Dynamically generated $J^P=1/2^{-}(3/2^{-})$ singly charmed and bottom heavy baryons

Approximate heavy-quark spin and flavor symmetry and chiral symmetry play an important role in our understanding of the nonperturbative regime of strong interactions. In this work, utilizing the unitarized chiral perturbation theory, we explore the consequences of these symmetries in the description of the interactions between the ground-state singly charmed (bottom) baryons and the pseudo-Nambu–Goldstone bosons. In particular, at leading order in the chiral expansion, by fixing the only parameter in the theory to reproduce the ${\mathrm{\Lambda }}_b(5912)[{\mathrm{\Lambda }}_b^{*}(5920)]$ or the ${\mathrm{\Lambda }}_c(2595)[{\mathrm{\Lambda }}_c^{*}(2625)]$, we predict a number of dynamically generated states, which are contrasted with those of other approaches and available experimental data. In anticipation of future lattice QCD simulations, we calculate the corresponding scattering lengths and compare them to the existing predictions from a $\mathcal{O}(p^3)$ chiral perturbation theory study. In addition, we estimate the effects of the next-to-leading-order potentials by adopting heavy-meson Lagrangians and fixing the relevant low-energy constants using either symmetry or naturalness arguments. It is shown that higher-order potentials play a relatively important role in many channels, indicating that further studies are needed once more experimental or lattice QCD data become available.

Figure 1

Loop function $G(M)$ as a function of the heavy-hadron mass $M$ in different regularization schemes: HQS, $\overline{\mathrm{MS}}$, the cutoff regularization scheme (CUT), and the exact heavy-quark limit (HH). The subtraction constants or cutoff values have been fixed by reproducing the ${\mathrm{\Lambda }}_b(5912)$ (left panel) or the ${\mathrm{\Lambda }}_c(2595)$ (right panel). In calculating the loop function $G$, the pseudoscalar meson mass is fixed at that of the pion $m=138\mathrm{MeV}$, and the renormalization scale in the dimensional regularization methods is fixed at $\mu =1\mathrm{GeV}$.

Figure 2

Thresholds of the coupled channels considered in different works for the singly charmed and bottom baryon sector with $J^P=1/2^{-}$ and $(S=0,I=0)$: Liang et al. [20, 21], Hofmann et al. [77], Garcia-Recio et al. [18, 19], and the experiment in Ref. [16]. In the left figure, two model spaces denoted by dot-dot-dashed lines (pseudoscalar-baryon) and dashed lines (vector-baryon), respectively, were studied in Ref. [21].