  We study interactions between the S-wave octet pseudo-scalar (PS) meson and
octet baryon in the flavor SU(3) limit using the HAL QCD method at the PS meson
mass $m_M\approx 670~\textrm{MeV}$. We focus on the singlet and two octet
channels, where the poles corresponding to $\Lambda(1405)$ have been predicted
in the chiral unitary model. For calculations with $\Lambda$-baryon source
operators with zero momentum, we employ the conventional stochastic calculation
combined with the covariant-approximation averaging to calculate the all-to-all
propagators. Due to a zero of the R-correlator (a kind of wave function), the
leading order (LO) potential obtained by the single channel analysis has a
singular point in all channels, which makes it difficult to obtain reliable
binding energies. To overcome this problem, we take a linear combination of two
octet R-correlators with a relative weight such that it does not cross zero, as
two octet channels are suggested to couple to the same low-energy states with
different weights. The potential calculated from such the linear combination
shows strong attraction without singularities, though its shape depends on the
relative weight. Our estimation for the binding energy in the octet channel is
$E^{8_{s(a)}}_{\textrm{bind}}=163(7)(^{+16} _{-64})~\textrm{MeV}$, which is
consistent with 156(8) MeV estimated from the two-point correlation function
within errors.
