Probability distribution of unstable particle produces by resonances.

In natural units (\( \hbar = c = 1 \)) , \[ f(E) = \frac{k}{(E^2 - M^2)^2 + M^2\Gamma^2} \] where \( k \) is constant of proportionality \[ k = \frac{2 \sqrt{2}M\Gamma\gamma}{\pi \sqrt{M^2+\gamma}}, \quad \gamma = \sqrt{M^2 (M^2 + \Gamma^2)}. \] \( E \) is the center-of-mass energy that produces the resonance, \( M \) is the mass of the resonance, and \( \Gamma \) is the resonance width (or decay width).