The Sill distribution for all partial waves
Abstract
In high-energy physics, short-lived resonances appearing in scattering processes are described by energy-dependent spectral functions. The relativistic Breit--Wigner distribution (rBW), obtained as a relativistic extension of the standard Breit--Wigner form, is commonly employed owing to its simplicity. However, when the lower-energy threshold lies sufficiently close to the resonance peak, sizable deviations from the rBW line shape are expected. The Sill distribution provides a simple way to incorporate the physical threshold while preserving exact normalization, but in its original formulation it is inherently restricted to s-wave decays. Here, we extend the Sill distribution to arbitrary partial waves. The correct ℓ-wave threshold behaviour is implemented while exact normalization is retained through a simple modification of the mass term of the propagator. As a benchmark, the p-wave Sill provides a very good description of the Δ(1232)++ line shape up to 1.35 GeV and simultaneously reproduces its on-shell mass and width and its complex pole position, in agreement with independent determinations compiled by the PDG.
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BibTeX
@misc{kyziol2026sill,
title = {{The Sill distribution for all partial waves}},
author = {Krzysztof Kyzioł and Francesco Giacosa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20975},
eprint = {2610.20975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20975},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Sill distribution for all partial waves
AU - Krzysztof Kyzioł
AU - Francesco Giacosa
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20975
UR - https://arxiv.org/abs/2610.20975
AB - In high-energy physics, short-lived resonances appearing in scattering processes are described by energy-dependent spectral functions. The relativistic Breit--Wigner distribution (rBW), obtained as a relativistic extension of the standard Breit--Wigner form, is commonly employed owing to its simplicity. However, when the lower-energy threshold lies sufficiently close to the resonance peak, sizable deviations from the rBW line shape are expected. The Sill distribution provides a simple way to incorporate the physical threshold while preserving exact normalization, but in its original formulation it is inherently restricted to s-wave decays. Here, we extend the Sill distribution to arbitrary partial waves. The correct ℓ-wave threshold behaviour is implemented while exact normalization is retained through a simple modification of the mass term of the propagator. As a benchmark, the p-wave Sill provides a very good description of the Δ(1232)^++ line shape up to 1.35 GeV and simultaneously reproduces its on-shell mass and width and its complex pole position, in agreement with independent determinations compiled by the PDG.
ER -