  We consider the S-matrix bootstrap of four dimensional scattering amplitudes
with $O(3)$ symmetry and no bound-states. We explore the allowed space of
scattering lengths which parametrize the interaction strength at threshold of
the various scattering channels. Next we consider an application of this
formalism to pion physics. A signature of pions is that they are derivatively
coupled leading to (chiral) zeros in their scattering amplitudes. In this work
we explore the multi-dimensional space of chiral zeros positions, scattering
length values and resonance mass values. Interestingly, we encounter lakes,
peninsulas and kinks depending on which sections of this intricate
multi-dimensional space we consider. We discuss the remarkable location where
QCD seems to lie in these plots, based on various experimental and theoretical
expectations.
