The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>-Instability of Mesons

Abstract

The following examples of $\ensuremath{\gamma}$-instability are investigated: (a) ${M}_{0}\ensuremath{\rightarrow}{\ensuremath{\gamma}}_{1}+{\ensuremath{\gamma}}_{2}$, (b) ${M}_{1}\ensuremath{\rightarrow}{\ensuremath{\gamma}}_{1}+{\ensuremath{\gamma}}_{2}+{\ensuremath{\gamma}}_{3}$, (c) ${M}_{1}\ensuremath{\rightarrow}{M}_{0}+\ensuremath{\gamma}$, (d) ${{M}_{1}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{{M}_{0}}^{\ifmmode\pm\else\textpm\fi{}}+\ensuremath{\gamma}$, where ${M}_{0}$ and ${M}_{1}$ mean a pseudoscalar and a (heavier) vector meson, respectively, and the superscript \ifmmode\pm\else\textpm\fi{} 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: ${\ensuremath{\tau}}_{a}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ sec., ${\ensuremath{\tau}}_{b}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ sec., ${\ensuremath{\tau}}_{c}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ sec., and ${\ensuremath{\tau}}_{d}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ sec. In all cases except (b) the calculation leads to logarithmically divergent integrals.