ρ→ππin the SLAC lattice quantum-chromodynamic theory

Using the SLAC lattice Hamiltonian QCD theory, we compute the decay width for the decay ${\rho }^{+}\to {\pi }^{+}{\pi }^0$. There is reasonable agreement between the theoretical result and observation. There are two key ingredients involved in our calculation. One is the vacuum-insertion technique of Lee, Primack, and Treiman for the evaluation of light-hadron matrix elements of effective low-energy interaction densities. The other is the identification of the SLAC lattice currents with the physical hadron currents to leading order in the SLAC order-$\frac{1}{g^2}$ effective Hamiltonian for the fluxless light-hadron sector—in the spirit of Gell-Mann's work in current algebra. Our result suggests that the SLAC theory, taken together with these two ingredients, provides a viable technique for calculating large-distance light-hadron dynamics.