Vector Dark Matter in the Fundamental Representation of $SU(2)_{L}$: Sommerfeld Enhancement and Indirect Detection

In this work, we study an extension of the Standard Model that includes a new massive vector field in the fundamental representation of $SU(2)_{L}$. The neutral component of this field provides a natural dark matter candidate. We compute the annihilation cross-section including Sommerfeld enhancement and the gamma-ray flux arising from dark matter annihilation. We derive constraints on the model parameter space using current gamma-ray observations and investigate the prospects for future searches. We find that the model exhibits resonances for dark matter masses in the range $2-10$ TeV, whose properties are influenced by the value of the Higgs portal coupling. We show that part of the remaining parameter space can be probed by CTA in the near future.