Effective range corrections from effective field theory with di-baryon fields and perturbative pions

TL;DR

This paper employs effective field theory with di-baryon fields and perturbative pions to analyze low-energy nucleon scattering, calculating phase shifts and effective range parameters, and examining the impact of renormalization scale on the theory's validity.

Contribution

It introduces a method to compute effective range corrections using di-baryon fields with perturbative pions, refining previous models by Cohen and Hansen.

Findings

Calculated ${}^1S_0$ and ${}^3S_1$ phase shifts at low energies.

Derived higher-order effective range parameters $v_2$, $v_3$, and $v_4$.

Analyzed the dependence of results on the renormalization scale $$.

Abstract

Contributions of perturbative pions around a non-trivial fixed point are studied by utilizing di-baryon fields. We calculate ${}^1S_0$ and ${}^3S_1$ phase shifts for the $np$ scattering at low energies up to one-pion-exchange contributions. We also calculate effective range parameters, $v_2$, $v_3$ and $v_4$ in the higher order of the effective range expansion, and obtain corrections of the effective range to the expressions previously reported by Cohen and Hansen. After the scattering length and the effective range are renormalized, we study the role of renormailzation scale parameter $\mu$ and discuss the range of validity of the theory.