A simple alternative to the relativistic Breit–Wigner distribution

• Published in: The European physical journal. A, Hadrons and nuclei Hadrons and nuclei, 2021-12, Vol.57 (12), Article 336
• Main Authors: Giacosa, Francesco, Okopińska, Anna, Shastry, Vanamali
• Format: Article
• Language: English
• Subjects: Decay; Energy distribution; Hadrons; Heavy Ions; Mesons; Nuclear Fusion; Nuclear Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Regular Article - Theoretical Physics; Relativistic effects; Wigner distribution
• ISSN: 1434-6001; 1434-601X
• DOI: 10.1140/epja/s10050-021-00641-2

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 , a 1 ( 1260 ) , and K ∗ ( 982 ) mesons as well as the Δ ( 1232 ) baryon. We also present a study of the 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 ( 1450 ) and the K 0 ∗ ( 700 ) - K 0 ∗ ( 1430 ) resonances as examples.