Low energy neutron deuteron scattering to N$^3$LO

\newcommand{\EFT}{EFT$_{\pi \! \! \! /}$}\newcommand{\Lam}{$\Lambda_{\pi \! \! \! /}$}We calculate the next-to-next-to-next-to-leading order (N\textsuperscript{3}LO) $nd$ scattering amplitude in the framework of nonrelativistic pionless effective field theory (\EFT). This theory is only valid when the typical momentum exchange in the scattering is smaller then the mass of the pion. The power counting parameter for \EFT \ is the ratio $\frac{Q}{\Lambda_{\pi \! \! \! /}}$, where $Q$ is the typical momentum exchange in the scattering and \Lam \ is the \EFT \ breakdown scale, \Lam $< m_{\pi}$. The calculation of the amplitude for $nd$ scattering at leading order requires summing an infinite set of diagrams. The first nonzero polarization-dependent observables occur at N\textsuperscript{2}LO. At N\textsuperscript{3}LO new 2-body forces appear, which introduce four new \EFT \ coefficients. These coefficients are fixed by the $^{3}P_{J}$ and $^{1}P_{1}$ phase shifts of NN scattering. We find that these terms have an important impact. The results of this calculation at N\textsuperscript{3}LO will be important for understanding spin polarization observables in $nd$ scattering, in particular the longstanding $A_{y}$ puzzle.