A simple alternative to the relativistic Breit–Wigner distribution

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) , and K∗(982) mesons as well as the Δ(1232) baryon. We also present a study of the f2(1270) which has more than one possible decay channels. Finally, we discuss the limitations of the Sill distribution using the a(980) -a(1450) and the K0∗(700)-K0∗(1430) resonances as examples.