  Neutral long-lived particles (LLPs) are highly motivated by many BSM
scenarios, such as theories of supersymmetry, baryogenesis, and neutral
naturalness, and present both tremendous discovery opportunities and
experimental challenges for the LHC. A major bottleneck for current LLP
searches is the prediction of SM backgrounds, which are often impossible to
simulate accurately. In this paper, we propose a general strategy for obtaining
differential, data-driven background estimates in LLP searches, thereby notably
extending the range of LLP masses and lifetimes that can be discovered at the
LHC. We focus on LLPs decaying in the ATLAS Muon System, where triggers
providing both signal and control samples are available at the LHC Run-2. While
many existing searches require two displaced decays, a detailed knowledge of
backgrounds will allow for very inclusive searches that require just one
detected LLP decay. As we demonstrate for the $h \to X X$ signal model of LLP
pair production in exotic Higgs decays, this results in dramatic sensitivity
improvements for proper lifetimes $\gtrsim 10$ m. In theories of Neutral
Naturalness, this extends reach to glueball masses far below the $\bar b b$
threshold. Our strategy readily generalizes to other signal models, and other
detector subsystems. This framework therefore lends itself to the development
of a systematic, model-independent LLP search program, in analogy to the highly
successful simplified-model framework of prompt searches.
