Emergence of 4H Jπ = 1− resonance in contact theories

Abstract

We obtain the s- and p-wave low-energy scattering parameters for n3H elastic scattering and the position of the 4H Jπ=1− resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between 1fm−1 and 10fm−1. Most remarkably, we find a cutoff-stable/RG-invariant resonance in the 4H Jπ=1− system. This p-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body s-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory's leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT.