Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory

A method to calculate the form factor for an external current with non-derivative coupling for the three-body system in an effective field theory (EFT) of short-range interactions is shown. Using this method the point charge radius of ${}^3\mathrm{He}$ is calculated to next-to-next-to-leading order (NNLO) in pionless EFT ($\mathrm{EFT}(\not{\!\pi})$), and the magnetic moment and magnetic radius of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are calculated to next-to-leading order (NLO). For the ${}^3\mathrm{He}$ charge and magnetic form factors Coulomb interactions are ignored. The ${}^3\mathrm{He}$ point charge radius is given by 1.74(4) fm at NNLO. This agrees well with the experimental ${}^3\mathrm{He}$ point charge radius of 1.7753(54) fm [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. The ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) magnetic moment in units of nuclear magnetons is found to be 2.92(35) (-2.08(25)) at NLO in agreement with the experimental value of 2.979 (-2.127). For ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) the NLO magnetic radius is 1.78(11) fm (1.85(11) fm) which agrees with the experimental value of 1.840(182) fm (1.965(154) fm) [I. Sick, Prog. Part. Nucl. Phys. 47, 245 (2001)]. The fitting of the low-energy constant $L_{1}$ of the isovector two-body magnetic current and the consequences of Wigner-SU(4) symmetry for the three-nucleon magnetic moments are also discussed.