Detector-size Upper Bounds on Dark Hadron Lifetime from Cosmology

We show that in a confining hidden valley model where the lightest hidden particles are dark hadrons that have mass splittings larger than $\mathcal{O}(0.1)$ GeV, if the lightest dark hadron is either stable or decays into Standard Model (SM) hadrons/charged leptons during the big-bang nucleosynthesis (BBN), at least one of the heavier dark hadrons needs to decay into SM particles within $\mathcal{O}(10)$ nanosec. Once being produced at collider experiments, this heavier dark hadron is likely to decay within $\mathcal{O}(1)$ meter distance, which strengthens the motivation of searching for long-lived particles with sub-meter scale decay lengths at colliders. To illustrate the idea, we study the lifetime constraint in scenarios where the lightest dark particle is a pseudo-scalar meson, and dark hadrons couple to SM particles either through kinetic mixing between the SM and dark photons or by mixing between the SM and dark Higgs. We study the annihilation and decay of dark hadrons in a thermal bath and calculate upper bounds on the lightest vector meson (scalar hadron) lifetime in the kinetic mixing (Higgs portal) scenario. We discuss the application of these lifetime constraints in long-lived particle searches that use the LHCb VELO or the ATLAS/CMS inner detectors.