Improved description of threshold pion electroproduction in chiral perturbation theory

We investigate neutral pion electroproduction off protons in the framework of heavy baryon chiral perturbation theory. The chiral expansion of the S--wave multipoles $E_{0+}$ and $L_{0+}$ is carried out to three orders. There appear several undetermined low--energy constants. Three are taken from a recent study of the new TAPS threshold $\pi^0$ photoproduction data, one is fixed from the proton Dirac form factor and the novel S--wave constants appearing at orders $q^4$ and $q^5$ are determined from a best fit (constrained by resonance exchange) to the recent NIKHEF and MAMI data at photon momentum transfer squared $k^2 = -0.1 \, \, {\rm GeV}^2$. The inclusion of a particular set of dimension five operators is forced upon the fit by a soft--pion theorem which severely constrains the momentum dependence of the longitudinal S--wave multipole $L_{0+}$ at order $q^4$. We give predictions for lower photon virtualities for the various multipoles and differential cross sections. Further improvements are briefly touched upon.