Analysis of the ${\mathrm{\Lambda }}_c(2625)$ and ${\mathrm{\Xi }}_c(2815)$ with QCD sum rules

In this article, we study the charmed baryon states ${\mathrm{\Lambda }}_c(2625)$ and ${\mathrm{\Xi }}_c(2815)$ with the spin-parity ${\frac{3}{2}}^{-}$ by subtracting the contributions from the corresponding charmed baryon states with the spin-parity ${\frac{3}{2}}^{+}$ using the QCD sum rules, and suggest a formula $\mu =\sqrt{M_{{\mathrm{\Lambda }}_c\mathrm{/}{\mathrm{\Xi }}_c}^2-{\mathbb{M}}_c^2}$ with the effective mass ${\mathbb{M}}_c=1.8\mathrm{G}\mathrm{e}\mathrm{V}$ to determine the energy scales of the QCD spectral densities, and make reasonable predictions for the masses and pole residues. The numerical results indicate that the ${\mathrm{\Lambda }}_c(2625)$ and ${\mathrm{\Xi }}_c(2815)$ have at least two remarkable under-structures.