Strong decays of singly heavy baryons from a chiral effective theory of diquarks

A chiral effective theory of scalar and vector diquarks is formulated, which is based on $SU(3{)}_R\times SU(3{)}_L$ chiral symmetry and includes interactions between scalar and vector diquarks with one or two mesons. We find that the diquark interaction term with two mesons breaks the $U(1{)}_A$ and flavor $SU(3)$ symmetries. To determine the coupling constants of the interaction Lagrangians, we investigate one-pion emission decays of singly heavy baryons $Qqq$ ($Q=c$, $b$ and $q=u$, $d$, $s$), where baryons are regarded as diquark–heavy-quark two-body systems. Using this model, we present predictions of the unobserved decay widths of singly heavy baryons. We also study the change of masses and strong decay widths of singly heavy baryons under partial restoration of chiral symmetry.

Figure 1

Schematic pictures for the effective interaction Lagrangian ${\mathcal{L}}_{SV}$ [Eq. (9)] between diquarks and mesons. The left figure (a) and right figure (b) describe ${\mathcal{L}}_{SV}^{(1)}$ [Eq. (10)] and ${\mathcal{L}}_{SV}^{(2)}$ [Eq. (11)], respectively. Arrows with “R” or “L” represent the right-handed or left-handed quark lines.

Figure 2

Kinematics employed for $A_Q\to S_Q\pi$ decays with pion momentm ${\overrightarrow{p}}_{\pi }$. ${\overrightarrow{P}}_{A_Q}$ and ${\overrightarrow{P}}_{S_Q}$ denote the momenta of initial- and final-state baryons, respectively, and $\overrightarrow{p}$ and $\overrightarrow{p^{\prime }}$ are the relative momenta between a diquark and a heavy quark in the initial and final states, respectively. ${\varphi }_{A,J}$ and ${\varphi }_S$ are the relative wave functions. $m_d$ ($d=A$, $S$) and $m_Q$ are the diquark mass and the heavy-quark mass, respectively, and $\mathcal{G}$ is the coupling constant.

Figure 3

Dependence of the singly charmed baryon masses and decay widths of ${\mathrm{\Sigma }}_c^{(*)}\to {\mathrm{\Lambda }}_c{\pi }^{\pm }$ on the chiral-symmetry breaking parameter $x$ in the range of $0.80\le x\le 1.00$.

Figure 4

Dependence of the singly bottom baryon masses and decay widths of ${\mathrm{\Sigma }}_b^{(*)}\to {\mathrm{\Lambda }}_b{\pi }^{\pm }$ on the chiral-symmetry breaking parameter $x$ in the range of $0.80\le x\le 1.00$.

Figure 5

Dependence of the coupling constant ratio from the diquark model ($|g_2/g_1|$) and the SHB model ($|{\tilde{g}}_2/{\tilde{g}}_1|$) on the quark-meson coupling constant $g_s$. $Q=c$, $b$ denotes the heavy quark inside the SHBs employed as inputs.