Search for trilepton resonances from $R$-parity violating chargino decays in the $B-L$ MSSM

This dissertation presents a search for the electroweak pair-production of charginos and the associated production of charginos and neutralinos in the $B-L$ Minimal Supersymmetric Standard Model with spontaneous $R$-parity violation. The chargino and neutralino each decay via $R$-parity violating couplings to a charged lepton or neutrino and a $W$, $Z$, or Higgs boson. This analysis searches for resonances in the trilepton invariant mass spectrum, targeting events with charginos decaying to three electrons or muons via a leptonically decaying $Z$ boson. The dataset includes $139\;\text{fb}^{-1}$ of $\sqrt{s}=13\;\text{TeV}$ proton-proton collisions produced at the Large Hadron Collider and collected by the ATLAS detector. With no significant excess observed, limits are set on chargino and neutralino masses between $100\;\text{GeV}$ and $1100\;\text{GeV}$, depending on the assumed branching fractions to leptons (electron, muon, or $\tau$-lepton) and bosons ($W$, $Z$, or Higgs).