Study of the Coulomb and nuclear breakup of $^{11}$Be using a Halo-EFT description at N$^2$LO

Background: The halo effective field theory (Halo-EFT) provides a very efficient description of loosely-bound nuclei in models of reaction. It offers a very systematical ranking of the significance of nuclear-structure observables in reaction calculations. This greatly helps to infer reliable structure information from reaction cross sections. However, for a meaningful analysis, the Halo-EFT scheme needs to have converged. Purpose: In a previous study [P. Capel, D. R. Phillips, and H.-W. Hammer, Phys. Rev. C 98, 034610 (2018)], NLO descriptions of 11Be have been developed and lead to excellent agreement with existing breakup data. However, the convergence of the scheme at NLO was not fully demonstrated. Moreover, a significant dependence on the regulator of the effective 10Be-n interaction has been observed. Method: We develop Halo-EFT descriptions of 11Be at N2LO and use them in an accurate breakup-reaction code. We compare our theoretical cross sections with experiment on Pb and C targets at about 70 MeV/nucleon. Results: On Pb, the N2LO descriptions of 11Be lead to little change to the NLO results of the previous study, confirming the convergence of that scheme. On C, the reaction is significantly affected by the presence of d resonances in the low-energy spectrum of 11Be. In the Halo-EFT power counting these resonances appear only at N2LO; our new descriptions include them naturally. Going to N2LO removes also the cutoff dependence observed in the previous study. Conclusions: We demonstrate the convergence of the Halo-EFT description of 11Be at NLO for Coulomb breakup and at N2LO for nuclear-dominated dissociation. The reliability of the nuclear-structure information inferred in the previous study is thus confirmed.