Low energy three- and four-body systems in EFTs

Effective field theory provides a powerful and relatively straightforward way to study few-body systems. I will talk about some recent progress in three- and four-body systems. I will discuss the utility of approximate symmetries in pionless EFT, including the Wigner-SU(4) symmetry and the large-$N_c$ ($N_c$ is the number of colors in QCD) expansion. In particular, I will demonstrate how the Wigner-SU(4) symmetry can affect the power counting of cold neutron-deuteron radiative capture and how the large-$N_c$ expansion can be used to constrain the relative contributions from dark matter currents to dark-matter-light-nuclei elastic scatterings. For four-body systems, I will discuss a diagrammatic method to include or subtract three-body poles systematically, which can help study the renormalization group behavior of four-body observables.