Fermion mass hierarchy and flavor signals from a $D_4$ dihedral symmetry within a 2HDM-Tx with four-zero textures
We propose an extended Texturized Two-Higgs Doublet Model (2HDM-Tx) where a discrete $D_4$ symmetry predicts a four-zero texture in the fermion mass matrices. In contrast to the standard ansatz where the underlying Yukawa matrices are assumed to be structurally identical, we introduce a novel configuration of non-equivalent matrices that complementarily generate a specific Hermitian four-zero mass structure. This framework naturally suppresses flavor-changing neutral currents and provides a structural rationale for the fermion mass hierarchy, while in addition including a dark matter candidate. As a concrete phenomenological application, we show that the model simultaneously accommodates the persistent neutral resonance excesses at $95\text{ GeV}$ and $152\text{ GeV}$, satisfies current \text{LHC} Higgs data, and is consistent with the stringent upper bounds from lepton flavor violation processes. These combined constraints severely restrict the parameter space of the scalar phenomenology. Finally, we study the prospects for the discovery of the lepton-flavor violating process $h \to τμ$ at the High-Luminosity LHC.