  Recent nuclear magnetic resonance (NMR) and calorimetric experiments have
observed that UTe$_2$ exhibits a transition between two distinct
superconducting phases as a function of magnetic field strength for a field
applied along the crystalline $b$-axis. To determine the nature of these
phases, we employ a microscopic two-band minimal Hamiltonian with the essential
crystal symmetries and structural details. We also adopt anisotropic
ferromagnetic exchange terms. We study the resulting pairing symmetries and
properties of these low- and high-field phases in mean field theory.
