Naturalness in a simple two Higgs doublet model

Abstract: We study the implications of a criterion of naturalness for a simple two Higgs doublet model in the context of the discovery of a Higgs like particle with a mass at 125 GeV. This condition which measures the amount of fine tuning further limits the parameter space of this particular model and together with other phenomenological constraints leads to an allowed range of masses for the other neutral or charged Higgs bosons: H, a^{\pm}, a^0.