Emergence of $^4$H $J^\pi=1^-$ resonance in contact theories
| Autor: | Contessi, Lorenzo, Schäfer, Martin, Kirscher, Johannes, Lazauskas, Rimantas, Carbonel, Jaume |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Physics Letters B 840, 137840 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physletb.2023.137840 |
| Popis: | We obtain the $s$- and $p$-wave low-energy scattering parameters for n$^3$H elastic scattering and the position of the $^4$H $J^\pi=1^-$ 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 $1\,\text{fm}^{-1}$ and $10\,\text{fm}^{-1}$. Most remarkably, we find a cutoff-stable/RG-invariant resonance in the $^4$H $J^\pi=1^-$ 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. Comment: 11 pages, 6 figures |
| Databáze: | arXiv |
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