Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

Abstract

The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions. In the present study, we determine the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. For this, the sheet structure of the amplitude is determined. To show the precision of the resonance extraction and discuss phenomena such as resonance interference, we discuss the S 11 amplitude in greater detail.

Chiral dynamics of the S11(1535) and S11(1650) resonances revisited

“…We end up with W 1535 = (1.506 − 0.140 i) GeV and W 1650 = (1.682 − 0.042 i) GeV, which is similar to values of similar approaches [5] and [13], as well to those of various phenomenological models listed in [12]. To analyze the structure of these states we consider the on-shell scattering matrix in the vicinity of the two poles, where it takes the form T on i j (s) g i g j s−s R , with g i (g j ) the complex coupling constant for the initial (final) transition of the meson-baryon system.…”

“…This led to a satisfactory description of the S 11 phase and a reasonable description of the inelasticity up to the ηN threshold. More recently, it was pointed out in a state-of-the-art unitary meson-exchange model that there is indeed strong resonance interference between the two S 11 resonances, as each of these resonances provides an energy-dependent background in the region of the other [5].…”

Coupled channels approach to photo-meson production on the nucleon

“…The dynamics of the Roper resonance turns out to be rich because of the two-pole structure reported in earlier studies [55,56], (see [40,57,58] for the recent status of the problem. ) The origin of the Roper resonance is also controversial.…”

Modern Dynamical Coupled-Channels Calculations for Extracting and Understanding the Nucleon Spectrum

“…Here, the poles A and B are well known as the double-pole (pole and shadow-pole [13]) structure of the Roper resonance with respect to the π∆ channel, which has been observed also in Refs. [3,[14][15][16] and mentioned by PDG [2], while the pole C corresponds to the N * (1710)1/2 + resonance. On the other hand, the so-called "bare" N * state, which has the real mass of 1763 MeV (the filled square in Fig.…”