2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52200We 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(Λ^2) (Λis the compositeness scale). It turns out that the argument of gauge-boson compositeness (with a large Λ) 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.11 pages, 3 figuresHigh Energy Physics - TheoryComplementarity between Gauge-Boson Compositeness and Asymptotic Freedom -- with scalar mattertext