Quantum Aspects of Natural Top Quark Condensation

TL;DR

This paper develops a quantum effective action framework for top quark condensation, revealing how quantum loops enhance the effective coupling and support a natural, semi-classical theory of the Higgs boson as a top-antitop bound state.

Contribution

It introduces a quantum effective action approach to top quark condensation, incorporating fermion loop effects and demonstrating the naturalness and coupling enhancement in the theory.

Findings

Quantum loops significantly enhance the effective 4-fermion coupling.

The theory remains natural with minimal fine-tuning.

A weaker topcolor interaction can produce the critical coupling needed for condensation.

Abstract

In top quark condensation the Brout-Englert-Higgs (BEH) boson is a $\bar{t}t$ bound state. With a UV completion of a single coloron exchange interaction, a recent semiclassical treatment gave a novel theory of the BEH boson as an extended object with composite scale $M_0\sim 6$ TeV. Presently we obtain the semiclassical theory as an effective action, using the source/Legendre transformation techniques of Jackiw, \etal, and fermion loop effects in the large-$N_c$ limit by deploying an auxiliary field to implement the sum of leading fermion loop diagrams. The theory remains natural at the loop level, with fine tuning at the level of a few \%, and the effective coupling of the 4-fermion interaction, $\bar{g}_0^2$, is significantly enhanced by quantum loops over the fundamental coloron coupling, $g_0^2$. Hence a relatively weaker ``topcolor'' theory can produce critical coupling in the effective BEH bound state theory.