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$nd$ Scattering and the $A_y$ Puzzle to Next-to-next-to-next-to-leading Order

Polarization observables in neutron-deuteron scattering are calculated to next-to-next-to-next-to-leading order ($\mathrm{N}^{3}\mathrm{LO}$) in pionless effective field theory ($\mathrm{EFT}_{\notπ}$). At $\mathrm{N}^{3}\mathrm{LO}$ the two-body $P$-wave contact interactions are found to be important contributions to the neutron vector analyzing power, $A_{y}(θ)$, and the deuteron vector analyzing power, $iT_{11}(θ)$. Extracting the two-body $P$-wave $\mathrm{EFT}_{\notπ}$ coefficients from two-body scattering data and varying them within the expected $\mathrm{EFT}_{\notπ}$ theoretical errors provides results that are consistent (at the $\mathrm{N}^{3}\mathrm{LO}$ level) with $A_y$ experimental data at low energies. Cutoff dependence of the $\mathrm{N}^{3}\mathrm{LO}$ correction of the doublet $S$-wave $nd$ scattering amplitude suggests the need for a new three-body force at $\mathrm{N}^{3}\mathrm{LO}$, which is likely one that mixes Wigner- symmetric and Wigner-antisymmetric three-body channels.