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

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 ($Qqqq\overline{q}$). For the three-quark SHBs, we prove that the inverse mass hierarchy for the negative-parity ${\mathrm{\Lambda }}_c$ and ${\mathrm{\Xi }}_c$ 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 ${\mathrm{\Xi }}_c$ excited state, either ${\mathrm{\Xi }}_c(2923)$ or ${\mathrm{\Xi }}_c(2930)$, 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 ${\mathrm{\Lambda }}_c$, 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.

Figure 1

Quark line diagrams for each term of the Lagrangian (6). The heavy quark is a spectator and omitted here.

Figure 2

Quark line diagrams for each term of the Lagrangian (7).

Figure 3

Quark line diagrams for each term of the Lagrangian (8).

Figure 4

Three types of the mass hierarchy listed in Eq. (16): (I) $M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(-)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(-)]$, (II) $M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(-)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(-)]$, and (III) $M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(+)]<M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(-)]<M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(-)]$. The detail is explained in the text.

Figure 5

Partial decay widths of the negative-parity SHBs for arbitrary values of $M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(-)]$ and $M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(-)]$. The blue and orange lines represent $g_1^{\prime }=0$ and ${\mu }_3=0$, respectively. The vertical and horizontal dashed lines are theoretical predictions of $M[{\mathrm{\Lambda }}_c^{[\mathbf{3}]}(-)]=2890^{*}\mathrm{MeV}$ and $M[{\mathrm{\Xi }}_c^{[\mathbf{3}]}(-)]=2765^{*}\mathrm{MeV}$, respectively.

Figure 6

Decay width of ${\mathrm{\Xi }}_c(2930)$ as a function of the ratio of three-quark states in ${\mathrm{\Xi }}_c(2930)$, where the horizontal axis is defined by $100\times (\cos {\theta }_{B_{-,i=1,2}}{)}^2$. The decay modes that can be treated in our present framework are ${\mathrm{\Xi }}_c(2930)\to {\mathrm{\Xi }}_c(2470)\pi$ and ${\mathrm{\Xi }}_c(2930)\to {\mathrm{\Lambda }}_c(2286)K$. Typically, only the colorless area is allowed from the experimental data of decays of ${\mathrm{\Xi }}_c(2930)$.

Figure 7

Mass spectrum of all SHBs treated in our present model with the parameter set (41). The details are provided in the text.

Figure 8

Mass of ${\mathrm{\Lambda }}_c^L(-)$ in ${\mu }_1^{\prime }$—$g_4$ plane. The purple and green lines represent boundaries constrained from the decay widths of ${\mathrm{\Xi }}_c(2970)$ and ${\mathrm{\Xi }}_c(2930)$, respectively.

Figure 9

Decay width of ${\mathrm{\Lambda }}_c(-)\to {\mathrm{\Sigma }}_c\pi$ in the allowed region of ${\mu }_1^{\prime }$—$g_4$ plane.

Figure 10

Schematic picture of generating the mass ordering of $M[{\mathrm{\Lambda }}_c^{[5]}(\pm )]<M[{\mathrm{\Xi }}_c^{[5]}(\pm )]$.