Extracting the mass scale of a second Higgs boson from a deviation in $h(125)$ couplings

We investigate the correlation between a possible deviation in the discovered Higgs boson $h(125)$ couplings from the Standard Model prediction and the mass scale ($M_{\text{2nd}}$) of the next-to-lightest Higgs boson in models with non-minimal Higgs sectors. In particular, we comprehensively study a class of next-to-minimal Higgs sectors which satisfy the electroweak $\rho$ parameter to be one at tree level. We derive an upper limit on $M_{\text{2nd}}$ by imposing bounds from perturbative unitarity, vacuum stability, triviality and electroweak precision data as functions of the deviation in the $hVV$ ($V=W,Z$) couplings. Furthermore, we discuss the complementarity between these bounds and the current LHC data, e.g., by considering direct searches for additional Higgs bosons and indirect constraints arising from the measured $h(125)$ signal strengths.