Analyzing Effective Field Theory results for ³He-α scatteirng using Bayesian methods

We analyze the cross section data from the recent ³He-α scattering experiment of Paneru et al. performed using the SONIK chamber at TRIUMF [1]. We employ Halo Effective Field Theory (EFT) up to next-to-next-to-leading order (NNLO) for this reaction, as developed by Higa, Rupak, & Vaghani [2], Zhang, Nollett, & Phillips [3], and Poudel & Phillips [4]. The EFT low-energy constants can be mapped to the effective-range parameters in the s- and p-waves of this process. We simultaneously calibrate those parameters and the hyperparameters that encode the convergence properties of the EFT expansion. Analyzing the portion of the Paneru et al. data for c.m. energies up to 2.05 MeV we find an EFT breakdown scale of Λ_b=140 MeV. This value reflects both the convergence of the EFT expansion through NNLO and the ability of the amplitude to describe data at the upper end of this energy range. We then extend the domain of vailidity of the EFT by incorporating an intermediate-energy f-wave 7/2^- resonant state of the ⁷Be compound system in the EFT at E_c.m.=2.98 MeV. We show that the f-wave amplitude can be systematically expanded in a small parameter in the vicinity of the resonance, and that two new parameters are required for an accurate description in this regime. We calibrate the resulting extended Halo EFT for ³He-α scattering to the entire Paneru data set (E_c.m.=0.385-3.13 MeV) and achieve a good description wihtin the EFT uncertainties. The breakdown scale of the EFT augmented by the 7/2^- resonance is somewhat higher than without it: this new analysis yields Λ_b=180 MeV. We also discuss the impact of the 5/2^- resonance at E_c.m.=5.13 MeV on our results.

[1] S.N. Paneru et al., Phys. Rev. C 109, 015802 (2024).

[2] R. Higa, G. Rupak, and A. Vaghani, Eur. Phys. J. A 54, 89 (2018).

[3] X. Zhang, K. Nollett, and D. R. Phillips, J. Phys. G 47, 054002 (2020).

[4] M. Poudel and D. R. Phillips, J. Phys. G 49, 045102 (2022); 099601 (2022).