On the Couplings of Vector Mesons in AdS/QCD

TL;DR

This work analyzes whether rho meson couplings are universal across vector hadrons in AdS/CFT. By decomposing hadronic form factors into vector-meson poles and evaluating both hard-wall and D3/D7 models, it shows that rho-dominance and hadron-independent couplings are not generic, though two limits yield approximate universality: (i) hadrons created by high-dimension operators and (ii) highly excited hadrons. In specific sectors of the D3/D7 model, exact universality for rho couplings emerges, but the universal value does not generally equal the Sakurai benchmark $m_\rho^2/f_\rho$. The results illuminate how AdS/QCD encodes vector-meson dynamics and suggest general constraints on universality in strongly coupled gauge theories, with limited immediate experimental applicability but potential guidance for understanding conserved-current vector mesons.

Abstract

We address, in the AdS/CFT context, the issue of the universality of the couplings of the rho meson to other hadrons. Exploring some models, we find that generically the rho-dominance prediction f_ρg_{ρH H}=m_ρ^2 does not hold, and that g_{ρH H} is not independent of the hadron H. However, we prove that, in any model within the AdS/QCD context, there are two limiting regimes where the g_{ρH H}, along with the couplings of all excited vector mesons as well, become H-independent: (1) when H is created by an operator of large dimension, and (2) when H is a highly-excited hadron. We also find a sector of a particular model where universality for the rho coupling is exact. Still, in none of these cases need it be true that f_ρg_ρ=m_ρ^2, although we find empirically that the relation does hold approximately (up to a factor of order two) within the models we have studied.