RESUMEN
We show that a slightly modified Breit-Wigner formula can successfully describe the total cross section even for the broad resonances, from the light ρ(770) to the heavy Z boson. In addition to the mass, width, and branching fraction, we include another resonance parameter that turns out to be directly related to the pole residue phase. The new formula has two mathematically equivalent forms: one with the pole and the other with the Breit-Wigner parameters.
RESUMEN
All resonances, from hydrogen nuclei excited by the high-energy gamma rays in deep space to newly discovered particles produced in Large Hadron Collider, should be described by the same fundamental physical quantities. However, two distinct sets of properties are used to describe resonances: the pole parameters (complex pole position and residue) and the Breit-Wigner parameters (mass, width, and branching fractions). There is an ongoing decades-old debate on which one of them should be abandoned. In this study of nucleon resonances appearing in the elastic pion-nucleon scattering we discover an intricate interplay of the parameters from both sets, and realize that neither set is completely independent or fundamental on its own.
RESUMEN
In spite of long-lasting discussions, the agreement on the existence of the N(1710) P11 resonance has not yet been reached, so the Particle Data Group declares it as a 3-star resonance only. We show that the proper inclusion of inelastic channels in the coupled-channel formalism indisputably demands the existence of the N(1710) P11 state, and that it presumably stays hidden within the continuum ambiguity of a typical single-channel partial-wave analysis. Consequently, the Particle Data Group confidence rating of this state should be raised to a 4-star resonance.