Strategies for probing nonminimal dark sectors at colliders: The interplay between cuts and kinematic distributions

In this paper, we examine the strategies and prospects for distinguishing between traditional dark-matter models and models with nonminimal dark sectors—including models of Dynamical Dark Matter—at hadron colliders. For concreteness, we focus on events with two hadronic jets and large missing transverse energy at the Large Hadron Collider (LHC). As we discuss, simple “bump-hunting” searches are not sufficient; probing nonminimal dark sectors typically requires an analysis of the actual shapes of the distributions of relevant kinematic variables. We therefore begin by identifying those kinematic variables whose distributions are particularly suited to this task. However, as we demonstrate, this then leads to a number of additional subtleties, since cuts imposed on the data for the purpose of background reduction can at the same time have the unintended consequence of distorting these distributions in unexpected ways, thereby obscuring signals of new physics. We therefore proceed to study the correlations between several of the most popular relevant kinematic variables currently on the market, and investigate how imposing cuts on one or more of these variables can impact the distributions of others. Finally, we combine our results in order to assess the prospects for distinguishing nonminimal dark sectors in this channel at the upgraded LHC.

Figure 1

A comparison of the normalized ${\alpha }_T$ (left panel), $|\mathrm{\Delta }{\varphi }_{jj}|$ (center panel), and $H_{T_{jj}}$ (right panel) distributions associated with traditional dark-matter candidates as well as DDM ensembles. In each panel, the black curves correspond to distributions for a representative set of traditional dark-matter candidates, while the red, green, and blue curves in each panel correspond to DDM ensembles with $m_0=200\mathrm{GeV}$, $\mathrm{\Delta }m=50\mathrm{GeV}$, $\delta =1$, and $\gamma =\{0,1,2\}$, respectively. All distributions shown correspond to a parent-particle mass $m_{\varphi }=1\mathrm{TeV}$.

Figure 2

A comparison of the normalized ${\cancel{E}}_T$ distributions associated with traditional dark-matter candidates as well as DDM ensembles. In each panel, the black curves correspond to distributions for a representative set of traditional dark-matter candidates, while the colored curves in the left, middle, and right panels correspond to the DDM parameter choices $m_{\varphi }=1\mathrm{TeV}$, $m_0=200\mathrm{GeV}$, $\delta =1$, and $\mathrm{\Delta }m=\{50,300,500\}\mathrm{GeV}$, respectively, with $\gamma =0$ (red), $\gamma =1$ (yellow), and $\gamma =2$ (blue).

Figure 3

Same as Fig. 2, but for normalized $M_{T2}$ distributions with trial mass $\tilde{m}=0$.

Figure 4

Same as Fig. 2, but with the additional cut ${\alpha }_T>0.55$.

Figure 5

Same as in Fig. 3, but with the additional cut ${\alpha }_T>0.55$.

Figure 6

Scatter plots illustrating the correlations between $M_{T2}$ and the selection variables ${\alpha }_T$ (top row), $|\mathrm{\Delta }{\varphi }_{jj}|$ (center row), and $H_{T_{jj}}$ (bottom row) for a trial mass $\tilde{m}=0$. The left panel in each row shows the results for traditional dark-matter models with $m_{\chi }=0$ (red), $m_{\chi }=400\mathrm{GeV}$ (green), and $m_{\chi }=800\mathrm{GeV}$ (blue). The center panel in each row shows the results for three DDM models, with $m_0=100\mathrm{GeV}$, $\mathrm{\Delta }m=50\mathrm{GeV}$, $m_{\varphi }=1\mathrm{TeV}$, and $\gamma =0$ (red), $\gamma =1$ (green), and $\gamma =2$ (blue). The right panel in each row shows the corresponding results for a DDM model with $\mathrm{\Delta }m=500\mathrm{GeV}$ and all other parameters unchanged.

Figure 7

The value of the statistic $G_{\min }$ for the $M_{T2}$ distributions (top row) and ${\cancel{E}}_T$ distributions (bottom row) associated with several DDM ensembles as a function of the minimum cut ${\alpha }_T^{\min }$ imposed on ${\alpha }_T$ (left column) or the minimum cut $H_{T_{jj}}^{\min }$ imposed on $H_{T_{jj}}$ (right column). In each case, the precuts in Sec. 3b are the only other cuts imposed on the data. The curves shown in all panels correspond to the parameter choices $m_0=100\mathrm{GeV}$, $\mathrm{\Delta }m=50\mathrm{GeV}$, and $\delta =1$, and the $M_{T2}$ curves correspond to a trial mass $\tilde{m}=0$. Further details are discussed in the text.