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arXiv · 2607.00778

Rethinking Partial Widths: Unitary Mixing and the $\Delta(1232)$ Pole Residue

S. Ceci·R. Omerović·H. Osmanović·M. Uroić·B. Zauner
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Abstract

The extracted $\pi N$ partial decay width of the $\Delta(1232)$ systematically exceeds its total width ($2|r|>\Gamma$). We demonstrate this anomaly is a natural consequence of S-matrix unitary mixing. Because exact multi-channel shadow poles are distant and model-dependent, we utilize a heuristic elastic model -- treating the overlapping $\Delta(1600)$ as fully elastic -- to isolate the core mechanism. We show that evaluating a perturbing S-matrix at a state's complex pole systematically inflates the residue magnitude. This proof of principle confirms complex residues reflect global amplitude topology rather than isolated intrinsic properties, challenging naive interpretations of branching fractions.

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S. Ceci, R. Omerović, H. Osmanović, M. Uroić, B. Zauner. 2026-07-01. Rethinking Partial Widths: Unitary Mixing and the $\Delta(1232)$ Pole Residue. https://arxiv.org/abs/2607.00778

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