such a feature has already been illustrated in figure~\ref{fig:width}. The NLO $K$-factors related to $t\bar{t}+\MET$ production (right panel of figure~\ref{fig:ttmet_sigma}) are found to vary from 0.96 to 1.15 in the range of masses examined here, the QCD corrections being more important in the low mass region. \begin{figure} \centering \includegraphics[width=0.48\textwidth]{Plots/dmsimp_LOxsec_LO_g4_ttmet_only_mb.pdf}\hfill \includegraphics[width=0.48\textwidth]{Plots/dmsimp_K_LO_g4_ttmet_only_mb.pdf} ]]>

2 m_t$ leads to a further reduction of the monojet production rate. In comparison with the $t\bar t+\MET$ case, the monojet search overall appears to be more constraining, especially for higher mediator mass values thanks to the larger monojet cross section. \begin{figure} \centering \includegraphics[width=0.48\textwidth]{Plots/dmsimp_DM_g4_monoj_only.pdf} ]]>

$250\,GeV) and populates the different signal regions of the CMS analysis. As a result, a better sensitivity is found than what one might expect from considering the total cross section alone. This feature leads to the exclusion of dark matter scenarios where $\my < 2 \mdm$, as depicted in figure~\ref{fig:monojet_g4}. \begin{table} \centering \renewcommand\arraystretch{1.2} \begin{tabular}{|lc|} \hline ($\my$, $\mdm$) & $\sigma_{\textrm{LO}}$ [pb] \\ \hline (100, 10) GeV & 0.605 \\ (300, 10) GeV & 0.194 \\ (100, 100) GeV & 0.00261 \\ \hline \end{tabular} \renewcommand\arraystretch{1.0} ]]>

$ 150\,GeV selection are shown in the second column. ]]>

20$\,GeV and $|\eta^\ell|<2.5$) are considered. We generate events for this process, and after applying the above fiducial selection requirements we obtain a cross section of 0.30\,fb for $(m_Y,m_X)=(100,10)$\,GeV and $g_t=g_X=1$. We show in figure~\ref{fig:monozh_g4} the $\MET$ and leading lepton transverse momentum distributions (red lines) without and with applying the selection strategy. While we have not performed a detailed study, simple estimates show good prospects for setting limits on the parameter space of the model using the mono-$Z$ analysis results. Using the upper limit of 0.85\,fb, scenarios with couplings close to $g_t\sim2$ could be excluded in the resonant region ($\my > 2 \mdm$) with $\my <100$\,GeV. For larger mediator masses, the cross section starts to fall due to the reduction of the phase space. In the off-shell region ($\my < 2 \mdm$), the mono-$Z$ cross section suffers from the same drastic decrease seen in figure~\ref{fig:xsec} for the $t\bar{t}+\MET$ and monojet cases. The same procedure can be repeated to constrain the parameter space of the model using mono-Higgs events on the basis of the results of the ATLAS search for dark matter production in association with a Higgs boson decaying into two bottom quarks~\cite{Aad-ml-2015dva}. This search results in a 95\% CL upper limit on the visible cross section of 3.6\,fb for a $\MET$ threshold of 150\,GeV. In order to estimate a limit, we generate events for $(m_Y,m_X)=(100,10)$\,GeV and $g_t=g_X=1$, and require the two $b$-quarks to have a transverse momentum $p_T^{b_1}>100$\,GeV and $p_T^{b_2}>25$\,GeV, a pseudorapidity $|\eta^b|<2.5$ and to be separated in the transverse plane by an angular distance $\Delta R(b_1,b_2)<1.5$. Moreover, we only select events exhibiting at least 150\,GeV of missing transverse energy. We show again in figure~\ref{fig:monozh_g4} the $\MET$ and leading $b$-quark transverse momentum distributions (blue lines) without and with applying the above-mentioned selection requirements. We then include a $b$-tagging efficiency of 60\% and extract an upper limit on the $g_t$ coupling by comparing our results to the ATLAS limit. Coupling values of $\gsm>2$ are found to be excluded for $\my > 2 \mdm$ with $\my <100$\,GeV. All other parameter space regions suffer from the same limitations as the mono-$Z$ case. From our naive parton-level analysis, we have seen that mono-$Z$ and mono-Higgs signals show promising signs of setting constraints on the parameter space of the model and therefore deserve dedicated studies, which will be reported elsewhere (see also ref.~\cite{Goncalves-ml-2016bkl}). The sensitivity to such signals will benefit from applying more aggressive $\MET$ thresholds to ensure the reduction of the corresponding backgrounds. As seen in figure~\ref{fig:monozh_g4}, we obtain a rather hard $\MET$ distribution~\cite{Mattelaer-ml-2015haa}, especially for mono-$Z$ production. The result implies that an increase in the $\MET$ threshold requirement in future analyses could lead to a significant improvement of the sensitivity, especially given the the fact that Standard Model backgrounds rapidly fall off with the increase in missing energy. ]]>

2m_t$), $t\bar{t}$ resonance searches~\cite{Aad-ml-2015fna,Khachatryan-ml-2015sma} can be used as probes of the model. In our setup, loop-induced resonant mediator contributions can indeed enhance the $t\bar t$ signal, in particular when there is a large coupling hierarchy ($\gsm\gg g_X$) or mass hierarchy ($2m_t<\my<2\mdm$). We derive constraints on our model from the ATLAS 8\,TeV $t\bar t$ resonance search~\cite{Aad-ml-2015fna} that relies on the reconstruction of the invariant mass of the top-quark pair to derive a 95\% CL exclusion on the existence of a new scalar particle coupling to top quarks. The associated cross section limits range from 3.0~pb for a mass of 400\,GeV to 0.03~pb for $\my=2.5$\,TeV, assuming that the narrow width approximation is valid with a mediator width being of at most $3\%$ of its mass and that there is no interference between the new physics and Standard Model contributions to the $t\bar t$ signal. Constraints are computed using the NNLO mediator production cross section (see figure~\ref{fig:xsec}) and the relevant top-antitop mediator branching ratio derived from the formulas presented in section~\ref{sec:model}. The latter is in fact very close to one in the relevant region, the mediator decays into dark matter particle pairs being kinematically forbidden and those into gluons and photons loop-suppressed. The results are presented in the $(\my, \gsm)$ plane in figure~\ref{fig:nonmet}. This shows that scalar mediators with masses ranging from 400\,GeV to 600\,GeV could be excluded for $\gsm$ couplings in the $[1, 4]$ range, the exact details depending on $\my$ and on the fact that the narrow-width approximation must be valid. This demonstrates the ability of the $t\bar{t}$ channel to probe a significant portion of the $\my > 2m_t$ region of the model parameter space. In the region where $2m_t, \,2\mdm<\my$, the partial decay $\y \to X\bar X$ reduces the $t \bar t$ signal and therefore limits the sensitivity of the search. \paragraph{Four-top signals.} Scenarios featuring a mediator mass above twice the top-quark mass can be probed via a four-top signal, since the mediator can be produced in association with a pair of top quarks and further decay into a top-antitop system. Theoretically, the Standard Model four-top cross section has been calculated with high precision~\cite{Bevilacqua-ml-2012em}, but the sensitivity of the 8\,TeV LHC run was too low to measure the cross section. Instead, an upper limit on the cross section at a centre-of-mass energy of 8\,TeV has been derived~\cite{Chatrchyan-ml-2013fea,Khachatryan-ml-2014sca}. The four-top production rate is constrained to be below 32\,fb~\cite{Khachatryan-ml-2014sca}, a value that has to be compared to the Standard Model prediction of about 1.3\,fb. Only models with new physics contributions well above the background (see \eg~ref.~\cite{Beck-ml-2015cga}) can therefore be constrained by the four-top experimental results. In our top-philic dark matter model, the new physics contributions to the four-top cross section can be approximated by the $t\bar{t}Y_0$ cross section, the branching ratio $B(Y_0\to t\bar t)\sim 1$. Using the NLO cross section (see figure~\ref{fig:xsec}), we derive limits that we represent in the $(m_Y, g_t)$ plane in figure~\ref{fig:nonmet}. A small region of the parameter space with $g_t >2.5$ and in which the mediator mass lies in the $[2m_t, \sim450~{\rm GeV}]$ mass window turns out to be excluded. The weakness of the limit is related to the steeply decreasing cross section for $pp\to Y_0t\bar t$ with the increase in $\my$. \paragraph{The mediator width.} In all the above studies where the final state does not contain any missing energy, the mediator width has been assumed narrow. Concerning the diphoton channel, this assumption holds within the entire excluded region as only loop-suppressed gluon and photon mediator decays are allowed. In the region where $\my>2m_t$, the width of the mediator rises quickly with its mass, and the width over mass ratio rapidly exceeds the 3\% value that has been imposed in the ATLAS $t\bar t$ resonance search~\cite{Aad-ml-2015fna} as can be seen in figure~\ref{fig:nonmet}. The reinterpretation of the ATLAS results to a generic $t\bar{t}$ resonance model should therefore be made carefully, as the limit cannot be necessarily applied to scenarios featuring significantly larger mediator widths. This is shown in figure~\ref{fig:nonmet} by a dotted line, and we can also observe that most of the points that would have been excluded by the ATLAS search do not fulfil the requirement of a width below 3\% of the mediator mass. In our excluded region of the parameter space, we allow the mediator width to reach 8\% of its mass, by the virtue of the experimental resolution on the invariant mass of the $t \bar{t}$ system. This leads to the exclusion of scenarios with mediator masses up to 600\,GeV. The ATLAS resonance $t \bar t$ study claims that varying the width of the resonance from 10\% to 40\% for the massive gluon model results in a loss in sensitivity by a factor 2 for a 1\,TeV resonance. An extension of the reinterpretation of the ATLAS limits on our simplified top-philic dark matter model to the case of larger resonance widths could then be performed by rescaling the limits by the appropriate correction factor. We have nonetheless found that no additional points are excluded even without rescaling the sensitivity of the search as the ATLAS analysis rapidly loses sensitivity for resonance masses above 600\,GeV. Considering model points with a mediator width to mass ratio of at most about $8\%$ therefore provides a realistic exclusion over the entire model parameter space. \paragraph{Concluding remarks on direct mediator searches.} Mediator resonance searches at 8\,TeV show good prospects of constraining our simplified top-philic dark matter model, especially in the mediator mass range of 150--345\,GeV and 400--600\,GeV by means of the diphoton and top-pair searches respectively. So far, the $t\bar{t}$ resonance searches are strictly applicable to a limited parameter space region of the simplified model, and considering larger widths in the interpretation of the future results would allow for a more straightforward reinterpretation of the limits to a wider range of parameters. Concerning the four-top analysis, it can presently only exclude a restricted part of the parameter space, but future measurements are expected to lead to more competitive bounds. Finally, the $pp \to t \overline{t}+j$ channel could also be used to probe dark matter models coupling preferably to top quarks. This has been for instance shown in ref.~\cite{Greiner-ml-2014qna} where a loop-induced production of $t\bar{t}j$ can in some cases lead to interesting constraints on top-philic models of new physics. In our case, they are nonetheless not expected to give more stringent constraints than the $t\bar{t}$ resonance searches. One could also consider the $pp \to t\bar{t} tj$ and $pp \to t\bar{t} Wt$ processes~\cite{Greiner-ml-2014qna}. Because of the magnitude of the electroweak couplings, these processes are characterised by smaller cross sections than when four top quarks are involved, and are hence not likely to set more stringent constraints on the class of models under consideration. ]]>

\my$ with $\my \in [150, 600]$\,GeV. This is the region where the mediator decay into a pair of dark matter particles is kinematically forbidden, ensuring large branching fractions for decays into Standard Model particles. The diphoton resonance search excludes points below the $2m_t$ threshold, while $t\bar{t}$ results constrain the $400<\my<600$\,GeV region. The four-top probe is able to exclude a narrow parameter space region close to $\my \sim 2m_t$, in agreement with the findings shown in figure~\ref{fig:nonmet}. \begin{figure} \centering \includegraphics[scale=0.5]{Plots/maddm_points_all_exclusion.pdf} ]]>

10^{-11}$\,GeV and the direct detection constraints (cf.~table~\ref{tab:co}).]]>

2\mdm$. Furthermore, we expect the branching ratio to missing energy to be lower in the region where $\my > 2m_t$ due to the kinematically allowed decays into a pair of top quarks. This in turn leads to a lower signal cross section in all channels with missing energy and hence a lower number of points which can be excluded by monojet searches in the $\my > 2m_t$ region. The points excluded by the 8\,TeV $t\bar{t}+\MET$ measurements lie in roughly the same region as the points excluded by the monojet search, but with a more defined edge of \mbox{$\my = 2 m_t$}. Conversely, the 8\,TeV $t\bar{t}$ resonance search provides constraints in the region of $\my \in [400, 600]$\,GeV and $\mdm \gtrsim 100$\,GeV, and is able to rule out $\gsm$ couplings of ${\cal O}(1)$. The four top searches constrain roughly the same region of the $(\my, \mdm)$ parameter space as the $t\bar{t}$ searches. However, the characteristic size of the couplings four top searches are able to constrain is significantly larger than the case of $t\bar{t}$. \looseness=-1 Finally the diphoton resonant search excludes $\my \in [150, 2m_t]$\,GeV with $2\mdm>\my$, ruling out $\gsm$ couplings larger than 0.6. In the $(\my, \mdm)$ plane, we can observe that the constraints arising from all mediator resonance searches, \ie~the diphoton and $t\bar{t}$ analyses, are largely complementary to those issued from searches in channels with large missing energy. ]]>

\mdm$ cannot accommodate the observed relic density, except near the resonance \mbox{$\my\sim 2\mdm$} and for $\mdm > m_t$. Direct detection data complementary excludes large portions of the parameter space in the $\my < \mdm$ region once experimental results from LUX and CDMSLite are accounted for. In the context of dark matter indirect detection, we studied prospects for further model constraints from gamma-ray flux measurements originating from dwarf spheroidal galaxies and the gamma-ray lines issued from the inner galactic region. In the specific model we consider, the dark matter annihilation cross section is $p$-wave suppressed, leading to indirect detection bounds which are too weak to provide additional constraints on the parameter space. Collider searches from LHC Run 1 at $\sqrt{s} = 8 \TeV$ can constrain the parameter space beyond the limits obtained from the relic density and direct detection, but apply mostly in the limit of coupling values $\gtrsim 1$. We found that for couplings of $\lesssim \pi$, the resonant $t\bar{t}$ and diphoton searches are able to exclude a fraction of model points in the regions of $\my \sim 400 - 600 \GeV$ and $\my \sim 150 - 350 \GeV$ respectively, even upon assuming astrophysical and relic density constraints. In addition to studying collider signatures of the top-philic dark matter simplified model as a complementary way of dark matter detection, we performed a study of collider constraints without assuming relic density and direct detection (as well as extended the parameter range to include coupling values of $< 2\pi$ and $\wy \le 0.5 \my$). Our results for a four dimensional parameter scan show that (in the scenario where astrophysical and cosmological constraints are not relevant),$\MET+j$ and $\MET+t\bar{t}$ 8\,TeV results provide meaningful bounds on the model parameter space in the $ 2 \mdm< \my < 2m_t$ region, but only for $\gsm, \gx \gtrsim \pi$. In the $\mdm > m_t$ region, the resonant $t\bar{t}$ searches are again able to exclude some model points in the $\my\sim 400-500 \GeV$ region, while $\gamma \gamma$ measurements provide constraints in the $\my < 2 m_t$ region. We have also explored the prospects of using rarer processes such as four-top production as well as mono-$Z$ and mono-Higgs production to constrain our model. While we have not performed a detailed analysis we have found that these processes show promising signs of further constraining the parameter space of our model and deserve dedicated studies. For the purposes of our study we have recast the CMS monojet and $\MET+t\bar{t}$ searches in the framework of \MA, which allows us to reliably extract constraints on our model, and can benefit future collider studies which go beyond our simplified model and even beyond dark matter searches. Another important aspect of our work, is the use of NLO QCD predictions for the $\MET+t\bar{t}$ process to constrain our model. While we find that $K$-factors for this process are close to one, the importance of taking higher order effects into account lies in the reduced theoretical uncertainties of the NLO results. We have shown that the uncertainties in the CL estimates significantly reduce with the inclusion of higher order QCD terms which clearly illustrates the importance of higher order corrections on the interpretation of dark matter searches at colliders. The work presented in this paper also represents a proof-of-concept for a unified numerical framework for dark matter studies at the interface of collider physics, astrophysics and cosmology in a generic model. ]]>

30$\,GeV and $|\eta|<2.4$ with one of them being $b$-tagged, as well as missing energy $\MET > 160$\,GeV. The signal region is defined by selecting events with a large amount of missing transverse energy \mbox{$\MET>320$} for which the transverse mass $M_T$ that is constructed from the lepton and the missing energy is larger than 160\,GeV. Moreover, the missing transverse momentum and the two leading jets are asked to be well separated in azimuth, $\Delta\Phi\left(j_{1,2},\MET \right)>1.2$, and the $M_{T2}^W$ variable~\cite{Bai-ml-2012gs} is enforced to be greater than 200\,GeV. \begin{table} \centering \begin{tabular}{|c|c|c|c|c|c|c|}\hline & Selection step & CMS & $\epsilon_i^{\rm CMS}$ & MA5& $\epsilon_i^{\rm MA5}$ & $\delta_i^{\rm rel}$ \\ \hline 0&Nominal &224510 & &224510 & & \\ 1&Preselection & & &15468.5 & 0.069& \\ 2&$\MET>320$\,GeV &4220.8 & & 4579.8 & 0.296& \\ 3&$M_T>160$\,GeV & 3390.1& 0.803& 3648.2 & 0.797& 0.75\%\\ 4&$\Delta\Phi(j_{1,2},\MET)>1.2$ & 2963.5& 0.874& 3124.3 & 0.856& 2.06\%\\ 5&$M_{T2}^{W}> 200$\,GeV & 2267.6& 0.765& 2403 & 0.769& -0.52\%\\ \hline \end{tabular} ]]>

80$\,GeV. The CMS monojet search relies on an integrated luminosity of 19.7\,fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 8$\,TeV. It focuses on a signal containing a very hard jet with a transverse momentum satisfying $p_T>110$\,GeV and a pseudorapidity smaller than 4.5 in absolute value. A second jet is moreover allowed, provided that its transverse momentum is larger than 30\,GeV, its pseudorapidity satisfies $|\eta|<4.5$ and if it is well separated from the first jet by 2.5 radians in azimuth. Events featuring more than two jets (with $p_T>30$\,GeV and $|\eta|<4.5$), isolated electrons or muons with a transverse momentum $p_T > 10$\,GeV or hadronically decaying tau leptons with a transverse momentum $p_T > 20$\,GeV and a pseudorapidity satisfying $|\eta|<2.3$ are discarded. The analysis then contains seven inclusive signal regions in which the missing energy $\MET$ is required to be above specific thresholds of 250, 300, 350, 400, 450, 500 and 550\,GeV respectively. \begin{table} \centering \begin{tabular}{|c|c|c|c|c|c|c|}\hline & Selection step & CMS & $\epsilon_i^{\rm CMS}$ & MA5& $\epsilon_i^{\rm MA5}$ & $\delta_i^{\rm rel}$ \\ \hline 0&Nominal &84653.7 & &84653.7& &\\ 1&One hard jet& 50817.2 & 0.6 &53431.28 & 0.631 & 5.2\% \\ 2&At most two jets&36061 & 0.7096& 38547.75 & 0.721 & 1.61\%\\ 3&Requirements if two jets& 31878.1 & 0.884& 34436.35 & 0.893 & 1.02\%\\ 4&Muon veto & 31878.1 & 1 & 34436.35 & 1.000 & 0 \\ 5&Electron veto& 31865.1 & 1 & 34436.35 & 1.000 & 0 \\ 6&Tau veto& 31695.1 & 0.995 & 34397.54 & 0.998 & 0.3\% \\\hline &$\MET > 250$\,GeV & 8687.22 & 0.274& 7563.04 & 0.219 & 20.00\%\\ &$\MET > 300$\,GeV & 5400.51 & 0.621& 4477.67 & 0.592 & 4.66\% \\ &$\MET > 350$\,GeV & 3394.09 & 0.628& 2813.70 & 0.628 & 0.00\%\\ &$\MET > 400$\,GeV & 2224.15 &0.6553& 1753.71 & 0.623 &4.93\%\\ &$\MET > 450$\,GeV & 1456.02 &0.654& 1110.92 & 0.633&3.21\% \\ &$\MET > 500$\,GeV & 989.806 &0.679& 722.83 & 0.650 & 4.27\%\\ &$\MET > 550$\,GeV & 671.442 &0.678& 487.54 & 0.674 &0.59\% \\ \hline \end{tabular} ]]>

250$\,GeV for which a disagreement of about 20\% has been observed. It is however not uncommon that low missing energy is difficult to simulate with a fast-simulation of the detector based on \DEL. We have verified that for missing energy values of interest, the description of the missing energy agree relatively well with CMS, as illustrated in figure~\ref{fig:histo_monojet} where we compare, for a benchmark scenario where the $Z'$ mass has been set to 900\,GeV, the missing energy distribution as obtained by CMS to the one derived with \MA. ]]>