Three-body system of $\pi \pi \Sigma_c$

TL;DR

This paper predicts a new resonance state formed by two soft pions and a $\Sigma_c$ baryon, arising from strong pion-baryon interactions, and suggests it may be related to the observed $\Lambda_c^+(2765)$ resonance.

Contribution

It demonstrates, using heavy hadron chiral perturbation theory, that a three-body $\pi \pi \Sigma_c$ system can form a near-threshold resonance without tuning parameters.

Findings

A resonance pole near the $\pi \pi \Sigma_c$ threshold is predicted.

The resonance has quantum numbers $I(J^P) = 1({rac{1}{2}}^+)$.

The predicted state may be related to the broad $\Lambda_c^+(2765)$ resonance.

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 $\Lambda_c^+(2765)$.