Effective theories of dark mesons with custodial symmetry
Dark mesons are bosonic composites of a new, strongly-coupled sector beyond the Standard Model. We consider several dark sectors with fermions that transform under the electroweak group, as arise from a variety of models including strongly-coupled theories of dark matter (e.g., stealth dark matter), bosonic technicolor (strongly-coupled indcued electroweak symmetry breaking), vector-like confinement, etc. We consider theories with two and four flavors under an SU(N) strong group that acquire variously chiral, vector-like, and mixed contributions to their masses. We construct the non-linear sigma model describing the dark pions and match the ultraviolet theory onto a low energy effective theory that provides the leading interactions of the lightest dark pions with the Standard Model. We uncover two distinct classes of effective theories that are distinguishable by how the lightest dark pions decay: “Gaugephilic”: where π 0 → Zh, π ± → W h dominate once kinematically open, and “Gaugephobic”: where π 0 →$\bar{f}f$, π ± →$\bar{f'}f$ dominate. Custodial SU(2) plays a critical role in determining the “philic” or “phobic” nature of a model. In dark sectors that preserve custodial SU(2), there is no axial anomaly, and so the decay π 0 → γγ is highly suppressed. In a companion paper, we study dark pion production and decay at colliders, obtaining the constraints and sensitsivity at the LHC.