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, $W^{\prime \pm }$ and $Z^{\prime }$, 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 $\gamma \gamma$ and $Z\gamma$ channels, and the other from the $Z^{\prime }\gamma$ annihilation channel.

Comments: 45 pages, 14 figures