Complementarity between Gauge-Boson Compositeness and Asymptotic Freedom -- with scalar matter

TL;DR

This paper investigates the conditions under which gauge bosons can be composite in theories with scalar matter, revealing a critical ratio of scalar fields to colors where compositeness aligns with the loss of asymptotic freedom.

Contribution

It derives and solves the compositeness condition for gauge bosons coupled with scalar matter at next-to-leading order, extending previous fermionic matter analyses.

Findings

Gauge boson compositeness requires N_s/N_c > 22.

Compositeness is linked to the failure of asymptotic freedom.

Scalar matter modifies the conditions for gauge boson compositeness.

Abstract

We derive and solve the compositeness condition for the SU(N_c) gauge boson coupling with N_s scalar fields at the next-to-leading order in 1/N_s and the leading order in ln(\Lambda^2) (\Lambda is the compositeness scale). It turns out that the argument of gauge-boson compositeness (with a large \Lambda) is successful only when N_s/N_c>22, in which the asymptotic freedom fails, as is in the previously investigated case with fermionic matter.