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We study interactions between the S-wave octet pseudo-scalar (PS) meson andoctet baryon in the flavor SU(3) limit using the HAL QCD method at the PS mesonmass $m_M\approx 670~\textrm{MeV}$. We focus on the singlet and two octetchannels, where the poles corresponding to $\Lambda(1405)$ have been predictedin the chiral unitary model. For calculations with $\Lambda$-baryon sourceoperators with zero momentum, we employ the conventional stochastic calculationcombined with the covariant-approximation averaging to calculate the all-to-allpropagators. Due to a zero of the R-correlator (a kind of wave function), theleading order (LO) potential obtained by the single channel analysis has asingular point in all channels, which makes it difficult to obtain reliablebinding energies. To overcome this problem, we take a linear combination of twooctet R-correlators with a relative weight such that it does not cross zero, astwo octet channels are suggested to couple to the same low-energy states withdifferent weights. The potential calculated from such the linear combinationshows strong attraction without singularities, though its shape depends on therelative 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 isconsistent with 156(8) MeV estimated from the two-point correlation functionwithin errors.

Study on Lambda(1405) in the flavor SU(3) limit in the HAL QCD method