Three-body system of $ππΣ_c$

Abstract: The existence of near-threshold charmed baryon $\Lambda_c(2595)^+$ implies that the pion and the lightest, isospin-$1$ charmed baryon $\Sigma_c$ interact very strongly at extremely low energies. Using the two-flavor version of heavy hadron chiral perturbation theory, I explore the direct consequences of this strong force by investigating whether the $\Sigma_c$ can trap two very soft pions to form any visible hadronic states. The answer is positive. It is found without tuning any free parameters or ultraviolet cutoff that the state in question, with quantum numbers $I(J^P) = 1({\frac{1}{2}}^+)$, presents itself as a resonance pole only a few MeVs away from the $\pi \pi \Sigma_c$ threshold. Subleading corrections are estimated with power-counting arguments, and the smallness of pion momenta is found to facilitate the reliability of the analysis. Because of its proximity in mass, this excited $\Sigma_c$ resonance is speculated to be related to the broad resonance labeled as $\Lambda_c^+(2765)$.