Search for heavy neutral leptons in decays of $W$ bosons using a dilepton displaced vertex in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

A search for a long-lived, heavy neutral lepton ($\mathcal{N}$) in 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data collected by the ATLAS detector at the Large Hadron Collider is reported. The $\mathcal{N}$ is produced via $W \rightarrow \mathcal{N} \mu$ or $W \rightarrow \mathcal{N} e$ and decays into two charged leptons and a neutrino, forming a displaced vertex. The $\mathcal{N}$ mass is used to discriminate between signal and background. No signal is observed, and limits are set on the squared mixing parameters of the $\mathcal{N}$ with the left-handed neutrino states for the $\mathcal{N}$ mass range $3$ GeV $< m_{\mathcal{N}} < 15$ 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.