Sommerfeld Enhancement in Spin-1 Electroweak Dark Matter

Abstract: We study a renormalizable spin-1 electroweakly interacting dark matter (DM) model in which the DM particle is the neutral component of a $Z_2$-odd $\mathrm{SU(2)}_L$ triplet vector boson. The model predicts an additional $Z_2$-even heavy vector triplet, $W'^{\pm}$ and $Z'$, which is generically heavier than the DM particle and whose mass is closely related to the DM mass. Taking into account the Sommerfeld enhancement due to long-range electroweak interactions, we evaluate the thermal relic abundance of the spin-1 DM. We find that the observed relic abundance is reproduced through the freeze-out mechanism for DM masses ($m_V$) in the range $3.6~\mathrm{TeV} \lesssim m_V \lesssim 9.2~\mathrm{TeV}$ within a perturbative regime. A heavier DM mass is favored when the heavy vector boson mass approaches the DM mass, since annihilation processes into a heavy vector boson and a Standard Model particle significantly enhance the effective annihilation cross section. This behavior is distinctive from spin-0 and spin-$1/2$ electroweak DM scenarios, which typically predict a DM mass around $3~\mathrm{TeV}$. We further investigate indirect detection prospects and find that the Cherenkov Telescope Array Observatory (CTAO) will probe the entire viable parameter region. In particular, for $m_V \gtrsim 7.5~\mathrm{TeV}$, the model predicts a characteristic double-peak gamma-ray signature: one peak arising from the unresolved $γγ$ and $Zγ$ channels, and the other from the $Z'γ$ annihilation channel.