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° 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.