Positive and negative-parity flavor-octet baryons in coupled QCD sum rules

Abstract

We apply the method of the QCD sum rule, in which positive- and negative-parity baryons couple with each other, to the flavor-octet hyperons and investigate the parity splittings. We also reexamine the nucleon in the method, which was studied in our previous paper, by carefully choosing the Borel weight. Both in the nucleon and hyperon channels the obtained sum rules turn out to have a very good Borel stability and also have a Borel window, an energy region in which the OPE converges and the pole contribution dominates over the continuum contribution. The predicted masses of the positive- and negative-parity baryons reproduce the experimental ones fairly well in the $\Lambda$ and $\Sigma$ channels, if we assign the $\Lambda(1670)$ and the $\Sigma(1620)$ to the parity partners of the $\Lambda$ and the $\Sigma$, respectively. This implies that the $\Lambda(1405)$ is not the party partner of the $\Lambda$ and may be a flavor-singlet or exotic state. In the $\Xi$ channel, the sum rule predicts the mass of the negative-parity state to be about 1.8 GeV, which leads to two possibilities; one is that the observed state with the closest mass, $\Xi(1690)$, is the parity partner and the other is that the parity partner is not yet found but exists around 1.8 GeV.Comment: 15 pages, 4 figure