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Pion-photon and photon-pion transition form factors in light-cone formalism

We derive the minimal Fock-state expansions of the pion and the photon wave functions in light-cone formalism, then we calculate the pion-photon and the photon-pion transition form factors of $γ^{\ast}π^{0}\to γ$ and $γ^{\ast}γ\to π^{0}$ processes by employing these quark-antiquark wave functions of the pion and the photon. We find that our calculation for the $γ^{\ast}γ\to π^{0}$ transition form factor agrees with the experimental data at low and moderately high energy scale. Moreover, the physical differences and inherent connections between the transition form factors of $γ^{\ast}π^{0}\to γ$ and $ γ^{\ast}γ\to π^{0}$ have been illustrated, which indicate that these two physical processes are intrinsically related. In addition, we also discuss the $π^{0}\to γγ$ form factor and the decay width $ \mathitΓ(π\to γγ)$ at $Q^{2}=0$.