Abstract
Chiral effective theory of scalar and vector diquarks is formulated according to the linear sigma model. The main application is to describe the ground and excited states of singly heavy baryons with a charm or bottom quark. Applying the potential quark model between the diquark and the heavy quark ($Q=c, b$), we construct a heavy-quark--diquark model. The spectra of the positive- and negative-parity states of $\Lambda_Q$, $\Sigma_Q$, $\Xi^{(')}_Q$ and $\Omega_Q$ are obtained. The masses and interaction parameters of the effective theory are fixed partly from the lattice QCD data and also from fitting low-lying heavy baryon masses. We find that the negative parity excited states of $\Xi_Q$ (flavor $\bar{\bf 3}$) are different from those of $\Lambda_Q$, because of the inverse hierarchy of the pseudoscalar diquark. On the other hand, $\Sigma_Q, \Xi'_Q$ and $\Omega_Q$ (flavor ${\bf 6}$) baryons have similar spectra. We compare our results of the heavy-quark--diquark model with experimental data as well as the quark model.
Highlights
Recent observation of multiquark exotic hadron stimulates discussion on various different structures of hadrons
There the scalar and pseudoscalar diquarks are chiral partners to each other, i.e., belonging to the same representation of chiral symmetry. Their mass difference comes from spontaneous chiral symmetry breaking, and they become degenerate when chiral symmetry is recovered
First we focus on the ground states and the λ-mode states with the S diquark and the ρ-mode states with the P diquark, which is explained in the previous work [31]
Summary
Recent observation of multiquark exotic hadron stimulates discussion on various different structures of hadrons. The most popular light diquarks for hadron spectroscopy is the scalar diquark with the spin-parity JP 1⁄4 0þ, color 3 ̄ and flavor 3 ̄. It appears most frequently in hadrons such as the ground states of ΛQ and ΞQ. Their mass difference comes from spontaneous chiral symmetry breaking, and they become degenerate when chiral symmetry is recovered This theory shows that UAð1Þ anomaly [37,38] leads to inverse hierarchy of diquark masses, that is, the nonstrange pseudoscalar diquark is heavier than that containing one strange quark, Mðud; 0−Þ > Mðds=su; 0−Þ.
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