  We study the fate of the so-called $\Theta_{II}$-loop-current order that
breaks both time-reversal and parity symmetries in a two-dimensional hot spot
model with antiferromagnetically mediated interactions, using Fermi surfaces
relevant to the phenomenology of the cuprate superconductors. We start from a
three-band Emery model describing the hopping of holes in the CuO$_{2}$ plane
that includes two hopping parameters $t_{pp}$ and $t_{pd}$, local on-site
Coulomb interactions $U_{d}$ and $U_{p}$ and nearest-neighbor $V_{pd}$
couplings between the fermions in the copper [Cu$(3d_{x^{2}-y^{2}})$] and
oxygen [O$(2p_{x})$ and O$(2p_{y})$] orbitals. By focusing on the lowest-energy
band, we proceed to decouple the local interaction $U_{d}$ of the Cu orbital in
the spin channel using a Hubbard-Stratonovich transformation to arrive at the
interacting part of the so-called spin-fermion model. We also decouple the
nearest-neighbor interaction $V_{pd}$ to introduce the order parameter of the
$\Theta_{II}$-loop-current order. In this way, we are able to construct a
consistent mean-field theory that describes the strong competition between the
composite order parameter made of a quadrupole-density-wave and $d$-wave
pairing fluctuations proposed in Efetov \emph{et al.} [Nat. Phys. \textbf{9},
442 (2013)] with the $\Theta_{II}$-loop-current order parameter that is argued
to be relevant for explaining important aspects of the physics of the pseudogap
phase displayed in the underdoped cuprates.
