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

Abstract

We analyze the decays $\phi \to K\bar{K}$ 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 $\phi \to K\bar{K}$, which is just above threshold. We show that the theoretical corrections resolve a puzzling $5\sigma$ discrepancy between theory and experiment for the branching ratio $R = \Gamma (\phi \to K^+K^-)/\Gamma(\phi \to K^0\bar{K}^0)$.