A new perspective on the $\Delta_{5/2^{+}}(2000)$ puzzle

TL;DR

This paper proposes reinterpreting the $ ext{PDG}$-listed $ ext{Delta}$ resonance as two separate states at different masses, based on solving the $ ext{Faddeev}$ equations with a fixed center approximation, revealing new bound state structures.

Contribution

It introduces a novel interpretation of the $ ext{Delta}_{5/2^{+}}(2000)$ resonance as two distinct states, supported by a solution to the $ ext{Faddeev}$ equations in a fixed center approximation.

Findings

$ ext{Delta}_{5/2^{+}}(2000)$ should be two resonances at 1740 and 2200 MeV

1740 MeV state is a $ ext{pi}-( ext{Delta} ho)$ bound state

1750 MeV $ ext{Delta}$ can be a $ ext{pi} N_{1/2^{-}}$ bound state

Abstract

We argue that $\Delta_{5/2^{+}}(2000)(\ast\ast),$ cataloged as a resonance in the Particle Data Book Review (PDG), should be interpreted instead as two distinctive resonances, $\Delta_{5/2^{+}}(\sim1740)$ and $\Delta_{5/2^{+}}(\sim2200)$. Our argument is based on a solution of the $\pi\Delta\rho$ problem in a Fixed Center Approximation (FCA) to the Fadeev equations. $\Delta_{5/2^{+}}(\sim1740)$ can then be interpreted as a $\pi-(\Delta \rho)_{N(1675)}$ bound state. As a corollary $\Delta_{1/2^{+}}(1750)(\ast)$ can be understood as a $\pi N_{1/2^{-}}(1650)$ bound state.