Chiral dynamics ofS-wave baryon resonances
Physical Review D
As the pion mass approaches a critical value m_π^ 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_π close to m_π^. 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
... small. The effective range of pion-baryon scattering is unexpectedly large, proportional to 4π f_π^2/m_π^3 when m_π is around m_π^. As a result, this unexpected large length scale causes universality relations to break down much sooner than naively expected.