Preserving unitarity for overlapping multichannel states: Breit-Wigner versus K matrix -- comparison, advantages and disadvantages

Abstract

The K-matrix method is often used to describe overlapping resonances. It guarantees the unitarity of the scattering matrix but its parameters are not resonances masses and widths. It is also unclear how to separate resonant and background contributions and to describe background in terms of phase shifts. The Breit-Wigner (BW) approach operates with parameters having direct experimental meaning but a simple sum of the BW functions is not unitary. We show how to construct the unitary S-matrix by taking into account the interference of the BW functions. The method is simple and straightforward, background can be added to resonance amplitudes in the standard quantum mechanics form. In examples we give a comparison between the K-matrix and unitary BW-approaches.