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In this letter we study the specific sensitivity and constraints to the softbreaking $Z_2$ parameter $m_{12}$ of the Two Higgs Doublet Model (2HDM).$m_{12}$ is considered here as an input parameter of the model together withthe masses of the Higgs bosons, $m_h$, $m_H$, $m_A$, $m_{H^\pm}$, the ratio ofthe two Higgs vacuum expectation values, $\tan \beta$, and$\cos(\beta-\alpha)$, with $\alpha$ and $\beta$ the mixing angles of the$\mathcal{CP}$-even and $\mathcal{CP}$-odd Higgs sector, respectively. Weexplore in particular the sensitivity to $m_{12}$ in the decays of the lightestHiggs boson $h$ to two photons, assuming: 1) that $h$ is the state observed atthe LHC at $\sim 125 \ \mathrm{GeV}$, and 2) the $h$ couplings to the SMparticles are SM-like, by going to the alignment limit, $\cos(\beta-\alpha) =0$. The aim of this work is to demonstrate possible constraints on $m_{12}$from the present measurement of the di-photon signal strength, $\mu_{\gamma\gamma}$. These constraints are relevant in the region of the 2HDM parameterspace that is allowed by all the other constraints, specifically, theoreticalconstraints as well as experimental constraints from LHC Higgs ratemeasurements, Higgs boson searches, flavor physics and precision observables.The exploration is performed in the four different Yukawa types of 2HDM, wherethe allowed region by all the other constraints depends on the model type. Wealso analyze the case that the Higgs-boson mass spectrum accommodates apossible new world average of $m_W$ including the recent CDF measurement.

Sensitivity and constraints to the 2HDM soft-breaking $Z_2$ parameter $m_{12}$