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.