$NN$ scattering in $^3S_1-^3D_1$ channels of EFT ($\notπ$)

Details $NN$ scattering in $^3S_1-^3D_1$ channels of EFT ($\notπ$) $NN$ scattering in $^3S_1-^3D_1$ channels of EFT ($\notπ$)

2011-12-23

arxiv.org/abs/1112.5537v2

Physics

Nuclear Physics

Nuclear Theory

23 pages, no figure, 7 tables

Scientific paper

The closed-form solutions of $NN$ scattering matrices for the coupled channels $^3S_1 - ^3D_1$ in EFT($\not\pi$) with the potentials truncated at order $\mathcal{O}(Q_{(\not\pi)}^4)$ are presented in details with the nonperturbative divergences parametrized in a general manner. The stringent constraints imposed by the closed-form of the $T$ matrices are analyzed with the help of the underlying theory perspective. The realization or implementation of subtractions and the manifestation of EFT power counting rules in nonperturbative regimes are shown to differ from perturbative cases and give rise to the concept of scenario that is intrinsic of nonperturbative renormalization of EFT. Then a number of scenarios of the EFT description of $NN$ scattering are compared with PSA data in details employing the effective range expansion. The problems and rationalities of various scenarios for describing realistic $NN$ scattering with large scattering lengths are given, showing that it is favorable to proceed in a scenario with conventional EFT couplings and reasonable prescriptions of renormalization. The natural appearance of and the roles played by the fine-tuning in terms of EFT couplings are also demonstrated in several places and interpreted in the underlying theory perspective. In addition, some of the approaches appearing in recent literature are also addressed in the perspective adopted here. Many technical details are also given for completeness of our presentation.

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