Probing light sterile neutrinos in left-right symmetric models with displaced vertices and neutrinoless double beta decay

A bstract An investigation of relatively light (GeV-scale), long-lived right-handed neutrinos is performed within minimal left-right symmetric models using the neutrino-extended Standard Model Effective Field Theory framework. Light sterile neutrinos can be produced through rare decays of kaons, D -mesons, and B -mesons at the Large Hadron Collider (LHC) and the Long-Baseline Neutrino Facility (LBNF) of Fermilab. Their decays could result in displaced vertices, which can be reconstructed. By performing Monte-Carlo simulations, we assess the sensitivities of the future LHC far-detector experiments ANUBIS, CODEX-b, FACET, FASER(2), MoEDAL-MAPP1(2), MATHUSLA, the recently approved beam-dump experiment SHiP, and the upcoming neutrino experiment DUNE at the LBNF, to the right-handed gauge-boson mass $$ {M}_{W_R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:msub> </mml:math> as functions of neutrino masses. We find that DUNE and SHiP could be sensitive to right-handed gauge-boson masses up to ~ 25 TeV. We compare this reach to indirect searches such as neutrinoless double beta decay, finding that displaced-vertex searches are very competitive.