Recently Regge effects have been studied in weak amplitudes by describing the final-state strong interaction with a Regge pole at $J=\phi \mathrm{}\left(t\right)\mathrm{}$. In particular, it has been shown that the double-helicity-flip amplitude $A_1\mathrm{}(s,t)\mathrm{}$ for the process $\gamma \pi \to \gamma \pi$ has a moving pole at $J=\phi \mathrm{}\left(t\right)-2\mathrm{}$ and a fixed pole at $J=-1\mathrm{}$, and that the electromagnetic form factor of the pion, $F_{\pi }\mathrm{}\left(s\right)\mathrm{}$, can be written as $F_{\pi }\mathrm{}\left(s\right)=1+G_P\mathrm{}\left(s\right)+G_{\rho }\mathrm{}\left(s\right)\mathrm{}$, where $G_{\rho }\mathrm{}\left(s\right)\mathrm{}\to s^{\phi \mathrm{}\left(0\right)-1\mathrm{}}[1+O(\frac{1}{\ln s}\left)\right]$. In the present paper, we demonstrate how these results can be obtained by a simple and direct method that draws out an immediate physical understanding of the results obtained. Our method involves the study of the asymptotic behavior of the relevant field-theoretic diagrams with the use of Sudakov variables.

Close

PrevNext

View figure in article