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

Abstract

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 ${\gamma }^{\ast }{\pi }^0\to \gamma$ and ${\gamma }^{\ast }\gamma \to {\pi }^0$ processes by employing these quark-antiquark wave functions of the pion and the photon. We find that our calculation for the ${\gamma }^{\ast }\gamma \to {\pi }^0$ 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 ${\gamma }^{\ast }{\pi }^0\to \gamma$ and ${\gamma }^{\ast }\gamma \to {\pi }^0$ have been illustrated, which indicate that these two physical processes are intrinsically related. In addition, we also discuss the ${\pi }^0\to \gamma \gamma$ form factor and the decay width $\Gamma (\pi \to \gamma \gamma )$ at $Q^2=0$.

Comments: 20 pages, 2 figures