Relic abundance of a new dark matter WIMP annihilating to WW* and ZZ*

We report calculations of the annihilation cross-section for the dark matter WIMP that we have proposed, here represented by H. For annihilation to real particles, WW and ZZ, we make the approximation that the W, Z, and H masses are nearly equal. We find that the total annihilation cross-section is more than an order of magnitude too large for $m_Z > m_H > m_W$, and about a factor of 2 larger still for $m_H > m_Z$. (Without this approximation, the cross-sections would be even larger.) For annihilation to one real particle and one virtual, WW* and ZZ*, we make the approximation of neglecting the masses of the fermions (which are all relatively small). If $m_H$ is well below $m_W$, the total cross-section is more than an order of magnitude too small. As the H mass approaches $m_W$ from below, however, there is resonant behavior involving the W propagator, and for a mass of about 72 GeV the cross-section has the value corresponding to the observed relic abundance. This annihilation cross-section is consistent with the limits set by observation of gamma-ray emissions from dwarf spheroidal galaxies by Fermi-LAT, and with gamma-ray emissions from the Galactic center that have been interpreted as possible evidence of dark matter annihilation.