https://doi.org/10.1140/epja/s10050-021-00641-2
Regular Article - Theoretical Physics
A simple alternative to the relativistic Breit–Wigner distribution
1
Institute of Physics, Jan Kochanowski University, ul. Uniwersytecka 7, 25-406, Kielce, Poland
2
Institute for Theoretical Physics, Johann Wolfgang Goethe—University, Max von Laue-Str. 1, 60438, Frankfurt, Germany
Received:
6
July
2021
Accepted:
23
November
2021
Published online:
18
December
2021
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 
, 
, and 
mesons as well as the 
baryon. We also present a study of the 
which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the 
-
and the 
-
resonances as examples.
© The Author(s) 2021
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