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arXiv · 0912.3454

A relativistic coupled-channel formalism for the pion form factor

E. P. Biernat·W. Schweiger·K. Fuchsberger·W. H. Klink
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Abstract

The electromagnetic form factor of a confined quark-antiquark pair is calculated within the framework of point-form relativistic quantum mechanics. The dynamics of theexchanged photon is explicitly taken into account by treating theelectromagnetic scattering of an electron by a meson as a relativistic two-channel problem for a Bakamjian-Thomas type mass operator. This approach guarantees Poincare invariance. Using a Feshbach reduction the coupled-channel problem can be converted into a one-channel problem for the elastic electron-meson channel. By comparing the one-photon-exchange optical potential at the constituent and hadronic levels, we are able to unambiguously identify the electromagnetic meson form factor. Violations of cluster-separability properties, which are inherent in the Bakamjian-Thomas approach, become negligible for sufficiently large invariant mass of the electron-meson system. In the limit of an infinitely large invariant mass, an equivalence with form-factor calculations done in front-form relativistic quantum mechanics is established analytically.

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E. P. Biernat, W. Schweiger, K. Fuchsberger, W. H. Klink. 2009-12-17. A relativistic coupled-channel formalism for the pion form factor. https://doi.org/10.1051/epjconf%2F20100303031

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