Bootstrapping QCD: the Lake, the Peninsula and the Kink

Abstract

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.

Comments: 6 pages, 7 figures