Pseudovector components of the pion,π0→γγ,andFπ(q2)

Abstract

As a consequence of dynamical chiral symmetry breaking the pion Bethe-Salpeter amplitude necessarily contains terms proportional to ${\gamma }_5\gamma \cdot P$ and ${\gamma }_5\gamma \cdot k,$ where $k$ is the relative and $P$ the total momentum of the constituents. These terms are essential for the preservation of low-energy theorems, such as the Gell-Mann–Oakes-Renner relation and those describing anomalous decays of the pion, and to obtaining an electromagnetic pion form factor that falls as ${1/q}^2$ for large $q^2,$ up to calculable $\ln q^2$ corrections. In a simple model, which correlates low- and high-energy pion observables, we find $q^2{F}_{\pi }{(q}^2)\sim 0.12–0.19{\mathrm{GeV}}^2$ for $q^2\gtrsim 10{\mathrm{GeV}}^2.$