Calculation of proton decay in the nonrelativistic quark model

We compute two-body branching ratios in proton decay in the SU(5) and SO(10) grand unification schemes. Using nonrelativistic approximation for quarks we can obtain algebraic relations between the matrix elements coming from spin-flavor symmetries. The absolute magnitude can be fixed from nonleptonic decays of hyperons, a similar phenomenon. We find branching ratios significantly different from previous works. Pion modes are very important due essentially to phase space (${\pi }^0{e}^{+}$, 37%, and ${\pi }^{+}{\overline{\nu }}_e$, 15%), and ${\omega }^0{e}^{+}$ is quite sizable (∼18%) due to its large matrix element. We find also an important $K^0{\mu }^{+}$ fraction (19%). Bound-state effects are quite crucial since we get, from two-body modes, a lifetime at the edge of the experimental limits, $\tau \mathrm{}\left(p\right)\mathrm{}\simeq 5\times {10}^{29} or 8\times {10}^{30}$ yr from $M_X=3\mathrm{}\times {10}^{14} or 6\times {10}^{14}$ GeV.