Calculation of the anomalous ${\hat{I}}^3\ddot{I}{€}^{\ast }\to \ddot{I}€\ddot{I}€$ form factor

Abstract

The form factor for the anomalous process ${\hat{I}}^3\ddot{I}{€}^{\ast }\to \ddot{I}€\ddot{I}€$, $F^{3\ddot{I}€}(s,t,u)$, is calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The chiral-limit value dictated by the electromagnetic, anomalous chiral Ward identity, $F^{3\ddot{I}€}(0,0,0)=e{N}_c/(12\ddot{I}{€}^2{f}_{\ddot{I}}{€}^3)$, is reproduced, {\it independent} of the details of the modelling of the gluon and quark 2-point Schwinger functions. Using a parametrisation of the dressed $u$-$d$ quark 2-point Schwinger function that provides a good description of pion observables, such as $\ddot{I}€$-$\ddot{I}€$ scattering-lengths and the electromagnetic pion form factor, $F^{3\ddot{I}€}(s,t,u)$ is calculated on a kinematic range that proposed experiments plan to explore. Our result confirms the general trend of other calculations; i.e., a monotonic increase with $s$ at fixed $t$ and $u$, but is uniformly larger and exhibits a more rapid rise with $s$.

13 Pages, 2 figures, REVTEX, uses epsfig