Possible explanation of Hoehler's clustering: effective partial-wave mixing induced by truncation

TL;DR

This paper explores how partial-wave truncation in scattering analysis can cause apparent resonance clustering, offering a plausible explanation for Hoehler's observed pattern.

Contribution

It demonstrates that truncation-induced mixing of partial waves can naturally lead to resonance clustering patterns in scattering data.

Findings

Truncation of partial-wave series can induce effective mixing of angular momenta.

Such mixing can cause resonance poles to appear clustered near common energies.

This mechanism provides a plausible explanation for Hoehler's clustering observations.

Abstract

Hoehler noted that resonance poles obtained from different partial waves in $\pi N$ scattering appear to bunch together near a small set of common complex energies, and suggested that this could indicate mixing between angular momenta. Here, we examine whether at least part of this pattern could arise effectively from the extraction procedure itself. Exact partial-wave unitarity preserves the separation of angular momenta in the infinite problem, whereas practical pole extraction from bilinear observables requires truncation of the partial-wave series. Combined with the truncation-induced mixing mechanism established in Ref.~\cite{Svarc2026}, this provides a natural source by which fitted partial-wave coefficients can inherit overlapping pole-bearing content, thereby offering a plausible contribution to Hoehler-type clustering.