Invariant amplitudes for electromagnetic pion production from the nucleon and its implication for separated structure functions

Explicit formal relations are developed for the transformation of the Chew-Goldberger-Low- Nambu (CGLN) amplitudes to invariant amplitudes by parameterizing it in terms of Lorentz-invariant functions. The invariant amplitudes are needed for nuclear applications, where the elementary pion production process on the free nucleon occurs in an arbitrary frame of reference for which the CGLN-amplitudes, which have been constructed in the center-of-mass system, can not be used. Formal expressions for another set of invariant amplitudes are also given. The constructed formulae are then used to evaluate the structure functions of the N(e, e')N reaction and compare them with the results using the CGLN-amplitudes from the MAID-2003 model. (author)