A short review on QCD sum rule studies of P-wave single heavy baryons

TL;DR

This review assesses how $P$-wave singly heavy baryons are understood through QCD sum rules and light-cone sum rules within the HQET framework, emphasizing the classification into $SU(3)_F$ multiplets and the construction of interpolating currents. It details systematic predictions for bottom and charmed baryons, including mass spectra, splittings, and decay widths, and analyzes mixing between $ ho$- and $ extlambda$-mode excitations with mixing angles around $37^ ext{o}$ to reconcile theory with observed states such as $ ext{Λ}_b(5912,5920)$, $ ext{Ξ}_b(6087,6095)$, and several $ ext{Ω}_c$ and $ ext{Ξ}_c$ resonances. The findings generally support the interpretation of observed states as $P$-wave excitations, while offering numerous additional narrow states as experimental targets, and reveal a consistent pattern where intra-multiplet splittings are robust against $1/m_Q$ corrections. A notable result is the prediction that the $ ho$-mode lies below the $ ext{λ}$-mode in mass, a feature that can be tested by future measurements and lattice QCD. The work also highlights extensions to hypothetical hadrons containing a single top quark, illustrating the versatility of the QCD sum-rule toolbox for heavy-baryon spectroscopy.

Abstract

Over the past few decades, the study of singly heavy baryons has entered a golden era, with numerous excited states observed by experimental collaborations. Various theoretical approaches have been developed to investigate their properties, with the QCD sum rule method being one of the most widely applied. This paper provides a review of these QCD sum rule studies. Over the last ten years, we have systematically studied $P$-wave singly heavy baryons using QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. These $P$-wave singly heavy baryons can explain many excited heavy baryons, including the $Λ_c(2595)^+$, $Λ_c(2625)^+$, $Ξ_c(2790)^{0/+}$, $Ξ_c(2815)^{0/+}$, $Σ_c(2800)^0$, $Ξ_c(2882)^0$, $Ξ_c(2923)^0$, $Ξ_c(2939)^0$, $Ξ_c(2965)^0$, $Ω_c(3000)^0$, $Ω_c(3066)^0$, $Ω_c(3090)^0$, $Ω_c(3050)^0$, $Ω_c(3119)^0$, $Λ_b(5912)^0$, $Λ_b(5920)^0$, $Ξ_b(6087)^0$, $Ξ_b(6095)^0/Ξ_b(6100)^-$, $Σ_b(6097)^\pm$, $Ξ_b(6227)^-$, $Ω_b(6316)^-$, $Ω_b(6330)^-$, $Ω_b(6340)^-$, and $Ω_b(6350)^-$, etc. Furthermore, we predict additional $P$-wave singly heavy baryons, including two $Λ_b$ states, two $Ξ_b$ states, three $Σ_b$ states, three $Ξ_b^\prime$ states, two $Ω_b$ states, two $Λ_c$ states, two $Ξ_c$ states, three $Σ_c$ states, and one $Ω_c$ state, all with relatively narrow decay widths, making them viable candidates for experimental observation. The study of singly heavy baryons is closely related to two meaningful questions:"What is the shortest possible lifetime of an observable particle?" and "How can one generally describe approximate (flavor) symmetries?".

Figures (7)

• Figure 1: Jacobi coordinates $\vec{\lambda}$ and $\vec{\rho}$ for a singly heavy baryon.
• Figure 2: Flavor $SU(3)$ multiplets $\mathbf{6}_F$ and $\mathbf{\bar{3}}_F$ of the ground-state charmed baryons. The symbols $\Xi_c$ and $\Xi_c^{\prime}$ are used to distinguish charmed-strange baryons belonging to different flavor representations. However, the prime is typically omitted for experimentally observed states, as these cannot be directly distinguished in experiments.
• Figure 3: Systematic categorization of $S$-, $P$-, and $D$-wave charmed baryons based on their internal quantum numbers and excitation modes.
• Figure 4: Dependence of (a) the convergence ratio (CVG) and (b) the pole contribution (PC), defined in Eqs. (\ref{['eq_convergence']}) and (\ref{['eq_pole']}), on the Borel mass $T$, evaluated using the interpolating current $J^\alpha_{3/2,-,\Omega_b^-,2,1,\lambda}$. The dashed, solid, and dotted curves correspond to $\omega_c = 1.98$, $2.08$, and $2.18~\mathrm{GeV}$, respectively.
• Figure 5: Dependence of (a) the residual mass $\overline{\Lambda}$ and (b) the decay constant $f$ on the Borel mass $T$, extracted using the interpolating current $J^\alpha_{3/2,-,\Omega_b^-,2,1,\lambda}$. The dashed, solid, and dotted curves correspond to $\omega_c = 1.98$, $2.08$, and $2.18~\mathrm{GeV}$, respectively.