Flavorful Two Higgs Doublet Model with a Twin

A two Higgs doublet model with flavorful Yukawa structure, in which the two doublets give mass to the third and the first two generations respectively, is combined with the twin Higgs mechanism to stabilize the Higgs mass against radiative corrections. We consider both a mirror twin and fraternal twin setup. We identify Higgs signal strength measurements and the decay $B_s \to \mu\mu$ as the most important indirect constraints on the parameter space of the model. We explore the collider phenomenology of the model and find that the heavy Higgs in the visible sector can give a sizable number of displaced decays into $b$-jets in regions of parameter space where the SM-like Higgs and the twin Higgs do not provide any striking signatures.