Partial-wave decomposition of isospin-projected subleading three-nucleon contact interactions

TL;DR

The study tackles subleading three-nucleon contact interactions at $N^4LO$ in $\chi$EFT and develops a framework to project them into isospin and partial-wave bases. It performs an isospin projection into $T=\frac{1}{2}$ and $T=\frac{3}{2}$ sectors and a detailed partial-wave decomposition of the resulting potential in $N$-$d$ elastic channels. The key findings are that only $11$ linear combinations of the $E_i$ contribute in the $T=\frac{1}{2}$ sector and that the $N$-$d$ analysis yields $10$ channel constants $E^{(c)}_i$ across the channels $J^\pi=\frac{1}{2}^+$, $\frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$. This provides a practical basis for including subleading $3N$ forces in few-body calculations and for guiding fits to data, while highlighting that fully accounting for all operator structures may require going beyond the present wave-function ansatz.

Abstract

We analyze the subleading three-nucleon contact interaction terms at N4LO in chiral effective field theory. We perform the isospin projection into $T=1/2$ and $T=3/2$ states, and find that only eleven of the thirteen operators contribute in the $T=1/2$ channel. By projection on the partial waves of the asymptotic configuration of $N-d$ scattering states in momentum space, we find contributions from ten combinations of LECs. These results provide a useful basis for including N4LO three-body forces in few-body calculations and for constraining them through numerical fits to data.