  We demonstrate that summation of connected diagrams to high order starting
from a BCS hamiltonian is a viable generic unbiased approach for strongly
correlated fermions in superconducting or superfluid phases. For the 3D
attractive Hubbard model in a strongly correlated regime, we observe
convergence of the diagrammatic series, evaluated up to 12 loops thanks to the
connected determinant diagrammatic Monte Carlo algorithm. Our study includes
the polarized regime, where conventional quantum Monte Carlo methods suffer
from the fermion sign problem. Upon increasing the Zeeman field, we observe the
first-order superconducting-to-normal phase transition at low temperature, and
a thermally activated polarization of the superconducting phase well described
by quasiparticle theory.
