Asymptotic Behavior of Form Factors and the Ratio of the Renormalization ConstantsZ1Z3

Abstract

The asymptotic behavior of the form factor of three scalar particles has been investigated using the Deser-Gilbert-Sudarshan-Ida-Nakanishi representation. For finite $Z_3$, we show that the form factor tends at most to a constant for large $s$. The compositeness condition $Z_3=0\mathrm{}$ implies that $Z_1=0\mathrm{}$ provided the renormalization function $Z_3\mathrm{}\left(s\right)\mathrm{}$ does not tend to zero faster than $\frac{1}{s}$ for $s\to \infty$. The relevance of our results to the Lee model and to the Zachariasen model is briefly discussed.