Pair Production ofs-Wave Pi Mesons

A theory for pair production of $s$-wave $\pi$ mesons is constructed along the lines of the Chew-Low-Wick formalism. A bilinear $s$-wave interaction of the form $\left(\frac{{\lambda }_0}{\mu }\right)\phi ·\phi +\left(\frac{\lambda }{{\mu }^2}\right)\tau ·\phi \times \pi$ as used by Drell, Friedman, and Zachariasen is added to the $p$-wave interaction ${\left(4\mathrm{}\pi \right)}^{\frac{1}{2}}\left(\frac{f}{\mu }\right)\sigma ·\nabla \tau ·\phi$ as used by Chew and Low. It is shown that if the $s$-wave interaction is limited to the ${\lambda }_0$ term (scalar pair theory) the cross section for pair production of $s$ waves vanishes.