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A recent result from Fermilab suggests that the measured W-boson mass deviates from the prediction of the Standard Model (SM) with a significance of >7, and there may exist new physics beyond the SM. It is proposed that the inert two Higgs doublet model (i2HDM) can well explain the new W-boson mass. Meanwhile, the lightest neutral scalar S in the i2HDM can be stable and play the role of dark matter with a preferred dark matter mass of 54--74 GeV. It is also found that part of the parameter space of this model can explain both the Galactic Center GeV gamma-ray excess detected by Fermi-LAT and the GeV antiproton excess detected by AMS-02 through a SSW^* annihilation. In this paper, we aim to test the possible common i2HDM origin of the three anomaly/excesses using the Fermi-LAT observations of Milky Way dwarf spheroidal galaxies. We perform single and stacking analyses on 19 dwarf spheroidal galaxies that have J-factor measurements. We find that our upper limits are below the favored parameters and seems to be able to exclude the possibility of a common origin of the three anomaly/excesses. However, because the J-factor measurements include relatively large uncertainties, which come from the measurements of stellar kinematics, whether this model could be reliably excluded needs to be further confirmed by future observations.
Zhu et al. (Mon,) studied this question.