Insight on confinement from the QCD effective charge
Abstract
Like the Gell-Mann--Low coupling α of QED, the effective charge αg1 is a physical, observable-defined running coupling that can serve as the QCD coupling αs. It can be represented by an analytic form consistent with renormalization-group evolution, holographic light-front QCD (HLFQCD), and the world data on αs. As an observable, αg1 has a physically relevant analytic structure that reflects the underlying partonic dynamics. It displays, in the long-distance regime, two imaginary conjugate singularities at Q2 = ± iΛs2, with Λs the QCD scale. To connect this structure to confinement, we combine known general relations between αg1 and the parton dressed propagators and vertices with a recent phenomenological representation of αg1 within HLFQCD. Since, unlike vertices, propagators characterize a field variation between separate locations, the two singularities are assigned to the propagators. This results in the parton propagators displaying a long-distance behavior e−Λs |x|/√2 |x|−5/2 + da where propagation is suppressed beyond distances of order 1/Λs, as expected from confinement. This offers an intuitive interpretation of confinement as the suppression of QCD Green's functions at long distance.
Versions
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BibTeX
@misc{deur2026insight,
title = {{Insight on confinement from the QCD effective charge}},
author = {A. Deur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05144},
eprint = {2607.05144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Insight on confinement from the QCD effective charge
AU - A. Deur
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2607.05144
UR - https://arxiv.org/abs/2607.05144
AB - Like the Gell-Mann--Low coupling α of QED, the effective charge α_g_1 is a physical, observable-defined running coupling that can serve as the QCD coupling α_s. It can be represented by an analytic form consistent with renormalization-group evolution, holographic light-front QCD (HLFQCD), and the world data on α_s. As an observable, α_g_1 has a physically relevant analytic structure that reflects the underlying partonic dynamics. It displays, in the long-distance regime, two imaginary conjugate singularities at Q^2 = ± iΛ_s^2, with Λ_s the QCD scale. To connect this structure to confinement, we combine known general relations between α_g_1 and the parton dressed propagators and vertices with a recent phenomenological representation of α_g_1 within HLFQCD. Since, unlike vertices, propagators characterize a field variation between separate locations, the two singularities are assigned to the propagators. This results in the parton propagators displaying a long-distance behavior e^−Λ_s |x|/√2 |x|^−5/2 + d_a where propagation is suppressed beyond distances of order 1/Λ_s, as expected from confinement. This offers an intuitive interpretation of confinement as the suppression of QCD Green's functions at long distance.
ER -