Pion-nucleon P_33 and P_11 scatterings in the Lippmann-Schwinger approach

TL;DR

This paper investigates pion-nucleon scattering in specific channels using an extended Lippmann-Schwinger approach to understand the nature of Delta and Roper resonances, challenging standard quark model interpretations.

Contribution

It introduces an extended Lippmann-Schwinger method to analyze resonance structures and questions the conventional quark model explanations for these states.

Findings

The approach validates some aspects of the standard quark model.

It reveals puzzles and limitations in the current understanding of the Delta and Roper resonances.

The study highlights the importance of including one-baryon states in scattering analyses.

Abstract

We study the pion-nucleon P_33 and P_11 scattering, where the Delta and the Roper resonances are seen, respectively. We use the Lippmann-Schwinger equation extended to couple to a one-body state, and investigate nature of these resonances by taking and omitting a one-baryon state into account. We see validity and puzzle of the standard quark model interpretation, for the Delta and the Roper resonances, respectively.