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Abstract First, we discuss the conditions under which the non-relativistic and relativistic types of the Breit–Wigner energy distributions are obtained. Then, upon insisting on the correct normalization of the energy distribution, we introduce a Flatté-like relativistic distribution -denominated as Sill distribution- that (i) contains left-threshold effects, (ii) is properly normalized for any decay width, (iii) can be obtained as an appropriate limit in which the decay width is a constant, (iv) is easily generalized to the multi-channel case (v) as well as to a convoluted form in case of a decay chain and - last but not least - (vi) is simple to deal with. We compare the Sill distribution to spectral functions derived within specific QFT models and show that it fairs well in concrete examples that involve a fit to experimental data for the ρ, a₁ (1260) a 1 (1260), and K^* (982) K ∗ (982) mesons as well as the (1232) Δ (1232) baryon. We also present a study of the f₂ (1270) f 2 (1270) which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the a₀ (980) a 0 (980) - a₀ (1450) a 0 (1450) and the K₀^* (700) K 0 ∗ (700) - K₀^* (1430) K 0 ∗ (1430) resonances as examples.
Giacosa et al. (Wed,) studied this question.