Radiative proton capture on ${}^{12}\mathrm{C}$ in cluster effective field theory

Radiative proton capture on ${}^{12}\mathrm{C}$ to the ground state of ${}^{13}\mathrm{N}$ is calculated in cluster effective field theory through next-to-leading order. At low energy the reaction is dominated by $s_{1/2}\to p_{1/2}$ $E1$ capture, which we treat in the long-wavelength limit. Its amp