Theγ-Instability of Mesons

The following examples of $\gamma$-instability are investigated: (a) $M_0\to {\gamma }_1+{\gamma }_2$, (b) $M_1\to {\gamma }_1+{\gamma }_2+{\gamma }_3$, (c) $M_1\to M_0+\gamma$, (d) ${M_1}^{\pm }\to {M_0}^{\pm }+\gamma$, where $M_0$ and $M_1$ mean a pseudoscalar and a (heavier) vector meson, respectively, and the superscript ± indicates the charge, if there is one. If the coupling constant and meson masses appropriate to the Schwinger mixture are used, the lifetimes are found to be: ${\tau }_a=1\mathrm{}\times {10}^{-16\mathrm{}}$ sec., ${\tau }_b=2\mathrm{}\times {10}^{-11\mathrm{}}$ sec., ${\tau }_c=1\mathrm{}\times {10}^{-18\mathrm{}}$ sec., and ${\tau }_d=4\mathrm{}\times {10}^{-18\mathrm{}}$ sec. In all cases except (b) the calculation leads to logarithmically divergent integrals.