Separation of one-pion exchange in the three-nucleon system

Ascertain whether, in the three-nucleon system, the long-range one-pion-exchange interaction can be cleanly separated from short-range interactions—analogous to the separation achieved for nucleon–nucleon scattering within the modified effective-range expansion and the modified Lüscher equation—so as to enable a practical finite-volume treatment for three-body systems.

Background

A central contribution of the paper is a finite-volume reformulation of the modified effective-range expansion that separates known long-range forces from unknown short-range physics in two-body scattering. Extending this separation to three-body systems would be valuable but is nontrivial.

The authors explicitly label as a major challenge the extension to three particles, specifically questioning whether the long-range one-pion exchange can be disentangled from short-range components in the three-nucleon case as neatly as in the two-nucleon case.

References

For instance, it remains to be seen, whether the long-range one-pion exchange force in the three-nucleon system can be separated as neatly from the short-range interactions as done in case of the nucleon-nucleon scattering.

— Lüscher equation with long-range forces  (2402.12985 - Bubna et al., 2024) in Section 6 (Conclusions), item (vi)

For the lighter pion masses, these cuts extend above the ground-state finite-volume energies, which means that in these cases both the Lüscher quantization condition and the effective-range expansion (ERE) are not strictly valid. Modifications to the Lüscher quantization condition and ERE (some of which are limited to single-particle exchange and hence not applicable to our case) have recently been proposed. Here, we neglect the left-hand cuts and proceed with the standard methods, leaving the implementation of more advanced formalisms to future work.

— Properties of the positive and negative parity charm-strange and bottom-strange mesons $D_s$, $D_s^*$, $D_{s0}^*$, $D_{s1}$, $B_s$, $B_s^*$, $B_{s0}^*$, $B_{s1}$ from lattice QCD: masses, decay constants, and compositeness  (2609.11026 - Guyton et al., 10 Sep 2026) in Section 2.4, “Application of Lüscher's Method to the Energy Levels” (Section \ref{sec:luscher})