# Dark Matter Searches with Top Quarks

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Models with BSM Signatures Involving Top Quarks

#### 2.1. Vector and Axial-Vector Mediators

#### 2.1.1. Flavor-Conserving Interaction

#### 2.1.2. Flavor-Changing Interaction

#### 2.2. Scalar and Pseudoscalar Mediators

#### 2.2.1. Color-Neutral Interaction

- Visible decay of a mediator produced via gluon-fusion to heavy-flavor quarks, resulting in a resonant $t\overline{t}$ or $b\overline{b}$ signal.
- Associated production of a mediator that decays either visibly or invisibly with heavy-flavor quarks, leading to a ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $t\overline{t}$/$b\overline{b}$ signature in the case of invisible mediator decay or characteristic fully visible $t\overline{t}t\overline{t}$, $t\overline{t}b\overline{b}$, $b\overline{b}b\overline{b}$ signatures.
- Associated production of an invisibly decaying mediator with a top quark and a light ($d,u,s,c$) quark, leading to a ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tj$ signature.
- Associated production of an invisibly decaying mediator with a top quark and a W boson, resulting in a ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tW$ signature.

#### 2.2.2. Color-Charged Interaction

#### 2.3. Extended Higgs Sectors

#### 2HDM with a Pseudoscalar Mediator

#### 2.4. EFT Model of Scalar Dark Energy

## 3. Experimental Signatures

#### 3.1. Final States with Invisible Decays

#### 3.1.1. ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + t

#### 3.1.2. ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tW$ and ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tj$

#### 3.1.3. ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $t\overline{t}$

#### 3.1.4. ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tW$, ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tj$ and ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $t\overline{t}$

#### 3.2. Final States without Invisible Decays

#### 3.2.1. Same-Sign $tt$

#### 3.2.2. $t\overline{t}$

#### 3.2.3. $t\overline{t}t\overline{t}$

#### 3.2.4. $tb{H}^{\pm}\left(tb\right)$

## 4. Results

#### 4.1. Vector and Axial-Vector Mediators

#### 4.1.1. Flavor-Conserving Interaction

#### 4.1.2. Flavor-Changing Interaction

#### 4.2. Scalar and Pseudoscalar Mediators

#### 4.2.1. Color-Neutral Interaction

#### 4.2.2. Color-Charged Interaction

#### 4.3. Extended Higgs Sectors

#### 4.3.1. 2HDM with a Pseudoscalar Mediator

#### 4.4. Scalar DE EFT Model

## 5. Discussion

## 6. Outlook

#### 6.1. LHC Run 3

#### 6.1.1. ALPs

#### 6.1.2. Composite Pseudo-Nambu–Goldstone Bosons

#### 6.1.3. Dark Mesons

#### 6.2. HL-LHC and HE-LHC

#### 6.3. FCC-hh

#### 6.4. Future ${e}^{+}{e}^{-}$ Colliders

#### 6.5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DM | Dark matter |

DE | Dark energy |

EFT | Effective field theory |

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**Figure 1.**Schematic representation of the dominant production and decay modes of the simplified model with an s-channel vector or axial-vector mediator ${Z}^{\prime}$ [19].

**Figure 2.**Schematic representation of the dominant production and decay modes of the VFC model [19].

**Figure 3.**Schematic representation of the dominant production and decay modes with heavy-flavor quarks in the final state in the simplified model with a scalar ($\varphi $) or pseudoscalar (a) mediator [19].

**Figure 4.**Schematic representation of ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + t production via a color-changing scalar mediator ${\eta}_{t}$ [19].

**Figure 5.**Schematic representation of relevant production and decay modes with top quarks leading to either top quarks in the final state or ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $h/Z$ signatures. From left to right: resonant production of a neutral scalar or pseudoscalar particle $H/A/a$ decaying to $t\overline{t}$ or $b\overline{b}$; associated production with $b\overline{b}$ or $t\overline{t}$ of a single $H/A/a$ decaying either visibly to heavy flavor or invisibly to DM; associated production of a top quark and a charged Higgs boson decaying to a W boson and an invisibly decaying mediator a; resonant $A/H$ production with subsequent decay to a $Z/h$ boson and an invisibly decaying mediator a [19].

**Figure 6.**Schematic representation of the leading process of DE production in association with a $t\overline{t}$ pair in an EFT model of scalar DE via the operator ${\mathcal{L}}_{1}$ [19].

**Figure 7.**Upper limits at 95% CL on the coupling ${g}_{q}$ of the mediator to quarks in a simplified model with a vector or axial-vector mediator obtained from different types of resonance searches using data from $pp$ collisions at $\sqrt{s}=13$ TeV. The DM mass is ${m}_{\chi}=10$ TeV and its coupling to the mediator is ${g}_{\chi}=1$ [76].

**Figure 8.**95% CL observed and expected exclusion regions on vector mediators in the DM–mediator mass plane from searches with visible and invisible final states released by the CMS Collaboration [84]. Exclusions are computed for a leptophobic scenario with ${g}_{l}=0$, a universal quark coupling of ${g}_{q}=0.25$, and a DM coupling of ${g}_{\mathrm{DM}}=1.0$.

**Figure 9.**Upper limits on the spin-independent DM–nucleon scattering cross-section (

**left**) and spin-dependent limits on the DM–neutron scattering cross-section (

**rigth**) as a function of the DM mass, obtained from searches with the ATLAS detector as well as relevant direct-detection experiments, are summarized [76]. The limits for the spin-independent (spin-dependent) case are derived for the hypothesis of a leptophobic (${g}_{l}=0$) vector (axial-vector) mediator with a universal quark coupling of ${g}_{q}=0.25$ and a DM coupling of ${g}_{\mathrm{DM}}=1.0$. The ATLAS limits are at 95% CL while the direct-detection results are at 90% CL.

**Figure 10.**Regions in the (${m}_{{Z}_{\mathrm{VFC}}^{\prime}}$,${g}_{ut}$) (

**left**) and the ($\mathcal{BR}\left(\chi \chi \right)$,${g}_{u}t$) plane (

**right**) of the VFC model excluded at 95% CL by searches in the same-sign $t\overline{t}$ and ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + t final states [19].

**Figure 11.**Exclusion limits for the VFC model in the two-dimensional plane spanned by the mediator mass and the coupling between the mediator and quarks released by the CMS Collaboration [44]. The observed exclusion range is shown as a yellow solid line, while the yellow dashed lines show the cases in which the predicted cross-section is shifted by the assigned theoretical uncertainty. The expected exclusion range is indicated by a black solid line, and the experimental uncertainties are shown in black dashed lines.

**Figure 12.**Expected (dashed line) and observed (solid line) upper limits at the 95% CL on the ratio of the excluded and predicted cross-section at leading-order for a DM particle with a mass of 1 $\mathrm{GeV}$ as a function of the mediator mass for a scalar (

**left**) and pseudoscalar (

**right**) mediator [57]. The green and yellow bands represent the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The mediator couplings are set to 1.

**Figure 13.**Upper limits at 95% CL on the production of a scalar $\varphi $ (

**left**) and pseudoscalar a (

**right**) mediator as a function of the mediator mass [76]. The limits are expressed in terms of the ratio of the excluded cross-section and the cross-section calculated for a coupling assumption of $g={g}_{q}={g}_{\chi}=1.0$. The latter was calculated at NLO for the ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $t\overline{t}$ signatures and at LO for the ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tW$/$tj$ and ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + j signatures.

**Figure 14.**Upper limits at 95% CL on the production of a scalar ((

**left**), called H here instead of $\varphi $) and pseudoscalar ((

**right**), called A here instead of a) mediator as a function of the mediator mass [76]. The limits are expressed in terms of an upper limit on the production cross-section times the branching ratio of the mediator to $t\overline{t}$ and compared to the cross-section calculated at LO for a coupling assumption of $g={g}_{q}={g}_{\chi}=1.0$ (here denoted as ${g}_{\mathrm{SM}}={g}_{\mathrm{DM}}=1.0$).

**Figure 15.**Regions in the 2HDM + a parameter space excluded at 95% CL by several individual searches targeting different signatures and a statistical combination of ${p}_{\mathrm{T}}^{\mathrm{miss}}$ +$Z(\ell \ell )$ and ${p}_{\mathrm{T}}^{\mathrm{miss}}$ +$h\left(b\overline{b}\right)$ searches. The results are shown in the (${m}_{a}$,${m}_{A}$) plane (left) and the (${m}_{a}$,$tan\beta $) plane (right). In the former case, $tan\beta =1$, while in the latter case, ${m}_{A}=600$ GeV. In both cases, the conditions $sin\theta =0.35$ and ${m}_{A}={m}_{H}={m}_{{H}^{\pm}}$ are imposed. All results are based on either the full 139 fb${}^{1}$ of $pp$ collision data at $\sqrt{s}=13$ TeV or a subset of that dataset amounting to 36 fb${}^{1}$ [76].

**Figure 16.**Regions in the plane of the effective coupling ${g}_{*}$ associated with the UV completion of the EFT model and the effective mass scale ${M}_{1}$ for the ${\mathcal{L}}_{\infty}$ operator excluded at 95% CL by searches in the ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $t\overline{t}$ final state [19].

**Figure 18.**Schematic representation of ${p}_{\mathrm{T}}^{\mathrm{miss}}$ + $tW$ production via DM–Higgs operators (left) and DM–top operators in an EFT of composite pNGBs [102].

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**MDPI and ACS Style**

Behr, J.K.; Grohsjean, A.
Dark Matter Searches with Top Quarks. *Universe* **2023**, *9*, 16.
https://doi.org/10.3390/universe9010016

**AMA Style**

Behr JK, Grohsjean A.
Dark Matter Searches with Top Quarks. *Universe*. 2023; 9(1):16.
https://doi.org/10.3390/universe9010016

**Chicago/Turabian Style**

Behr, J. Katharina, and Alexander Grohsjean.
2023. "Dark Matter Searches with Top Quarks" *Universe* 9, no. 1: 16.
https://doi.org/10.3390/universe9010016