Chiral dynamics of S-wave baryon resonances

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.