π0 → γγ in the Spinor Strong Interaction Theory

Abstract

An expression for the decay rate Γ(π⁰ γγ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, π⁺ → μ⁺ ν, e⁺ν, and π⁰ e⁺ν, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V → PP has been taken over here to apply to P(π⁰) →VV(ρ⁺ ρ⁻) → γγ(plus π⁺ and π⁻ which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V(ϕ) → PP(K⁺K⁻), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).