Heavy neutral leptons without prejudice

Heavy neutral leptons (HNLs) provide a compelling extension to the Standard Model, addressing the neutrino masses, baryogenesis, and dark matter problems. We perform a model-independent collider study, decoupling the active-sterile mixing angle (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>V</a:mi></a:mrow></a:math>) from the Yukawa coupling (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>y</c:mi></c:math>), and explore sensitivities at the HL-LHC for prompt and displaced decays. We also consider the possibility of HNLs being long-lived particles decaying in far detectors as FASER. In addition, we study the expected reach at FCC-ee for the prompt and displaced cases. For zero mixing, FCC-ee and HL-LHC sensitivities to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>y</e:mi></e:math> are comparable, with Higgs width measurements imposing the strongest constraints. With nonzero mixing, sensitivities are dominated by <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>V</g:mi></g:math>, significantly constraining parameter space. This work highlights the importance of precision Higgs studies and displaced searches in probing HNLs at current and future colliders.