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A recent result from Fermilab suggests that the measured W-boson massdeviates from the prediction of the Standard Model (SM) with a significance of$>7\sigma$, and there may exist new physics beyond the SM. It is proposed thatthe inert two Higgs doublet model (i2HDM) can well explain the new W-bosonmass. Meanwhile, the lightest neutral scalar $S$ in the i2HDM can be stable andplay the role of dark matter with a preferred dark matter mass of $\sim 54-74$GeV. It is also found that part of the parameter space of this model canexplain both the Galactic center GeV gamma-ray excess detected by $Fermi$-LATand the GeV antiproton excess detected by AMS-02 through a $SS\rightarrow WW^*$annihilation. In this paper, we aim to test the possible common i2HDM origin ofthe three anomaly/excesses using the $Fermi$-LAT observations of Milky Waydwarf spheroidal (dSph) galaxies. We perform single and stacking analyses on 19dSphs that have J-factor measurements. We find that our upper limits are belowthe favored parameters and seems to be able to exclude the possibility of acommon origin of the three anomaly/excesses. However, because the J-factormeasurements include relatively large uncertainties, which come from themeasurements of stellar kinematics, whether this model could be reliablyexcluded needs to be further confirmed by future observations.

physical review. d/physical review. d.

Using $\gamma$-ray observations of dwarf spheroidal galaxies to test the  possible common origin of the W-boson mass anomaly and the GeV  $\gamma$-ray/antiproton excesses