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

Abstract

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 (${\mathrm{EFT}}_{/\pi }$). 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, $A_y(\theta )$, and the deuteron vector analyzing power, $i{T}_{11}(\theta )$. Extracting the two-body $P$-wave ${\mathrm{EFT}}_{/\pi }$ coefficients from two-body scattering data and varying them within the expected ${\mathrm{EFT}}_{/\pi }$ 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.

Comments: 18 pages, 7 figures