Sommerfeld Enhancement from Background Force and the Galactic Center GeV Excess

We study the impact of background-induced forces on dark matter (DM) annihilation and their implications for indirect detection. In the presence of a finite number density of background particles, loop-level interactions can generate an effective force that is significantly enhanced relative to the vacuum case. We construct a two-component DM model in which the dominant component is a fermionic particle $\chi$ and the subdominant component is an ultralight pseudoscalar particle $\phi$. The annihilation of $\chi$ proceeds through the p-wave channel and produces gamma-ray emission. The finite density of $\phi$ particles induces a background-enhanced force between $\chi$ particles, leading to a sizable Sommerfeld enhancement of the annihilation. We show that a viable region of parameter space in this model can account for the gamma-ray excess observed in the Galactic Center using Fermi-LAT data. The background-induced force substantially amplifies the Sommerfeld enhancement and thus enlarges the parameter space capable of explaining the excess, highlighting the importance of background effects in astrophysical environments.