Nonperturbative NNNN scattering in 3S1–3D13S1–3D1 channels of EFT(⁄π)

•Closed-form unitary TT matrices for NNNN scattering are obtained in EFT(⁄π).•Nonperturbative properties inherent in such closed-form TT matrices are explored.•Nonperturbative renormalization is implemented through exploiting these properties.•Unconventional power counting of couplings is shown to be less favored by PSA data.•The ideas about nonperturbative renormalization here might have wider applications.

The closed-form TT matrices in the 3S1–3D13S1–3D1 channels of EFT(⁄π) for NNNN scattering with the potentials truncated at order O(Q4)O(Q4) are presented with the nonperturbative divergences parametrized in a general manner. The stringent constraints imposed by the closed form of the TT matrices are exploited in the underlying theory perspective and turned into virtues in the implementation of subtractions and the manifestation of power counting rules in nonperturbative regimes, leading us to the concept of EFT scenario. A number of scenarios of the EFT description of NNNN scattering are compared with PSA data in terms of effective range expansion and 3S13S1 phase shifts, showing that it is favorable to proceed in a scenario with conventional EFT couplings and sophisticated renormalization in order to have large NNNN scattering lengths. The informative utilities of fine tuning are demonstrated in several examples and naturally interpreted in the underlying theory perspective. In addition, some of the approaches adopted in the recent literature are also addressed in the light of EFT scenario.