Self-healing of unitarity in effective field theories and the onset of new physics

TL;DR

This paper challenges the common link between unitarity violation and the onset of new physics in effective field theories, showing that unitarity self-healing can occur before new physics appears, with implications for understanding resonance structures and inelasticity.

Contribution

It demonstrates that unitarity violation is not a reliable indicator of new physics onset and introduces the concept of self-healing in effective theories, especially in chiral perturbation theory.

Findings

Unitarity violation can be self-healed without new physics.

Resonant structures emerge from unitarity self-healing.

Inelasticity onset better indicates new physics than unitarity violation.

Abstract

In effective field theories it is common to identify the onset of new physics with the violation of tree-level unitarity. However, we show that this is parametrically incorrect in the case of chiral perturbation theory, and is probably theoretically incorrect in general. In the chiral theory, we explore perturbative unitarity violation as a function of the number of colors and the number of flavors, holding the scale of the "new physics" (i.e. QCD) fixed. This demonstrates that the onset of new physics is parametrically uncorrelated with tree-unitarity violation. When the latter scale is lower than that of new physics, the effective theory must heal its unitarity violation itself, which is expected because the field theory satisfies the requirements of unitarity. In the chiral theory, the self-healing results in a resonant structure with scalar quantum numbers. In the electroweak variant of this argument, the structure must have the properties of the Higgs and must couple proportional to the mass in both gauge boson and fermion scattering. A similar example can be seen in the case of general relativity coupled to multiple matter fields, where iteration of the vacuum polarization diagram restores unitarity. We present arguments that suggest the correct identification should be connected to the onset of inelasticity rather than unitarity violation. We describe how the onset of inelasticity can occur in the effective theory, although it does not appear possible to predict the onset reliably.