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Off-diagonal terms in Yukawa textures of the Type-III 2-Higgs doublet model and light charged Higgs boson phenomenology

We discuss flavor-violating constraints and consequently possible charged Higgs boson phenomenology emerging from a four-zero Yukawa texture embedded within the Type-III 2-Higgs Doublet Model (2HDM-III). Firstly, we show in detail how we can obtain several kinds of 2HDMs when some parameters in the Yukawa texture are absent. Secondly, we present a comprehensive study of the main B-physics constraints on such parameters induced by flavor-changing processes, in particular on the off-diagonal terms of such a texture: i.e., from $μ-e$ universality in $τ$ decays, several leptonic B-decays ($B \to τν$, $D \to μν$ and $D_s \to {l} ν$), the semi-leptonic transition $B\to D τν$, plus $B \to X_s γ$, including $B^0-\bar B^0$ mixing, $B_s \to μ^+ μ^-$ and the radiative decay $Z\to b \bar{b}$. Thirdly, having selected the surviving 2HDM-III parameter space, we show that the $H^- c \bar{b}$ coupling can be very large over sizable expanses of it, in fact, a very different situation with respect to 2HDMs with a flavor discrete symmetry (i.e., ${\mathcal{Z}}_2$) and very similar to the case of the Aligned-2HDM (A2HDM) as well as of models with three or more Higgs doublets. Fourthly, we study in detail the ensuing $H^\pm$ phenomenology at the Large Hadron Collider (LHC), chiefly the $c\bar b \to H^+$ production mode and the $H^+\to c\bar b$ decay channel while assuming $τ^+ν_τ$ decays in the former and $t\to bH^+$ production in the latter, showing that significant scope exists in both cases.