Expect the Unexpected

In the absence of evidence for new physics at the LHC, it is important to
think beyond the standard scenarios of natural theories and the
signatures they predict. I will motivate two non-standard theories
that may address the naturalness problem: supersymmetric models with
R-parity violation and models of neutral naturalness. Both scenarios
predict non-standard LHC signatures in the form of displaced decays.
We derive the first limits on classes of non-standard supersymmetric
models with long-lived lightest superpartners, as well as the first
constraints on a displaced Higgs boson with a lifetime less than 10
cm. After obtaining the results from LHC Run 1, we propose search
strategies and present projections for LHC Run 2.