Search for Heavy Neutral Leptons in Decays of $W$ Bosons Using a Dilepton Displaced Vertex in $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ $pp$ Collisions with the ATLAS Detector

A search for a long-lived, heavy neutral lepton ($N$) in $139\text{}\text{}{\mathrm{fb}}^{-1}$ of $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ $pp$ collision data collected by the ATLAS detector at the Large Hadron Collider is reported. The $N$ is produced via $W\to N\mu $ or $W\to Ne$ and decays into two charged leptons and a neutrino, forming a displaced vertex. The $N$ mass is used to discriminate between signal and background. No signal is observed, and limits are set on the squared mixing parameters of the $N$ with the left-handed neutrino states for the $N$ mass range $3\text{}\text{}\mathrm{GeV}<{m}_{N}<15\text{}\text{}\mathrm{GeV}$. For the first time, limits are given for both single-flavor and multiflavor mixing scenarios motivated by neutrino flavor oscillation results for both the normal and inverted neutrino-mass hierarchies.