  Using a first principles derived two-orbital model ($d_{x^2-y^2}$,
$d_{3z^2-r^2}$) and a random phase approximation treatment of the
spin-fluctuation pairing vertex, we calculate the $d$-wave and $s^\pm$-wave
pairing strengths for a model of the recently discovered Ba$_2$CuO$_{3+\delta}$
superconductor. We find that there is significant pairing strength in both of
these channels. These results provide an interesting perspective on the
relationship between the cuprates and Fe-based superconductors and the
high-$T_c$ pairing mechanism.

Superconductivity