Structure of vector mesons in a holographic model with linear confinement

Abstract

Wave functions and form factors of vector mesons are investigated in the holographic dual model of quantum chromodynamics with oscillator-like infrared cutoff. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state ($\ensuremath{\rho}$-meson), we show that, in this model, the basic elastic form factor exhibits the perfect vector meson dominance, i.e., it is given by the $\ensuremath{\rho}$-pole contribution alone. The electric radius of the $\ensuremath{\rho}$-meson is calculated, $⟨{r}_{\ensuremath{\rho}}^{2}{⟩}_{C}=0.655\text{ }\text{ }{\mathrm{fm}}^{2}$, which is larger than in the case of the hard-wall cutoff. The squared radii of higher excited states are found to increase logarithmically rather than linearly with the radial excitation number. We calculate the coupling constant ${f}_{\ensuremath{\rho}}$ and find that the experimental value is closer to that calculated in the hard-wall model.