Finite-volume effects on smeared spectral densities
Abstract
Using two distinct approaches, we derive a universal expression for the leading finite-volume effects of the smeared vector-vector spectral density (proportional to the smeared hadronic R-ratio) in a periodic cubic spatial volume of side length L. First, building on the results of previous work for finite-volume effects on Euclidean two-point functions, we show that the L dependence is exponentially suppressed for a certain class of smearing kernels, and that the leading effects can be expressed universally in terms of the pion form factor. The same representation is then derived starting from the Lellouch-Lüscher-Meyer expression for the spectral decomposition of the correlator. The results may prove useful for controlling the L → ∞ extrapolation of smeared spectral densities, in particular by defining a scaling regime in which the finite-volume effects are dominated by the leading terms in a large L expansion and thus can be reliably estimated. To illustrate this point, we also present numerical estimates based on various kernels and models of particle interactions. Despite focusing on the vector channel, our derivation defines a general framework applicable to other cases as well.
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BibTeX
@misc{bresciani2026finitevolume,
title = {{Finite-volume effects on smeared spectral densities}},
author = {Francesca A. Bresciani and Mattia Bruno and Maxwell T. Hansen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.14349},
eprint = {2606.14349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14349},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-volume effects on smeared spectral densities
AU - Francesca A. Bresciani
AU - Mattia Bruno
AU - Maxwell T. Hansen
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.14349
UR - https://arxiv.org/abs/2606.14349
AB - Using two distinct approaches, we derive a universal expression for the leading finite-volume effects of the smeared vector-vector spectral density (proportional to the smeared hadronic R-ratio) in a periodic cubic spatial volume of side length L. First, building on the results of previous work for finite-volume effects on Euclidean two-point functions, we show that the L dependence is exponentially suppressed for a certain class of smearing kernels, and that the leading effects can be expressed universally in terms of the pion form factor. The same representation is then derived starting from the Lellouch-Lüscher-Meyer expression for the spectral decomposition of the correlator. The results may prove useful for controlling the L → ∞ extrapolation of smeared spectral densities, in particular by defining a scaling regime in which the finite-volume effects are dominated by the leading terms in a large L expansion and thus can be reliably estimated. To illustrate this point, we also present numerical estimates based on various kernels and models of particle interactions. Despite focusing on the vector channel, our derivation defines a general framework applicable to other cases as well.
ER -