Perturbative pion-photon transition form factors with transverse momentum corrections

We perform a perturbative QCD analysis of the quark transverse momentum effect on the pion-photon transition form factors $F_{\pi \gamma }$ and $F_{\pi {\gamma }^{*}}$ in the standard light-cone formalism, with two phenomenological models of the wave function as the input of the nonperturbative aspect of the pion. We point out that the transverse momentum dependence in both the numerator and the denominator of the hard scattering amplitude is of the same importance and should be considered consistently. It is shown that after taking into account the quark transverse momentum corrections, the results obtained from different model wave functions are consistent with the available experimental data at finite $Q^2$.