Holographic Wave Functions, Meromorphization and Counting Rules

We study the large-Q^2 behavior of the meson form factor F_M (Q^2) constructed using the holographic light-front wave functions proposed recently by Brodsky and de Teramond. We show that this model can be also obtained within the Migdal's regularization approach (``meromorphization''), if one applies it to 3-point function for scalar currents made of scalar quarks. We found that the asymptotic 1/Q^2 behavior of F_M (Q^2) is generated by soft Feynman mechanism rather than by short distance dynamics, which causes very late onset of the 1/Q^2 asymptotic behavior. Using meromorphization for spin-1/2 quarks, we demonstrated that resulting form factor F^{spinor}_M (Q^2) has 1/Q^4 asymptotic behavior. Now, owing to the late onset of this asymptotic pattern, F^{spinor}_M (Q^2) imitates the 1/Q^2 behavior in the few GeV^2 region. We discuss analogy between meromorphization and local quark-hadron duality model for the pion form factor, and show that adding the O(\alpha_s) correction to the spectral function brings in the hard pQCD contribution that has the dimensional counting $1/Q^2$ behavior at large Q^2. At accessible Q^2, the O(\alpha_s) term is a rather small fraction of the total result. We conclude that the ``observed'' quark counting rules for hadronic form factors is an approximate phenomenon resulting from Feynman mechanism in its preasymptotic regime.