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A significant part of the phase diagram of the two-dimensional fermionicHubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$)is governed by effective Fermi liquid physics with weak BCS-type instabilities.We access this regime in a controlled way by a combination of the bold-linediagrammatic Monte Carlo method with an additional ladder-diagram summationtrick and semi-analytic treatment of the weak instability in the Cooperchannel. We obtain the corresponding ground-state phase diagram in the $(n,U)$plane describing the competition between the $p-$ and $d-$wave superfluidstates. We also claim the values of the dimensionless BCS coupling constantscontrolling the superfluid $T_c$ at the phase boundaries, which prove to bevery small up to $U=4, n = 0.6$.

Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram