Softening the UV without New Particles

TL;DR

This paper introduces a class of quantum field theories where hierarchy problems are addressed through new dynamics involving a large charge pseudo-Nambu-Goldstone boson, avoiding the need for new particles and saturating quantum corrections at a lower scale.

Contribution

It presents a novel framework where quantum corrections are saturated at a lower scale without new particles, using a large charge pseudo-NG boson in weakly coupled theories.

Findings

Quantum corrections are saturated at a lower scale than the UV cut-off.

The framework avoids introducing new particles to solve hierarchy problems.

High powers of the Goldstone field are essential for accurate physics.

Abstract

We explore an odd class of QFTs where a hierarchy problem is resolved with new dynamics as opposed to new particles. The essential element of our construction is a $U(1)$ pseudo-NG boson with symmetry breaking interactions all characterized by a large number $N$ of units of the fundamental charge. In the resulting effective theory, quantum corrections, like those to the effective potential and mass, which are normally power divergent and saturated at the UV cut-off, are instead saturated at a much lower scale. This critical scale, which does not involve any new particle, corresponds to the onset of unsuppressed multiparticle production in scattering processes. Remarkably this all happens within the tractable domain of weak coupling. Terms involving arbitrarily high powers of the Goldstone field must however be taken into account. In particular, a truncation to the renormalizable part of the effective Lagrangian would completely miss the physics.