Interpretation of the gamma-ray excess and AMS-02 antiprotons: Velocity
  dependent dark matter annihilations
  The two messenger results of the GeV gamma-ray excess at the Galactic center
and a probable antiproton excess in the recent AMS-02 observation suggest that
these two anomalies may be owing to the same origin --- the dark matter (DM)
annihilation into $b \bar b$, while these results seem in tension with the
dwarf spheroidal galaxy observations. To give a compatible explanation about
it, we consider the pseudoscalar DM particles $S_d^+ S_d^-$ annihilating via
$S_d^+ S_d^- \rightarrow S_d^0 S_d^0$, with the process mediated by a new
scalar $\phi$ and $S_d^0$ quickly decaying into $b \bar{b}$. For the particles
$S_d^+$, $S_d^-$ and $S_d^0$ in a triplet with degenerate masses, the
annihilation cross section of DM today is linearly dependent on the relative
velocity $v_r$, and thus constraints from the dwarf spheroidal galaxies are
relaxed. The parameter spaces are derived with corresponding constraints.
Though traces from the new sector seem challenging to be disclosed at collider
and in DM direct detections, the indirect search of the gamma-ray line from the
$S_d^0$'s decay has the potential to shed light on DM annihilations, with the
energy of the gamma-ray line $\sim m_{S_d^0} /2$, i.e. about 50$-$75 GeV.
