Corrections to Fermi's Golden Rule in $ϕ\to K\bar{K}$ Decays

Abstract

We analyze the decays $ϕ\to K\bar{K}$ utilizing a formulation of transition rates which explicitly exhibits corrections to Fermi's Golden Rule. These corrections arise in systems in which the phase space and/or matrix element varies rapidly with energy, as happens in $ϕ\to K\bar{K}$, which is just above threshold. We show that the theoretical corrections resolve a puzzling $5σ$ discrepancy between theory and experiment for the branching ratio $R = Γ(ϕ\to K^+K^-)/Γ(ϕ\to K^0\bar{K}^0)$.