Effective field theory for low-energy two-nucleon systems

We illustrate how effective field theories work in nuclear physics by using an effective Lagrangian in which all other degrees of freedom than the nucleonic one have been integrated out to calculate the low-energy properties of two-nucleon systems, viz., the deuteron properties, the $\mathrm{np}$ ${}^1{S}_0$ scattering amplitude, and the $M1\mathrm{}$ transition amplitude entering into the radiative $\mathrm{np}$ capture process. Exploiting a finite cutoff regularization procedure, we find all the two-nucleon low-energy properties to be accurately described with little cutoff dependence, in consistency with the general philosophy of effective field theories.