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.

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