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

In recent decades, the spectroscopy of singly heavy baryons has made significant progress, with many excited states observed experimentally. Among the various theoretical approaches used to study their properties, the QCD sum rule method has been widely applied. In this paper, we review QCD sum rule studies of singly heavy baryons, with particular emphasis on our systematic investigations of $$P$$ -wave states over the past ten years using QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. These studies provide plausible interpretations for many observed excited heavy baryons, including the $$\Lambda_c(2595)^+$$ , $$\Lambda_c(2625)^+$$ , $$\Xi_c(2790)^{0/+}$$ , $$\Xi_c(2815)^{0/+}$$ , $$\Sigma_c(2800)^0$$ , $$\Xi_c(2882)^0$$ , $$\Xi_c(2923)^0$$ , $$\Xi_c(2939)^0$$ , $$\Xi_c(2965)^0$$ , $$\Omega_c(3000)^0$$ , $$\Omega_c(3050)^0$$ , $$\Omega_c(3066)^0$$ , $$\Omega_c(3090)^0$$ , $$\Omega_c(3119)^0$$ , $$\Lambda_b(5912)^0$$ , $$\Lambda_b(5920)^0$$ , $$\Xi_b(6087)^0$$ , $$\Xi_b(6095)^0/\Xi_b(6100)^-$$ , $$\Sigma_b(6097)^\pm$$ , $$\Xi_b(6227)^-$$ , $$\Omega_b(6316)^-$$ , $$\Omega_b(6330)^-$$ , $$\Omega_b(6340)^-$$ , and $$\Omega_b(6350)^-$$ . While the absolute masses extracted from QCD sum rules may have sizable systematic uncertainties, the relative mass splittings and qualitative decay patterns are generally more robust and thus provide useful guidance for phenomenological assignments and future experimental searches. We also predict a number of yet-unobserved $$P$$ -wave singly heavy baryons, many of which are expected to have relatively narrow decay widths and are therefore promising for experimental observation. More broadly, the study of singly heavy baryons is closely related to two fundamental questions: “What is the shortest possible lifetime of an observable particle” and “How can one generally describe approximate (flavor) symmetries”.