Stop Decay with LSP Gravitino in the final state: $\tilde{t}_1\to\widetilde{G}\,W\,b$

TL;DR

This paper calculates the lifetime of the stop particle decaying into a gravitino, W boson, and b quark within the MSSM, considering full intermediate state contributions and the goldstino approximation, highlighting differences at higher gravitino masses.

Contribution

It provides a detailed analytical calculation of the stop decay lifetime including full intermediate states and compares gravitino and goldstino cases, extending previous approximations.

Findings

Stop decay dominated by 3-body mode for certain mass spectra.

Calculated stop lifetime including top, sbottom, and chargino contributions.

Lifetime differences up to 100% for higher gravitino masses.

Abstract

In MSSM scenarios where the gravitino is the lightest supersymmetric particle (LSP), and therefore a viable dark matter candidate, the stop $\tilde{t}_1$ could be the next-to-lightest superpartner (NLSP). For a mass spectrum satisfying: $m_{\widetilde{G}}+m_t>m_{\tilde{t}_1}>m_{\widetilde{G}}+m_b+m_W$, the stop decay is dominated by the 3-body mode $\tilde{t}_1\rightarrow b\,W\,\tilde{G}$. We calculate the stop life-time, including the full contributions from top, sbottom and chargino as intermediate states. We also evaluate the stop lifetime for the case when the gravitino can be approximated by the goldstino state. Our analytical results are conveniently expressed using an expansion in terms of the intermediate state mass, which helps to identify the massless limit. In the region of low gravitino mass ($m_{\widetilde{G}}\ll m_{\tilde{t}_1}$) the results obtained using the gravitino and goldstino cases turns out to be similar, as expected. However for higher gravitino masses $m_{\widetilde{G}} \lesssim m_{\tilde{t}_1}$ the results for the lifetime could show a difference of O(100)\%.