Chiral symmetry breaking for large "Nf" and the properties of the "rho" meson near the conformal window

Abstract

We study how the ground-state properties of the rho meson respond when the number of light-quark flavors N_f is driven towards the conformal window. The interaction is a symmetry-preserving, confining vector--vector contact interaction whose effective coupling carries a flavor dependence designed to encode the screening produced by fermion loops in the deep infrared. That interaction feeds the Schwinger--Dyson equation for the dressed-quark propagator and the homogeneous Bethe--Salpeter equation in the rainbow-ladder truncation, regularized in the Schwinger proper-time scheme so that quark production thresholds are absent while chiral symmetry remains broken. Raising N_f weakens the coupling, suppresses the dynamically generated mass and restores chiral symmetry together with deconfinement at a critical flavor number N^{c}_{f}. The vector channel responds differently from the pseudoscalar one. Because the $ρ$ is not a Goldstone boson, its mass is not protected by the symmetry that is being restored, and it simply follows the shrinking constituent scale, while the canonically normalized amplitude E_rho and the leptonic decay constant f_rho soften along the way. In this framework the rho sits above the nominal q\bar{q} threshold for every flavor number examined, so the state survives only as long as confinement removes that threshold. Dissociation is therefore governed by the divergence of the confinement length scale rather than by a crossing of the bound-state mass, and we contrast both criteria. The three elastic electromagnetic form factors G_E, G_M and G_Q, computed in the generalized impulse approximation, flatten as N_f grows, the zero crossing of G_E migrates towards the infrared and the charge radius expands, whereas the magnitude of the quadrupole moment decreases. The rho thus becomes a larger and rounder object as the theory approaches conformality.