The waning of the WIMP: endgame?

Abstract

We give a fresh look at the WIMP paradigm by considering updated limits and prospects for direct and indirect dark matter detection and covering realistic dark matter models, beyond the so-called simplified models, which have been the target of experimental scrutiny. In particular, we investigate dark matter scenarios featuring dwindled direct detection signals, due to loop or momentum suppression. Therefore, this review extends previous reviews in different aspects and motivates the search for WIMP dark matter in light of the present and near-future detectors.

Fig. 1

Most relevant constraints (both current and projected) applied in this work. The left panel shows the DD limits in the $(m_{\text{DM}}.{\sigma }_{\mathit{DMp}}^{\text{SI}})$ plane while the right panel refers to the ID constraints in the $(m_{\text{DM}},⟨\sigma v⟩)$ plane. See text body for the detailed description

Fig. 2

Model points of spin-0s-channel portal models with relic density equal or below the cosmologically favoured values. From left to right the different panels refer to the cases of scalar, fermionic and vector DM. The model points are shown in the $(m_S,m_{\chi ,\psi .V})$ bidimensional plane. The variation of the colors of the point correspond to a variation of the DM relic density according to the (log10) scales put at the right of each panel

Fig. 3

Summary of plausible constraints for the simplified portals with a CP-even scalar mediator. The top row shows results for a scalar DM $\chi$. The middle row depicts the same for a fermionic DM $\Psi$ while the bottom row refers to the case of a vector DM V. Each row contains three panels corresponding to different assignations of the pertinent couplings (see Eq. (25)), as reported at the top of each plot. In each plot, the black coloured contour corresponds to the correct DM relic density. The blue (purple) coloured region corresponds to the current (projected) exclusions related to the missing experimental signatures coming from the SI interactions. The yellow coloured regions describe the excluded parameters space from the absence of ID signals from the DM annihilation processes

Fig. 4

Example of Feynman diagram responsible for the loop induced SI scattering cross-section of DM in the simplified model with pseudoscalar mediator

Fig. 5

Same as Fig. 2 but for the case of a simplified model with a s-channel pseudoscalar mediator

Fig. 6

Summary of constraints, in the $(m_a,m_{\psi })$ plane for a simplified s-channel portal with a fermionic DM $\Psi$ and a CP-odd mediator a. The three panels refer to different assignations of the relevant couplings (see Eq. (36)), reported at the top of each plot. The colour code is the same as of the ones used for Fig. 3

Fig. 7

Same as Fig. 2 but for scalar DM coupled to a spin-1 portal. The two panels refer, respectively, to the case $A_f^{\prime }=0\forall f$ and $V_f^{\prime }=0\forall f$

Fig. 8

Summary of constraints for a simplified model with a complex scalar DM interacting via an s-channel spin-1 mediator $Z^{\prime }$. The constraints are shown in the $(m_{Z^{\prime }},m_{\chi })$ plane. For each plot, the viable parameters space is the area where the black coloured isocontours, representing the correct DM relic density, lie outside the blue and purple coloured regions. The colour code is the same as of the ones used for Fig. 3. The phrases “Scalar DM Vectorial Coupling” (top row) and “Scalar DM Axial Vectorial Coupling” (bottom row) refer to $A_f^{\prime }=0\forall f$ and $V_f^{\prime }=0\forall f$, respectively. We refer to the main text for details on the assignations of the couplings

Fig. 9

Examples of loop diagrams inducing, at one loop, SI cross-section via exchange of $Z^{\prime }$ in the internal lines

Fig. 10

Same as Fig. 2 but for fermionic DM coupled to a spin-1s-channel portal. The different panels refer, from left to right, to the following cases: $(A_{\psi }^{\prime }=0,A_f^{\prime }=0\forall f)$, $(A_{\psi }^{\prime }=0,V_f^{\prime }=0\forall f)$, $(V_{\psi }^{\prime }=0,A_f^{\prime }=0\forall f)$, $(V_{\psi }^{\prime }=0,V_f^{\prime }=0\forall f)$

Fig. 11

Summary of constraints for a simplified model with a fermionic DM interacting via an s-channel spin-1 mediator $Z^{\prime }$. The constrains are shown in the $(m_{Z^{\prime }},m_{\psi })$ plane. For each plot, the viable parameters space is the area where the black coloured isocontours, representing the correct DM relic density, lie outside the blue and purple coloured regions. The colour code is the same as of the ones used for Fig. 3. The phrases used, “Vectorial Coupling” (top row), “Vectorial/Axial-Vectorial Coupling” (second row), “Axial-Vectorial/Vectorial Coupling” (third row) and “Axial-Vectorial Coupling” (bottom row) refer to $(A_{\psi }^{\prime }=0,A_f^{\prime }=0\forall f)$, $(A_{\psi }^{\prime }=0,V_f^{\prime }=0\forall f)$, $(V_{\psi }^{\prime }=0,A_f^{\prime }=0\forall f)$, $(V_{\psi }^{\prime }=0,V_f^{\prime }=0\forall f)$, respectively. We refer to the main text for details on the assignations of the couplings

Fig. 12

Feynman diagrams contributing to the Wilson coefficients in the effective Lagrangian for the DM DD in the case of a real/complex scalar DM ${\Phi }_{\text{DM}}$. Diagram (b) has a partner (not shown) interchanging ${\Psi }_{f_i}$ with $f_i$

Fig. 13

Feynman diagrams contributing to the Wilson coefficients in the effective Lagrangian for the DM DD in the case of a Dirac fermion DM ${\Psi }_{\text{DM}}$

Fig. 14

Summary of constraints for models of t-channel portals in which SI interactions arise mostly at the tree level when a complex scalar (Dirac fermion) DM couples to the first generation of quarks via a coloured mediator, charged under the $SU{(3)}_C$, is depicted via the left (right) plot. For simplicity, only the case of coupling with the $SU{(2)}_L$ doublet has been accounted for. According to the customary colour coding, we show black coloured isocontours corresponding to the correct DM relic density while the blue, purple coloured regions correspond to the current, projected exclusion on the SI interactions. In the case of a Dirac fermion DM, the SD bounds (green coloured) have also been reported. The gray-coloured region corresponds to unstable DM and hence, is excluded. In the orange coloured region, the correct DM relic density cannot be achieved with perturbative couplings

Fig. 15

Same as the Fig. 14 but considering t-channel portals in which SI interactions arise at the one-loop level. The first (last) two plots of the top row depict the cases when a complex (real) scalar DM couples to the second and third generations of $SU{(2)}_L$ quarks. The bottom row represents the same for a Dirac (Majorana) fermion DM, respectively. To correct wrong axis labels and text on the grey-coloured regions, see my comments in Fig. 8

Fig. 16

Summary of the DM constraints for two sample t-channel models in which the states are coupled only with the second generation of the $SU{(2)}_L$ leptons. The left (right) plot depicts the case of a complex (real) scalar DM. The colour coding is the same as Fig. 14

Fig. 17

Feynman diagrams contributing to the Wilson coefficients in the effective Lagrangian 117

Fig. 18

The SI cross-section, as a function of the DM mass, for a Majorana DM candidate having gauge interactions with the EW SM gauge bosons. The various curves correspond to different assignations of the parameter pair (n, Y) (see text for details). The blue coloured region is excluded by the current experimental limits given by LZ. The purple coloured region is the one which will be excluded in case of negative detection by DARWIN. The yellow coloured regions correspond, finally, to the $\nu$ floor

Fig. 19

Illustration of the DM constraints for the SM Higgs portal in the $(M_s,{\lambda }_{\mathit{Hss}})$. The black coloured line represents the model points featuring the correct DM relic density. The blue coloured region is excluded by the current SI DD limits while the yellow coloured region corresponds to exclusion form ID. The yellow dot-dashed line represent a projected exclusion from increased statistics by the FERMI experiment.. The purple region would be excluded in the absence of signals at the DARWIN experiment while the orange one in case of negative signals by the future CTA experiments.. Finally, the grey coloured region represents the complementary exclusion, for light DM masses, by searches of the invisible Higgs decay at the LHC

Fig. 20

Illustration of the DM constraints for the SM Higgs portal in the relevant bidimensional planes for a fermionic (left panel) and vectorial (right panel) DM. The color code is the same as Fig. 19

Fig. 21

Combination of the DM constraints for a model with a fermionic DM interacting via a singlet extension of the SM Higgs sector. The three panels differ for the assignations of the $(M_{H_2},sin\theta )$ ($H_1$ is identified with the 125 GeV SM-like Higgs boson), as mentioned on the top. In each plot, the orange coloured region corresponds to the non-perturbative values of the DM Yukawa coupling. The remaining colour coding is the same as of Fig. 20

Fig. 22

Outcome of a parameter scan (see main text for details) for the model with a fermionic DM coupled to a Higgs sector made by the SM doublet H and a real SM gauge singlet S through the mass mixing. This framework is dubbed Singlet Extension Fermionic DM as mentioned on the top of each plot. The two panels show the $(M_{\chi },M_{H_2})$ (left) and $(M_{H_2},sin\theta )$ (right) planes. In each panel, the blue coloured points feature the correct DM relic density and pass all the present experimental constraints. The purple coloured points correspond to the parameter assignation compatible with an eventual future bound by the DARWIN experiment

Fig. 23

Summary of the DM constraints for the dark U(1) vector DM model. The colour codes and the $(M_{H_2},sin\theta )$ values are the same as the fermionic DM model described in Fig. 21. In addition to these regions, exclusion regions from the ID constraints are shown in yellow colour while the green coloured regions represent the parameter space not compatible with the perturbative unitarity of the concerned scalar sector couplings

Fig. 24

Parameter scan for the dark U(1) vector DM model. The colour convention is the same as Fig. 22

Fig. 25

Same as Fig. 23 but for the SU(2) case

Fig. 26

Summary of the DM constraints for SU(3) vector DM model. The colour convention is the same as Fig. 23. The top (bottom) row corresponds to $M_{H_2}=300$ GeV, $sin\theta =0.05$ ($M_{H_2}=1000$ GeV, $sin\theta =0.1$). The left column refers to the case where the DM is composed of the three cosmologically stable almost mass degenerate vectors $V^{1,2,3}$. The right column considers the case in which only $V^3$ is not cosmologically stable

Fig. 27

Parameter scan for the dark SU(3) vector model considering the cases of both single component (top row) and two-component (bottom row) DM. For both scenario the results are shown in the $(M_V,M_{H_2})$ (left) and $(M_{H_2},sin\theta )$ planes. As usual, blue coloured points correspond to parameter assignations compatible with the current constraints, as given by XENON1T/XENONnT/LZ, but ruled out by negative results at the DARWIN experiment. Purple coloured points correspond to a viable parameter space even no DM signals gets detected by DARWIN

Fig. 28

The summary of the DM constraints on the dark SU(3) model in the configuration with a scalar/vector two component DM in the $(M_{\psi },\tilde{g})$ bidimensional plane. The orange-coloured region is excluded from the fact that $M_V<M_{\psi }$ in this part. The remaining colour codes are the same as of Fig. 26. The other relevant parameter assignations are shown on top of the two panels

Fig. 29

Summary of the DM constraints in the $(M_{\psi },M_V)$ plane for the dark SU(3) model in the regime of a two component scalar/vector DM for three benchmark parameter assignations, summarised on the top of the panels. Here the orange-coloured region is excluded from the bound on the invisible Higgs decay while the grey-coloured area is excluded from the fact that $M_{\Psi }>M_V$ for this region. The remaining colour codes are the same as of Fig. 28

Fig. 30

Parameter assignations of the Inert Doublet Model (see main text for details) leading to a relic density below the experimental value. Outside this region the DM is overabundant if thermal freeze-out is assumed. The color code tracks $Log{\Omega }_{\text{DM}}{h}^2$ according the scale put on the right

Fig. 31

Model points with the correct DM relic density (black coloured) obtained from a scan over the parameters of the IDM (see main text for details) in the $(m_{H^0},|{\lambda }_L|)$ bidimensional plane. The blue coloured region is excluded by the current constraints on the DM SI interactions while the purple coloured region is the projected sensitivity reach of the DARWIN experiment. The cyan coloured region corresponds to the parameter space giving $Br(h\to \text{invisible})>0.11$

Fig. 32

Summary of the DM constraints for the Singlet-Doublet model with a Majorana fermion DM in the bidimensional plane $(m_D,m_S)$ by taking $y=1(0.2)$ in the top (bottom) row and $tan\theta =\pm 4$. The black coloured lines are the isocontours corresponding to the correct DM relic density. The blue coloured (green coloured) region is excluded by the LZ limit on the SI (SD) interactions while the purple coloured region corresponds to the expected sensitivity of the DARWIN experiment. The cyan coloured regions correspond to the exclusions from the invisible decays of the SM Higgs and Z bosons. Finally, the red-coloured region (top row only) depicts the exclusion area from the EWPT

Fig. 33

Summary of the DM constraints for the Singlet-Doublet+2HDM model in the $(m_S,m_D)$ plane for benchmark assignations of the set $(tan\beta \equiv t_{\beta },tan\theta \equiv t_{\theta },y)$ and of the masses of the BSM Higgs states $M_H,M_{H^{\pm }},M_A$, reported on the top of each panel. These plots are for a Type-I 2HDM where four different types ($dd,du,ud,uu$) of couplings exist between the BSM fermionic DM and the Higgs states. The remaining colour codes are the same as of Fig. 32

Fig. 34

Same benchmarks as Fig. 33 but for positive $tan\theta$

Fig. 35

This is analogous to Fig. 33, but for a Type-II 2HDM scenario fixing $M_H=M_{H^{\pm }}=M_A=800$ GeV

Fig. 36

Same as Fig. 35, but for positive $tan\theta$

Fig. 37

Results of a parameter scan of the 2HDM+s. The two pairs of panels refer, as reported on their tops, to the Type-I and Type-II configurations of the Yukawa coupling. For each pair, the first plots shows the model points in the $\left(\left|M_{S_1},-,2,m_{\chi }\right|,/,M_{S_1},,,\left|M_{S_2},-,2,m_{\chi }\right|,/,M_{S_2}\right)$, bidimensional plane with color patter following $Log{\Omega }_{\chi }{h}^2$. The second plot shows, instead the DM relic density as function of the mass. The color pattern of the scatter plot is determined by the mass of the lightest BSM CP-even scalar

Fig. 38

Parameter scan of the 2HDM+Singlet model (dubbed 2HDM+s) coupled to a SU(2) singlet fermionic DM (see main text for details). The top row refers to the Type-I 2HDM configuration of Yukawa couplings while the bottom row depicts the same for Type-II. The colour convention is the same as Fig. 27

Fig. 39

Relic density ${\Omega }_{\chi }{h}^2$ as a function of the DM mass $m_{\chi }$ for the 2HDM+a model. The left panel refers to the Type-I configuration of the Yukawa couplings while the right one corresponds to Type-II. The different colours, namely, red, blue and green, correspond to different assignations of $sin\theta$, $0.7,0.3,0.1$, respectively, as reported in the plots. Solid lines correspond to $y_{\chi }=1$ case while the dashed lines belong to $y_{\chi }=0.1$. In both cases, $m_a=50\text{GeV}$ while for what concerns $M_A=M_H=M_{H^{\pm }}$, a value of 500 GeV has been considered for the Type-I scenario while a value of 800 GeV has been considered for the Type-II case

Fig. 40

Generic Feynman diagrams for the loop-induced scattering of the DM particle on quarks in the 2HD+a model. Analogous diagrams with a replaced by A and h replaced by H contribute to DD

Fig. 41

Summary of constraints in the $(m_{\chi },m_a)$ plane for the 2HDM+a coupled to an SM gauge singlet fermionic DM. The top (bottom) row corresponds to the Type-I (Type-II) configuration of Yukawa couplings with $M=M_A=M_H=m_{H^{\pm }}=600(800)$ GeV. $tan\beta =5$ is fixed for all the plots while $sin\theta =0.1$ (left column), 0.3 (middle column) and 0.7 (right column). The green (red) coloured region is excluded from the bound on the invisible decay of the SM-like Higgs ($pp\to a\to {\mu }^{+}{\mu }^{-}$ cross-section). The remaining colour coding is the same as of Fig. 35

Fig. 42

Parameter scan of the 2HDM+a coupled with an SM gauge singlet fermionic DM (see main text for details). The colour convention is the same as Fig. 27. The top (bottom) row refers to the Type-I (Type-II) configuration for Yukawa couplings

Fig. 43

The combined DM constraints in the relevant bidimensional planes $(m_{Z^{\prime }},m_{\chi })$ and $(m_{Z^{\prime }},m_{\psi })$ for the scalar (left column) and fermionic (right column) DM, respectively, interacting with a $Z^{\prime }$, kinetically coupled to the SM Z boson. In the top row, the kinetic mixing parameter $\delta$ has been set to the maximal value, as a function of $m_{Z^{\prime }}$, consistent with the EWPT constraints while for the bottom row plots, $\delta$ has been set to a constant value of 0.01. We set $g_X=1$ for all these plots. In these plots, the black coloured curves represent the isocontour of the correct DM relic density. The blue coloured region is excluded by the current constraints from LZ while the purple coloured regions correspond to the expected sensitivity reach of the DARWIN experiment

Fig. 44

Combination of constraints for $B-L$ model with a scalar DM ${\varphi }_{\text{DM}}$. The value of the $g_X$ is 1 (0.1) for the left (right) panel. The red, orange, pink and green coloured regions represent the exclusion limits from the LHC searches of dijets, di-leptons, monojet and the LEP experiment, respectively. The blue (purple) coloured region is based on the sensitivity reach of the current (next generation) DM detection experiments

Fig. 45

Outcome of the parameter scan for the $B-L$ model with a scalar DM ${\varphi }_{\text{DM}}$. According to the usual colour coding, the blue coloured points correspond to the assignations of the model parameter compatible with the current experimental constraints. The purple coloured points will evade a negative signal by DARWIN. The left panel shows the $(M_{Z^{\prime }},m_{{\varphi }_{\text{DM}}})$ plane while the right panel shows the $(M_{H_2},m_{{\varphi }_{\text{DM}}})$ one

Fig. 46

Summary of constraints in the $(m_{N_1},m_{Z^{\prime }})$ plane for three benchmark parameter assignations ($M_{H_2},sin\theta ,g_X$) of the $B-L$ model with a Majorana Neutrino DM $N_1$. The parameter $g_X$ is kept fixed at 1 while $M_{H_2},sin\theta$ values are $(300\text{GeV},0.1)$ (left), $(500\text{GeV},0.3)$ (middle) and $(70\text{GeV},0.05)$ (right), respectively. The cyan (black) coloured region is excluded from the bound on the invisible decay of the SM-like Higgs (perturbative unitarity bound on the model parameters). The remaining colour coding is the same as in Fig. 44

Fig. 47

Same as Fig. 46 but considering the $(M_{H_2},m_{N_1})$ plane. The three rows correspond to the three assignations of $sin\theta$, namely, 0.3 (top), 0.1 (middle), and 0.05 (bottom), respectively. The left column corresponds to the assignation $M_{Z^{\prime }}/m_{N_1}=3$ and $g_X=1$, while the right column to $M_{Z^{\prime }}/m_{N_1}=0.5$ and $g_X=1$

Fig. 48

Outcome of the parameter scan of the $B-L$ model with a Majorana neutrino DM $N_1$. Using the conventional colour coding, as of Fig. 45, the model assignations complying with the current and near future constraints are shown in the $(M_{Z^{\prime }},m_{N_1})$ plane (left panel), $(m_{N_1},g_X)$ plane (middle panel) and $(M_{H_2},sin\theta )$ plane (right panel), respectively

Fig. 49

Same as Fig. 44 but for a vector-like Dirac fermion DM $\psi$, charged under $B-L$, including exclusion region (yellow coloured) from the ID limits of the DM. The value of $g_X$ is 1 (0.1) for the right (left) plot, as written on the top

Fig. 50

Similar to Fig. 46 but for a model with a Majorana fermion DM $\chi$ and a $Z^{\prime }$,having only axial couplings with the SM fermions, including green and yellow coloured regions which are excluded from the SD interactions and the EWPT, respectively. Unlike Fig. 46, here we considered $g_X=0.1$ and $sin\delta =0.1$ although panel-wise assignations of $M_{H_2},sin\theta$ remain the same

Fig. 51

Summary of constraints for the $2HDM+U{(1)}_X$ model with a Majorana neutrino DM $N_1$ and $X=B-L$. The results are illustrated in the $(M_{Z^{\prime }},m_{N_1})$ bidimensional plane for two values of $g_X$, namely, 1 (left) and 0.1 (right). Following the usual conventions, the relic density isocontours (black coloured) are compared with the various excluded regions. The red, orange, cyan, purple and, grey coloured regions are excluded from the LHC searches of the dijet, monojet, dilepton, the perturbative unitarity bound on $Y^{N_1}$ and, the APV, respectively. For the right panel, additionalclusions appear from the SD interactions (green coloured) and $H^{\pm }$ searches at the collider (light green coloured)

Fig. 52

Combined constraints for the hMSSM considering some benchmark assignations of the model parameters. The isocontours of the correct relic density and the current/future excluded regions from direct and indirect searches for DM follow the conventional color coding adopted for this work. In addition, the various panels show regions marked in gray which are excluded by LHC searches (see main text for details)

Fig. 53

pMSSM model points, compatible with theoretical constraints, constraints from the Higgs sector and from flavour physics, displayed in the $(|\mu |,M_1$ (left) and $(M_1,M_2)$ planes. The color pattern corresponds to $Log{\Omega }_{{\chi }_1^0}{h}^2$

Fig. 54

Upper Left Panel: pMSSM model points from parameter scan (see main text for details) in the $\left(m_{{\chi }_1^0},,,{\sigma }_{{\chi }_1^0}^{\text{SI}}\right)$ bidimensional space. As customary, the blue (purple) region represents the current (near future) exclusion from DD experiments. Upper Right Panel: Same model points but in the $(m_{{\chi }_1^0},⟨\sigma v⟩)$ bidimensional space. The yellow (orange) region represent the current exclusion (project sensitivity) from the FERMI (CTA) experiment. Lower left panel: pMSSM model points with relic density below the experimental limit, in the $\left(m_{{\chi }_1^0},,,r,{\sigma }_{{\chi }_1^0}^{\text{SI}}\right)$ with $r={\Omega }_{{\chi }_1^0}/{\Omega }_{DM,exp}$. The color coding tracks $Log{\Omega }_{{\chi }_1^0}{h}^2$. Lower right panel: Same model points as the lower left panel but in the $\left(m_{{\chi }_1^0},,,r^2,⟨\sigma v⟩\right)$ bidimensional plane

Fig. 55

Left panel: Model points, for a NMSSM realization with heavy sfermions, complying with the requirement of the correct relic density assuming the thermal freeze-out paradigm, shown in the $(m_{{\chi }_1^0},{\sigma }_{{\chi }_1^{0}p}^{\text{SI}})$ bidimensional plane. The points lying within the blue region, correspond to parameter assignations non compatible with present constraints from DD. The point lying outside the blue region and inside the purple region will be excluded in absence of detection of DM signals by the next future DARWIN experiment. Right panel: Same model points as the left panel but this time displayed in the $(m_{{\chi }_1^0}/(\mu sin2\beta ),{\sigma }_{{\chi }_1^{0}p}^{\text{SI}})$ plane. This second panel evidences the occurrence of blind spots at $m_{{\chi }_1^0}/(\mu sin2\beta )=(-)1$ for singlino-higgsino (bino-higgsino) DM