Extraction of resonances from meson-nucleon reactions

Abstract

We present a pedagogical study of the commonly employed Speed-Plot (SP) and Time-delay (TD) methods for extracting the resonance parameters from the data of two particle coupled-channels reactions. Within several exactly solvable models, it is found that these two methods find poles on different Riemann sheets and are not always valid. We then develop an analytic continuation method for extracting nucleon resonances within a dynamical coupled-channel formulation of πN and γN reactions. The main focus of this paper is on resolving the complications due to the coupling with the unstable π∆, ρN, σN channels which decay into ππN states. By using the results from the considered exactly solvable models, explicit numerical procedures are presented and verified. As a first application of the developed analytic continuation method, we present the nucleon resonances in some partial waves extracted within a recently developed coupled-channels model of πN reactions. The results from this realistic πN model, which includes πN , ηN , π∆, ρN , and σN channels, also show that the simple pole parametrization of the resonant propagator using the poles extracted from SP and TD methods works poorly.

Light-Quark Baryon Spectroscopy from ANL-Osaka Dynamical Coupled-Channels Analysis

“…See Refs. [17,18] for the details of the analytic continuation method employed for our analysis. The DCC model for the Λ * and Σ * sector with strangeness S = −1 can be constructed in the same way as the N * and ∆ * sector by replacing the reaction channels withKN, πΣ, πΛ, ηΛ, πΣ * , and K * N, where the last two are the quasi two-body channels for the three-body ππΣ and πKN channels, respectively, and by modifying the Green's functions and transition potentials appropriately.…”

Effect of three-pion unitarity on resonance poles from heavy meson decays

“…The procedure for finding the pole position suitable for our model has been developed [7]. A pole position is at a complex energy (W ) for…”

P11 resonance extracted from πN data and its stability

“…We find the poles with the method of analytic continuation discussed in detail in Refs. [3,9]. In Table 1, we also present pole positions from JLMS [4] and SAID-EDS (energy-dependent) [5].…”