Excesses in the low-mass Higgs-boson search and the W-boson mass measurement

The CDF collaboration recently reported a measurement of the $W$-bosos mass, $M_W$, showing a large positive deviation from the Standard Model (SM) prediction. The question arises whether extensions of the SM exist that can accommodate such large values, and what further phenomenological consequences arise from this. A different type of deviation from the SM has been observed experimentally in the searches for light Higgs bosons. CMS has observed two local $\sim 3\,\sigma$ excesses in the $\gamma\gamma$ and $\tau^+\tau^-$ final states for a hypothetical Higgs-boson mass of $\sim 95$ GeV. These two excesses are compatible with the corresponding ATLAS limits. A third excess was observed in the Higgs-boson searches at LEP in the $b \bar b$ final state at the local $\sim 2\,\sigma$ confidence level at about the same Higgs-boson mass. It was shown recently that the three excesses can be described the the 2HDM extended with a real singlet (N2HDM) of Yukawa type IV, while being in agreement with all other theoretical and experimental constraints. We demonstrate that the parameter space that accomodates the three excesses can also give a large contribution to $M_W$ in agreement with the recent CDF measurement. We discuss further phenomenological consequences of this scenario.