Axial anomaly effect on three-quark and five-quark singly heavy baryons

Abstract

Effects of the $U(1)_A$ axial anomaly on the mass spectrum of singly heavy baryons (SHBs) is studied in terms of the chiral effective theory based on the chiral linear representation for light flavors. We consider SHBs made of both three quarks ($Qqq$) and five quarks ($Qqqq\bar{q}$). For the three-quark SHBs we prove that the inverse mass hierarchy for the negative-parity $Λ_c$ and $Ξ_c$ is realized only when the $U(1)_A$ anomaly is present. For the five-quark SHBs, in contrast, it is found that the $U(1)_A$ anomaly does not change the mass spectrum at the leading order, and accordingly their decay properties induced by emitting a pseudoscalar meson are not affected by the anomaly. Moreover, taking into account small mixings between the three-quark and five-quark SHBs, we find that the observed $Ξ_c$ excited state, either $Ξ_c(2923)$ or $Ξ_c(2930)$, can be consistently regarded as a negative-parity SHB that is dominated by the five-quark component. We also predict a new negative-parity five-quark dominant $Λ_c$, whose mass is around $2700$ MeV and the decay width is of order a few MeV, which provides useful information for future experiments to check our description.