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 $N\to l\rho$ 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.