Structure of vector mesons in a holographic model with linear confinement

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 ($\rho$-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 $\rho$-pole contribution alone. The electric radius of the $\rho$-meson is calculated, $⟨r_{\rho }^2{⟩}_C=0.655{\mathrm{fm}}^2$, 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 $f_{\rho }$ and find that the experimental value is closer to that calculated in the hard-wall model.

Figure 1

$Q^2$-multiplied $\rho$-meson form factor ${\mathcal{F}}_{00}(Q^2)$ (displayed in ${\mathrm{GeV}}^2$) as a function of $Q^2$ (given in ${\mathrm{GeV}}^2$) in hard-wall (upper line, red online) and soft-wall (lower line, blue online) models.