A Simple Parametrisation of the Pion Form Factor

We discuss a novel and simple parametrisation of the pion vector form factor that transparently connects spacelike and timelike regions of the momentum transfer $q^2$. Our parametrisation employs the framework of conformal mapping and respects the known analyticity properties of the form factor, accounting explicitly for the $\rho (770)$-meson pole. The parametrisation manifestly fulfils the normalisation condition at $q^2=0$ as well as further restrictions at the pion production threshold and in the limit $\mathrm{\mid }{q}^2\mathrm{\mid }\to \mathrm{\infty }$. In contrast to the widely used Omnès parametrisation, our approach does not use the pion-pion scattering phase shift as input. We confront the parametrisation with experimental data from $\pi H$ scattering and ${\tau }^{-}\to {\pi }^{-}{\pi }^0\nu$ decay. We already find a good description of the data with only five free parameters, which include the pole mass and decay width of the $\rho (770)$.