Calculation of the anomalous $γπ^* \to ππ$ form factor

Details Calculation of the anomalous $γπ^* \to ππ$ form factor Calculation of the anomalous $γπ^* \to ππ$ form factor

1995-10-12

arxiv.org/abs/hep-ph/9510284v1

Phys.Lett.B369:101-107,1996

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 Pages, 2 figures, REVTEX, uses epsfig

Scientific paper

10.1016/0370-2693(95)01517-5

The form factor for the anomalous process $\gamma \pi ^* \to \pi \pi$, $F^{3\pi}(s,t,u)$, is calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The chiral-limit value dictated by the electromagnetic, anomalous chiral Ward identity, $F^{3\pi}(0,0,0)= e N_c/(12\pi^2 f_\pi^3)$, 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 $\pi$-$\pi$ scattering-lengths and the electromagnetic pion form factor, $F^{3\pi}(s,t,u)$ 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 $s$.

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