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 and antiproton excesses

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 $>7\sigma$, 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 $\sim 54–74\mathrm{GeV}$. 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 $SS\to W{W}^{*}$ 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.

Figure 1

Bin-by-bin flux upper limits at a 95% confidence level for the four dwarf spheroidal galaxies with the biggest $J$ factors considered in this work. For other sources, please see Fig. 4.

Figure 2

Upper limits at a 95% confidence level on the cross section of the $SS\to W{W}^{*}$ annihilation (thick black line). The contours demonstrate the favored DM parameters of $SS\to W{W}^{*}$ via fitting to the antiproton and GC excess data ($1\sigma$ and $2\sigma$ from inside to outside, extracted from [33]). The colored regions represent the allowed parameters to interpret the $W$-boson mass of CDF II derived in [32]. Three colors are for different DM production mechanisms in the early Universe: SA coannihilation (purple), Higgs resonance (cyan), and $SS\to W{W}^{*}$ annihilation (yellow). The parameters that can simultaneously interpret the $W$-boson mass anomaly in the i2HDM model are around the star symbols. The shaded band illustrates the variation of the limits considering the flattening of the dSphs [56]. Since our constraints are relatively marginal, if the constraints are weakened by, e.g., a factor of 3 (dashed line) due to the uncertainties of the $J$ factors, the parameters of interest cannot be ruled out (see the discussion in Sec. 4 for details).

Figure 3

Upper limits based on a combined likelihood analysis which gives results consistent with those in Fig. 2.

Figure 4

Bin-by-bin flux upper limits at a 95% confidence level for the rest dSphs considered in this work, as a supplement to Fig. 1.