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

TL;DR

This paper investigates how the $U(1)_A$ axial anomaly influences the mass spectrum of singly heavy baryons, revealing different effects for three-quark and five-quark configurations and proposing new baryon states for experimental verification.

Contribution

It demonstrates the anomaly's role in the mass hierarchy of three-quark baryons and shows it does not affect five-quark baryons at leading order, also predicting a new $ ext{Λ}_c$ state.

Findings

The inverse mass hierarchy for negative-parity $ ext{Λ}_c$ and $ ext{Ξ}_c$ occurs only with the anomaly.

The $U(1)_A$ anomaly does not alter the five-quark baryon spectrum at leading order.

A new negative-parity five-quark $ ext{Λ}_c$ state around 2700 MeV is predicted.

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 $\Lambda_c$ and $\Xi_c$ 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 $\Xi_c$ excited state, either $\Xi_c(2923)$ or $\Xi_c(2930)$, 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 $\Lambda_c$, 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.