Probing a left-right symmetric model from a displaced shower at the CMS muon system

We study the potential collider discovery for the right-handed neutrinos (RHNs) in the minimal left-right symmetric model (LRSM). In this model, the RHNs can be either produced from the right-handed gauge boson $W_R^\pm$, or the scalar triplet $\Delta$ decays. The RHNs can subsequently decay via the heavy $W_R^\pm$, making them potentially long-lived. In looking for such long-lived RHNs, a search for displaced shower at CMS muon system is reinterpreted for either the processes, $pp \rightarrow W_R^\pm \rightarrow \ell^\pm N$ or $pp \rightarrow \Delta \rightarrow N N$. From the former process, we exclude $M_{W_R} \lesssim 3.6$ TeV using current CMS data, or $\lesssim 8.0$ TeV at the future HL-LHC. For the $pp \rightarrow \Delta \rightarrow N N$ process, HL-LHC is able to probe much larger parameter space as long as the proper decay length of the RHNs, 0.01 m $\lesssim L_0 \lesssim$ 1 m. This implies that the displaced shower searches are able to explore the parameter space of the LRSM which have not been excluded yet.