${}^3\mathrm{H}\mathrm{e}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory

We study the three-body systems of ${}^3\mathrm{H}\mathrm{e}$ and $pd$ scattering and demonstrate, both analytically and numerically, that a new $pd$ three-body force is needed at next-to-leading order in pionless effective field theory. We also show that at leading order these observables require no new three-body force beyond what is necessary to describe $nd$ scattering. We include electromagnetic effects by iterating only diagrams that involve a single photon exchange in the three-body sector.