Nondecoupling of charged scalars in Higgs decay to two photons and symmetries of the scalar potential

A large class of two- and three-Higgs-doublet models with discrete symmetries has been employed in the literature to address various aspects of flavor physics. We analyze how the precision measurement of the Higgs to diphoton signal strength would severely constrain these scenarios due to the nondecoupling behavior of the charged scalars, to the extent that in the presence of exact discrete symmetry, the number of additional noninert scalar doublets can be constrained no matter how heavy the nonstandard scalars are. We demonstrate that if the scalar potential is endowed with appropriate global continuous symmetries together with soft breaking parameters, decoupling can be achieved thanks to the unitarity constraints on the mass-square differences of the heavy scalars.