Chiral dynamics of S-wave baryon resonances

Abstract

As the pion mass approaches a critical value $m_{\pi }^{\star }$ from below, an $S$-wave resonance crosses pion-baryon threshold and becomes a bound state with arbitrarily small binding energy, thus driving the scattering length to diverge. I explore the consequences of chiral symmetry for the values of $m_{\pi }$ close to $m_{\pi }^{\star }$. It turns out that chiral symmetry is crucial for an $S$-wave resonance to be able to stand very near threshold and in the meantime to remain narrow, provided that the mass splitting is reasonably small. The effective range of pion-baryon scattering is unexpectedly large, proportional to $4\pi f_{\pi }^2/m_{\pi }^3$ when $m_{\pi }$ is around $m_{\pi }^{\star }$. As a result, this unexpected large length scale causes universality relations to break down much sooner than naively expected.

12 pages, 2 figures. The introductory text was modified. Matches the published version

References in corpus (11)

• Charmed bottom baryon spectroscopy from lattice QCD
• Pion Interactions in the X(3872)
• The s-wave charmed baryon resonances from a coupled-channel approach with heavy quark symmetry
• Charmed baryon spectroscopy and light flavour symmetry from lattice QCD
• Remarks on pole trajectories for resonances
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• Galilean-Invariant XEFT
• Hadron mass scaling near the s-wave threshold
• Large Nc Weinberg-Tomozawa interaction and negative parity s--wave baryon resonances
• Narrow resonances and short-range interactions
• Power counting for three-body decays of a near-threshold state

Cited by in corpus (4)

• Resonance on top of thresholds: the ${\Lambda }_c(2595{)}^{+}$ as an extremely fine-tuned state
• Power counting for nuclear forces in chiral effective field theory
• Are there near-threshold Coulomb-like Baryonia?
• Large-N_c sum rules for charmed baryons at subleading orders