Searching for the Tetraneutron Resonance on the Lattice

The nature of the tetraneutron ($4n$) system remains a pivotal question in nuclear physics. We investigate the $4n$ system using nuclear lattice effective field theory in finite volumes with a lattice size up to $L=30$~fm, employing both a high-precision N$^3$LO interaction and a simplified SU(4) symmetric one. The ground-state energy is found to decrease smoothly with increasing box size, showing no plateau characteristic of a resonance. We further compute the dineutron-dineutron scattering phase shift using Lüscher's finite-volume method. At the smallest relative momenta, the extracted $2n$--$2n$ $S$-wave phase shift is small, consistent with a weak interaction in the dilute limit. At intermediate momenta, it exhibits a weak attraction with a peak of approximately $10^\circ$ at relative momentum of 60--84~MeV. While this structure does not constitute a resonance, the corresponding confined $4n$ energy of 1.7--3.3~MeV lies close to the experimentally observed low-energy peak.