Analysis of Overlapping Resonances with Unitary Breit–Wigner and K-Matrix Approaches

Abstract

We compare two methods for obtaining the parameters of overlapping resonances. The convenience of the Breit–Wigner (BW) approach is based on the fact that it operates with the masses and widths of the states. For several resonances with the same quantum numbers, a sum of BW functions violates the unitarity of the S-matrix. However, unitarity can be maintained by introducing interference phases to a BW implementation of scattering matrix formalism. A background can be added to the BW amplitudes in the standard way by using background phases. The K-matrix method is often used to analyze data related to several resonances with the same quantum numbers. It guarantees the unitarity of the S-matrix, but its parameters can be considered as resonance masses and widths only for well-spaced states. It also does not allow the separation of the resonant and background contributions in scattering amplitudes, which is critically important for determining parameters of wide resonances. To demonstrate the features of these methods, we consider several examples using simulated data.