The flavor of a light charged Higgs

The ATLAS Collaboration has recently reported a search for light-charged Higgs in $t\to H^+ b$ decay, with $H^+\to c\bar b$. An excess with a local significance of approximately $3\sigma$ is found at $m_{H^+}\approx130$ GeV, with a best-fit value of ${\rm BR}(t\to H^+b)\times {\rm BR}(H^+\to c\bar b)=(1.6\pm0.6)\times10^{-3}$. We study the implications of such a hypothetical signal in multi-Higgs doublet models. We take into account constraints from searches for other charged Higgs decays and from flavor-changing neutral current processes. Two Higgs doublet models with flavor structure dictated by natural flavor conservation (NFC), minimal flavor violation (MFV), or the Froggatt-Nielsen (FN) mechanism cannot account for such excess. A three-Higgs doublet model with NFC can account for the signal. The Yukawa couplings of the neutral pseudoscalar $A$ in the down sector, $\hat Y_A^D$, should be larger by a factor of $4-6$ compared to the corresponding Yukawa couplings of the Higgs $h$, $\hat Y_h^D$. We further present two minimal scenarios, one in which a single Yukawa coupling in the down sector, $(\hat Y_A^D)_{bb}$, gives the only significant contribution, and one in which two Yukawa couplings in the up sector, $(\hat Y_A^U)_{tt}$ and $(\hat Y_A^U)_{tc}$, give the only significant contributions, and we discuss possible tests of these scenarios.