$d$-wave and $s^{\pm }$ Pairing Strengths in Ba${}_2$CuO${}_{3+\delta }$

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.