Charged Higgs Decay to Bottom and Charm Quarks from $Z_3$-Flavored Two Higgs Doublet Models

The phenomenology of a charged Higgs present in a model with two Higgs SU(2) doublets and a $Z_3$ flavor symmetry is analyzed. It is shown that it is possible to generate an enhancement of its flavor changing coupling to c and b quarks and also to reproduce the ATLAS excess associated to the process $H^{\pm }\to bc$ for a charge Higgs mass of $130$~GeV. Furthermore, by considering the possibility of a search at the future LHeC, the analysis suggests viability for its detection.