Equal-velocity scenario for hiding dark matter at the LHC

We consider a light supersymmetric top-quark (top-squark) scenario, where a top squark and a neutralino are the lightest supersymmetric particles and the top-squark mass is close to the sum of the neutralino mass and the top-quark mass. In this scenario, the top quark and the neutralino coming from the decay of a top squark have almost equal velocity vectors, and hence the missing transverse momentum in top-squark pair production events at colliders is suppressed, which makes the top-squark search challenging, as in the degenerate scenario where the top-squark mass and the neutralino mass are similar. In this paper, we propose a novel analysis technique aimed at discovering the top-squark pair production signal in such an “equal-velocity” scenario. The key is to look for events where the missing transverse momentum vector is proportional to the transverse momentum vector of the top-quark pair with specific values for the proportionality coefficient, as this coefficient is equal to the ratio of the neutralino mass over the top-quark mass in the equal-velocity limit. We examine the possibility that the top-squark signal can be identified at the $\sqrt{s}=14\mathrm{TeV}$ LHC using our analysis method.

Figure 1

The scatter plots of events of the process (10) after the selection cuts (12) and (12) in $\sqrt{s}=14\mathrm{TeV}$ $pp$ collisions, in the plane spanned by the azimuthal angle between the missing transverse momentum vector ${\overrightarrow{\cancel{p}}}_T$ and the top-pair transverse momentum vector ${\overrightarrow{p}}_{t\overline{t}T}$, $\mathrm{\Delta }\varphi ({\overrightarrow{\cancel{p}}}_T,{\overrightarrow{p}}_{t\overline{t}T})$, and the ratio of their absolute values, ${\cancel{p}}_T/p_{t\overline{t}T}$. It is assumed that the top-quark-pair momentum is perfectly reconstructed and that missing transverse momentum solely comes from neutralinos. The four panels are for $(m_{{\tilde{t}}_1},m_{{\tilde{\chi }}_1^0})=(223\mathrm{GeV},50\mathrm{GeV})$ (a), (223 GeV, 48 GeV) (b), (323 GeV, 150 GeV) (c), and (323 GeV, 148 GeV) (d), respectively. The thick horizontal line inside each figure corresponds to the line of ${\cancel{p}}_T/p_{t\overline{t}T}=m_{{\tilde{\chi }}_1^0}/m_t$.

Figure 2

The production cross section of a pair of top squarks of mass $m_{{\tilde{t}}_1}$ (black upper solid line), that of a pair of top squarks associated with one parton whose transverse momentum is above 300 GeV (red middle solid line), and that of a pair of top squarks associated with one parton whose transverse momentum is above 500 GeV (blue lower solid line) in $\sqrt{s}=14\mathrm{TeV}$ $pp$ collisions, calculated at the leading order in perturbative QCD. Also shown are the production cross sections of an SM top-quark pair and an SM top-quark pair associated with one parton whose transverse momentum is above 300 GeV. For the top-quark pair production, the cross sections are calculated both at the leading order and at the next-to-leading order in perturbative QCD. The brown upper and green lower dashed lines correspond to the top-quark pair-production cross sections calculated at the leading order and the next-to-leading order, respectively. The brown upper and green lower solid lines correspond to the production cross sections for a top-quark pair plus one jet with $p_T>300\mathrm{GeV}$, calculated at the leading order and the next-to-leading order, respectively.

Figure 3

The scatter plots of top-squark pair-production events and SM top-quark pair-production events at the $\sqrt{s}=14\mathrm{TeV}$ LHC that pass the selection cuts (16)–(16), in the plane spanned by the azimuthal angle between the missing transverse momentum vector ${\overrightarrow{\cancel{p}}}_T$ and the top-pair transverse momentum vector ${\overrightarrow{p}}_{t\overline{t}T}$, $\mathrm{\Delta }\varphi ({\overrightarrow{\cancel{p}}}_T,{\overrightarrow{p}}_{t\overline{t}T})$, and the ratio of their absolute values, ${\cancel{p}}_T/{\overrightarrow{p}}_{t\overline{t}T}$. Panel (a) displays top-squark pair-production events with a mass spectrum of $(m_{{\tilde{t}}_1},m_{{\tilde{\chi }}_1^0})=(223\mathrm{GeV},48\mathrm{GeV})$, panel (b) shows those with (323 GeV, 148 GeV), and panel (c) shows SM top-quark pair-production events, which give the dominant contribution to the background. In panels (a) and (c) one dot corresponds to one event with $100{\mathrm{fb}}^{-1}$ of data, while in panel (b) one dot corresponds to one event with $500{\mathrm{fb}}^{-1}$ of data. The thick horizontal lines inside panels (a) and (b) correspond to the lines of ${\cancel{p}}_T/{\overrightarrow{p}}_{t\overline{t}T}=m_{{\tilde{\chi }}_1^0}/m_t$.