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Register a new userPion polarizabilities: No conflict between dispersion theory and ChPT
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Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected to non-analytic structures
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Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.
We reply to the Comment by Filkov and Kashevarov, arXiv:0805.4486 [hep-ph]. We show that the discrepancies between ChPT and dispersion theory, reported for the polarizability of the pion, result from applying dispersion theory to non-analytic functions.
We review recent developments in the theoretical investigation of the nucleon polarizabilities. We first report on the static polarizabilities as measured in real Compton scattering, comparing and interpreting the results from various theoretical approaches. In a second step, we extend the discussion to the generalized polarizabilities which can be accessed in virtual Compton scattering, showing how the information encoded in these quantities can provide a spatial interpretation of the induced polarization densities in the nucleon.
The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.
Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $Delta$(1232) resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the $ u_mu nto mu^-npi^+$ channel, where higher-order contributions might still be significant. The $Delta$ resonance mechanisms lead to sizeable contributions in all channels, especially in $ u_mu pto mu^- ppi^+$, even though the considered energies are close to the production threshold. The present study provides a well founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments.
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