Proton Decay Rate

The pionic two-body decay amplitude of the proton in the SU(5) grand unified gauge theory is computed by using the soft-pion method in the reference frame of the pion at rest. The normalization condition of the relativistic three-body Bethe-Salpeter wave function of the proton is used in the computation. It is shown that the partial decay rate of the process, proton →$e^{+}{\pi }^0$, is (${0.86\times {10}^{30}\mathrm{y}\mathrm{r})}^{-1\mathrm{}}$ and (${1.4\times {10}^{31}\mathrm{y}\mathrm{r})}^{-1\mathrm{}}$ for $m_X=4.0\mathrm{}\times {10}^{14} \mathrm{GeV}\mathrm{and} 8.0\times {10}^{14} \mathrm{GeV}$, respectively. These values are on the boundary of the present experimental limit.