Finite $3\pi$ Cut Approximation for the $\pi N\bar{N}$ Form Factor

Assuming the length of the $3\pi$ cut to be finite and approximating the integrated amplitude by a constant, we derive an expression for the $\pi N\bar{N}$ form factor which is very close to that given by a simple pole. The specific predictions of the obtained form factor for the region of small momentum transfer are discussed along the lines of the Goldberger-Treiman relation.