Constraining the dark matter origin of the halo-like 20 GeV $\gamma$-ray excess with the AMS-02 antiproton data

Very recently, a significant $\sim 20$ GeV gamma-ray excess in the Milky Way halo has been reported and a dark matter origin has been suggested. The inferred dark matter parameters are $m_{\chi }\sim 0.5-0.8$ TeV and $⟨\sigma v⟩\sim (5-8)\times {10}^{-25}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ for the $b\bar{b}$ channel. If correct, prominent antiproton emission is produced and can be directly tested by the AMS-02 data. In this work we calculate the corresponding antiproton emission and show that the expected flux at $\sim 100$ GeV is already above the AMS-02 observation. A proper treatment on the antiproton background resulting from the high energy cosmic ray propagation would suggest an annihilation cross section of $<2\times {10}^{-26}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, which is a few$\times 10$ times lower than that needed to interpret the potential signal. We therefore conclude that the $\sim 20$ GeV gamma-ray excess in the Milky Way halo is not a viable dark matter signal.