Same-resonance entrance-channel cross-section ratio (${\sigma }_a/{\sigma }_b=(g_a/g_b)(p_b^2/p_a^2)({\Gamma }_a/{\Gamma }_b)$)

Compare two entrance channels feeding the same isolated resonance and the same selected exit channel, each at its own resonance energy. The exit partial decay width and the resonant denominator cancel. Different entrance momenta, spin weights and entrance widths remain. The formula assumes the same resonance, the stated unpolarized spin average and negligible nonresonant interference; a ratio at one shared laboratory energy would generally be different.