 Breit-Wigner resonance cross section

For an isolated particle resonance of spin $J_R$, the Breit-Wigner approximation relates a production-and-decay cross section to its partial decay widths. In natural units, $p_i$ is either incident particle's momentum magnitude in the centre-of-momentum frame, $g=(2J_R+1)/[(2J_a+1)(2J_b+1)]$ for unpolarized incident particles, and $\Gamma$ is the total width. The formula assumes the stated spin counting and neglects nonresonant backgrounds and their interference. Multiplication by $(\hslash c{)}^2$ converts an inverse-squared-energy cross section to area when momenta are expressed in energy units.