Techniques for mass peak reconstruction in Searches for Long-Lived Heavy Neutral Leptons Decaying to a Lepton and a \(\rho\) Meson
The precise reconstruction of the mass peak of long-lived heavy neutral leptons (HNLs) helps to improve the sensitivity for sterile neutrino searches in both fixed-target and collider environments (e.g., SHiP and the LHC). We present an analytical framework for reconstructing the HNL mass peak in the semileptonic HNL decay channel \(N\rightarrow l\rho\) with \(\rho\to\pi\pi^0\), using only the lepton and the charged pion emerging from the decay vertex together with kinematic constraints and the known particle masses. Incorporating mass constraints from intermediate resonances (e.g., the \(\rho\) meson) or the parent particle (e.g., the \(W\) boson at the collider experiments), we propose two methods, suitable for experiments with displaced vertex tracking capabilities. The particle-level simulation's results demonstrate that the \(\rho\)-mass constraint method yields promising HNL mass resolution in both beam-dump and collider-based environments. The W-mass constraint method, limited to the HNLs produced via \(W\)-boson decays at the collider-based experiments, shows better HNL mass resolution than the \(\rho\)-mass constraint method.