AbstractFirst, 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 $$\rho $$
ρ
, $$a_1(1260)$$
a
1
(
1260
)
, and $$K^*(982)$$
K
∗
(
982
)
mesons as well as the $$\varDelta (1232)$$
Δ
(
1232
)
baryon. We also present a study of the $$f_2(1270)$$
f
2
(
1270
)
which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the $$a_0(980)$$
a
0
(
980
)
-$$a_0(1450)$$
a
0
(
1450
)
and the $$K_0^*(700)$$
K
0
∗
(
700
)
-$$K_0^*(1430)$$
K
0
∗
(
1430
)
resonances as examples.
A simple alternative to the relativistic Breit–Wigner distribution
