Scalar Top Quark as the Next-to-Lightest Supersymmetric Particle

TL;DR

The authors analyze a gauge-mediated SUSY framework in which the lightest scalar top quark $\widetilde{t}_1$ is the NLSP and lighter than the top quark, forcing the dominant decay $\widetilde{t}_1 \to W^+ b \widetilde{G}$. They develop the MSSM formalism with Goldstino couplings and examine four representative wino/Higgsino mixing scenarios to model the stop decay amplitude, rates, and kinematics. A key result is that the observable $m(eb)$ distribution from leptonic $W$ decays in stop events has a distinct shape and endpoint compared to $t\overline{t}$ events, enabling stop identification and approximate mass determination (about 5 GeV precision). They also show that the longitudinal $W$ polarization fraction $r$ in stop decays generally deviates from the SM top value $r_t \approx 0.71$, with the deviation sensitive to SUSY parameters and intermediate states, offering a potential parameter-diagnostic tool. Together, these findings suggest that Tevatron-era measurements of these observables could confirm or refute the light-stop NLSP scenario and illuminate the SUSY-breaking structure.

Abstract

We study phenomenologically the scenario in which the scalar top quark is lighter than any other standard supersymmetric partner and also lighter than the top quark, so that it decays to the gravitino via stop -> W^+ b G. In this case, scalar top quark events would seem to be very difficult to separate from top quark pair production. However, we show that, even at a hadron collider, it is possible to distinguish these two reactions. We show also that the longitudinal polarization of the final $W^+$ gives insight into the scalar top and wino/Higgsino mixing parameters.

Figures (7)

• Figure 1: Feynman diagrams for the process ${\widetilde{t}_1} \to bW{\widetilde{G}}$. All diagrams are drawn in terms of 2-component fermion notation. $\tilde{G}$ denotes the Goldstino. The label on the $\widetilde{W}$/$\widetilde{h}$ internal lines labels the vertex with which the chargino couples to the top quark.
• Figure 2: Decay length for the lightest scalar top quark $\tilde{t}_1$ as a function of its mass in four different scenarios. The parameters $\sqrt{F}=30$ TeV, $\tan\beta=1.0$, $m_{\tilde{b}_L}=300$ GeV, and $\sin {\theta_t}=-0.8$ are assumed in all four scenarios.
• Figure 3: Typical $eb$ and $Wb$ invariant mass distributions for $\widetilde{t}_1$ decay. The distributions are shown at two different assumed $\widetilde{t}_1$ masses, $m_{\tilde{t}_1}=130$ (dotted lines) and 170 GeV (dashed lines), under the scenario (1). The other parameters are chosen as $\tan\beta=1.0$, $m_{\tilde{b}_L}=300$ GeV, and $\sin {\theta_{t}}=-0.8$. The solid line shows, for comparison, the $m_{eb}$ spectrum for the standard top quark decay.
• Figure 4: Invariant mass spectra under different scenarios at the two mass values $m_{\tilde{t}_1}$: (a)$m_{\tilde{t}_1}=170$ GeV, (b) $m_{\tilde{t}_1}=150$ GeV. For each case, the parameters are: solid line: scenario (1), $\sin {\theta_{t}}=0.0$, $\tan\beta=1.0$, $m_{\tilde{b}_L}=300$ GeV; dotted line: scenario (2), $\sin {\theta_{t}}=-0.8$, $\tan\beta=1.0$, $m_{\tilde{b}_L}=300$ GeV; dashed line: scenario (3), $\sin {\theta_{t}}=0.9$, $\tan\beta=50.0$, $m_{\tilde{b}_L}=200$ GeV; dot-dashed line: scenario (3), $\sin {\theta_{t}}=0.0$, $\tan\beta=1.0$, $m_{\tilde{b}_L}=300$ GeV; long-dashed line: scenario (4), $\sin {\theta_{t}}=0.4$, $\tan\beta=8.0$, $m_{\tilde{b}_L}=200$ GeV.
• Figure 5: Longitudinal W production ratio for the stop $\tilde{t}_1$ decay as a function of $m_{\widetilde{t}_1}$ under different scenarios. The dot-dash, dotted, dashed, and dot-dot-dash lines refer, respectively, to the chargino scenarios (1), (2), (3), (4) given at the end of Section 2. The two figures show (a) $\tilde{t}_R$-like cases with $sin{\theta_{t}}=-0.8$, $tan\beta=1.0$, and $m_{\tilde{b}_L}=300$ GeV. (b) pure $\tilde{t}_L$-like cases with $sin {\theta_{t}}=0.0$, $tan\beta=1.0$, and $m_{\tilde{b}_L}=300$ GeV.