Searching for metastable particles with sub-millimeter displaced vertices at hadron colliders

A variety of new-physics models predict metastable particles whose decay length is $\lesssim 1$ mm. Conventional displaced-vertex searches are less sensitive to this sub-millimeter decay range, and thus such metastable particles have been looked for only in usual prompt decay searches. In this paper, we show that an additional event-selection cut based on the vertex reconstruction using charged tracks considerably improves the sensitivity of ordinary searches which rely only on kinematic selection criteria, for particles with a decay length of $\gtrsim 100\mu \text{m}$. To that end, we consider a metastable gluino as an example, and study the impact of this new event-selection cut on gluino searches at the LHC by simulating both the signal and Standard Model background processes. Uncertainty of the displaced-vertex reconstruction due to the limited resolution of track reconstruction is taken into account. We also discuss possibilities for optimization of the kinematic selection criteria, which takes advantage of significant reduction of background through the requirement of displaced vertices. In addition, we demonstrate that using the method discussed in this paper it is possible to measure the lifetime of metastable particles with an $O\left(1\right)$ accuracy at the high-luminosity LHC. Implications for a future 100 TeV collider are also studied, where produced particles tend to be more boosted and thus it is easier to detect the longevity of metastable particles.