Narrow-width approximation limitations

−∞ dqD(q). The scattering cross section σ thus approximately decouples into on-shell production (σp) and decay as shown in Eq. (1) for a scalar process [1]. The generalization to multiple resonances is straightforward. We use the notation of [2], Sec. 38. Based on the scales occurring in D(q), the conventional error estimate is O(Γ/M). The branching fraction for the considered decay mode is then given by BR = ΓX/Γ = σNWA/σp, where ΓX is the partial decay width. We define the effective branching ratio BReff ≡ σ/σp, which is related to the branching ratio via BReff = (1 + R) BR with R ≡ σ/σNWA − 1 = R +O(Γ2).