Scalar simplified models for dark matter

We introduce a set of minimal simplified models for dark matter interactions with the Standard Model, connecting the two sectors via either a scalar or pseudoscalar particle. These models have a wider regime of validity for dark matter searches at the LHC than the effective field theory approach, while still allowing straightforward comparison to results from noncollider dark matter detection experiments. Such models also motivate dark matter searches in multiple correlated channels. In this paper, we constrain scalar and pseudoscalar simplified models with direct and indirect detection experiments, as well as from existing LHC searches with missing energy plus tops, bottoms, or jets, using the exact loop-induced coupling with gluons. This calculation significantly affects key differential cross sections at the LHC, and must be properly included. We make connections with the Higgs sector, and conclude with a discussion of future searches at the LHC.

Figure 1

A heuristic diagram presenting the successive levels of effective theories that must be expanded as the momentum flow (proportional to the MET) through the interaction increases. On the left we have the EFT ${\mathcal{O}}_G={\alpha }_s/{\mathrm{\Lambda }}^3\overline{\chi }\chi G_{\mu \nu }{G}^{\mu \nu }$. In the center two effective theories with either ($m_{\varphi }\to \infty$, finite $m_t$) (top) or (finite $m_{\varphi },$, $m_t\to \infty$) (bottom). On the right the Full Theory with finite $(m_{\varphi },m_t)$.

Figure 2

Sample of the leading-order Feynman diagrams, in the Full Theory with finite top mass effects, contributing to the scalar plus jet production at the LHC.

Figure 3

Missing energy distribution for the process $pp\to \overline{\chi }\chi +j$ in the EFT ${\mathcal{O}}_G={\alpha }_s/{\mathrm{\Lambda }}^3\overline{\chi }\chi G_{\mu \nu }{G}^{\mu \nu }$ (equivalent to the left panel of Fig. 1), for a finite mediator mass with an effective coupling to gluons $m_t\to \infty$ (lower center panel of Fig. 1) and the Full Theory including the top mass effects (right panel of Fig. 1). On the left panel we display the results for a light mediator and on the right for a very heavy one (equivalent to the upper center panel of Fig. 1). These distributions were generated at the parton level with MCFM and LHC at 8 TeV.

Figure 4

The width $\mathrm{\Gamma }$ of the scalar $\varphi$ (left) and pseudoscalar $A$ (right) decaying into pairs of 10 GeV dark matter (black dotted), top quarks (green), bottom quarks (red), tau leptons (blue), $\gamma \gamma$ (black dashed), and the total width (black solid), as a function of the parent mass $m_{\varphi }$ or $m_A$. Widths are calculated assuming $g_v=g_{\chi }=1$.

Figure 5

Contour plot of 95% C.L. upper bounds on the coupling combination $g_{\chi }{g}_v$ from LUX [70] and CDMS-lite [71] direct detection searches on the scalar mediator benchmark model as a function of the mediator mass $m_{\varphi }$ and dark matter mass $m_{\chi }$.

Figure 6

Contour plot of 95% C.L. upper bounds on $g_{\chi }{g}_v$ derived from indirect detection constraints set by the FGST dwarf spheroidal analysis [80] in the $b\overline{b}$ channel, as a function of the pseudoscalar mediator mass $m_A$ and the dark matter mass $m_{\chi }$. The width is set assuming $g_v=g_{\chi }$, which is relevant only near resonance.

Figure 7

Required values of $g_{\chi }{g}_v$ as a function of mediator mass $m_{\varphi (A)}$ and dark matter mass $m_{\chi }$ assuming that dark matter is a thermal relic and the only annihilation channel is $\overline{\chi }\chi \to \varphi (A)\to \overline{f}f$, for the scalar (left) and pseudoscalar (right) simplified models.

Figure 8

Missing transverse momentum differential cross sections for the scalar (left panel) and pseudoscalar (right panel) mediators. The leading-order effective gluon couplings are shown as dashed lines, and the exact loop-induced calculations are solid. We assume the LHC at 8 TeV.

Figure 9

Lower limit on the coupling $g_{\chi }{g}_v$ set by the CMS monojet search as a function of dark matter mass $m_{\chi }$, assuming mediators of 100 GeV, ${\mathrm{\Gamma }}_{\varphi (A)}/m_{\varphi (A)}=10^{-3}$, and exclusively on-shell production of dark matter. The constraint on the scalar mediator is shown in red and pseudoscalars in blue.

Figure 10

Representative Feynman diagrams contributing to heavy quark flavor plus dark matter production at the LHC in our simplified models.

Figure 11

95% C.L. upper limits on $g_{\chi }{g}_v$ for scalar mediators from collider searches as a function of ${\mathrm{\Gamma }}_{\varphi }/m_{\varphi }$, assuming 40 GeV dark matter and 100 GeV (left) and 375 GeV (right) scalar mediators. The limit from the CMS monojet search is shown as the solid colored (red or blue) line for the full theory including heavy quark mass effects MCFM calculation. The MadGraph effective operator CMS monojet constraint is shown in dashed color. The shaded region indicates an extrapolation of the finite width effects to the MCFM results. The constraint from the top pair plus missing energy search is the dashed black line, and the $b$-jet plus missing energy search limit is the dotted black line. The horizontal solid black line shows the direct detection limit from LUX and CDMS-lite. The grayed-out region indicates where the minimum width consistent with $g_{\chi }{g}_v$ is greater than the assumed width.

Figure 12

95% C.L. upper limits on $g_{\chi }{g}_v$ for pseudoscalar mediators from collider searches as a function of ${\mathrm{\Gamma }}_A/m_A$, assuming 40 GeV dark matter and 100 GeV (left) and 375 GeV (right) pseudoscalar mediators. The limit from the CMS monojet search is shown as the solid colored (red or blue) line for the Full Theory including heavy quark mass effects MCFM calculation. The MadGraph effective operator CMS monojet constraint is shown in dashed color. The shaded region indicates an extrapolation of the finite width effects to the MCFM results. The constraint from the top pair plus missing energy search is the dashed black line, and the $b$-jet plus missing energy search limit is the dotted black line. The horizontal solid black line shows the indirect detection limit in the $b\overline{b}$ channel from FGST.

Figure 13

95% C.L. upper limits on $g_{\chi }{g}_v$ for the 125 GeV Higgs from collider searches as a function of the width $\mathrm{\Gamma }$, assuming 40 GeV dark matter. The limit from the CMS monojet search is shown as the solid colored (red or blue) line for the Full Theory including heavy quark mass effects MCFM calculation. TheMadGraph effective operator CMS monojet constraint is shown in dashed color. The shaded region indicates an extrapolation of the finite width effects to the MCFM results. The constraint from the top pair plus missing energy search is the dashed black line, and the $b$-jet plus missing energy search limit is the dotted black line. The horizontal solid black line shows the direct detection limit from LUX and CDMS-lite. Three vertical lines show experimental limits on the 125 GeV Higgs’s width assuming Standard Model couplings and an invisible branching ratio of 54% [154] (dotted purple), the upper limit on the width from interference with the $Z$ [159] (dashed purple), and the maximum possible width from the $4\ell$ line shape (solid purple) [161].