Rare Top Decays as Probes of Flavorful Higgs Bosons

We study a version of Two Higgs Doublet Models with non-standard flavor violation in the up quark sector. We find branching ratios for the rare top decays $t\to hc$ and $t\to hu$ that are within reach of current and future colliders, while other flavor constraints from rare $B$ decays and neutral $D$ meson mixing, as well as constraints from Higgs signal strength measurements remain under control. The most prominent collider signature of the considered setup is $pp \to t H \to tt \bar c$, providing continued motivation to search for same-sign tops at the LHC as well as a simple framework to interpret these searches. As a byproduct of our study, we provide updated SM predictions for the rare top decays BR$(t \to h c)_\text{SM} = (4.19^{+1.08}_{-0.80} \pm 0.16) \times 10^{-15}$ and BR$(t \to h u)_\text{SM} = (3.66^{+0.94}_{-0.70} \pm 0.67) \times 10^{-17}$ with the main uncertainties coming from higher order QCD and CKM matrix elements.