Charge splitting in ${\pi}N\Delta$ formfactor

TL;DR

This paper analyzes charge splitting in $ ext{π}N ext{Δ}$ form factors using experimental $ ext{π}N$ scattering data and a $K$-matrix approach, revealing that $ ext{Δ}^{++}$ and $ ext{Δ}^{0}$ have different sizes in $ ext{π}N$ interactions.

Contribution

It demonstrates that the sign change in phase difference can be explained by different form factors for $ ext{Δ}^{++}$ and $ ext{Δ}^{0}$, indicating different interaction sizes.

Findings

Charge splitting observed in phase shifts.

Different form factors for $ ext{Δ}^{++}$ and $ ext{Δ}^{0}$ explain sign change.

$ ext{Δ}^{++}$ and $ ext{Δ}^{0}$ have different sizes in $ ext{π}N$ interactions.

Abstract

Experimental data on $\pi N $ scattering in the elastic energy region $W \leq 1.45 GeV $ are analyzed within the $K$-matrix approach with effective Lagrangians. The charge splitting in $\delta^{++}_{33} $ and $\delta^{0}_{33}$ phases obtaned in the phase shift analisys is studed . It is shown that the change in the sign in the energy dependence of the phase difference can be obtained with different formfactors of the $\Delta^{++}$ and $\Delta^{0}$ only . This means that $\Delta^{++}$ and $\Delta^{0}$ has a different size in $\pi N $ interaction.The underlying nature of the observed phenomena is discussed.