  We study the superconducting order in a two-dimensional square lattice
Hubbard model with weak repulsive interactions, subject to a Zeeman field and
weak Rashba spin-orbit interactions. Diagonalizing the non-interacting
Hamiltonian leads to two separate bands, and by deriving an effective
low-energy interaction we find the mean field gap equations for the
superconducting order parameter on the bands. Solving the gap equations just
below the critical temperature, we find that superconductivity is caused by
Kohn-Luttinger type interaction, while the pairing symmetry of the bands are
indirectly affected by the spin-orbit coupling. The dominating attractive
momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$
of the system, and it is therefore possible to change the momentum dependence
of the order parameter by tuning $n$. Moreover, $n$ also determines which band
has the highest critical temperature. Rotating the magnetic field changes the
momentum dependence from states that for small momenta reduce to a chiral $p_x
\pm i p_y$ type state for out-of-plane fields, to a nodal p-wave type state for
purely in-plane fields.
