Determination of the η-η′ Mixing Angle from Fη(′)γ(Q2) within the Self-consistent Light-front Quark Model
Abstract
We study the η-η′ system in the self-consistent light-front quark model (LFQM) with the quark flavor mixing scheme, where the single mixing angle is constrained by the transition form factors (TFFs) Fη(′)γ(Q2). A continuous combined χ2 fit to the CLEO and BABAR data gives θ=41.55+0.57−0.60 ∘, in close agreement with the recent LHCb result (41.6+1.0−1.2)∘. Using this mixing angle, we calculate the decay constants, light-cone distribution amplitudes (LCDAs), Gegenbauer moments, ξ-moments, transverse momentum moments, electromagnetic interaction radii and two-photon decay widths of the η and η′ mesons. The predicted a2η and ⟨ξ2⟩η are consistent with the latest BABAR results, and the electromagnetic interaction radii also agree well with the A2 and BESIII measurements. These results demonstrate that TFF data strongly constrain the light-front description of the nonperturbative properties of the η-η′ system. After the fit and LFQM-input uncertainties are propagated, the predicted widths are 0.428+0.038−0.035 keV and 3.067+0.190−0.180 keV for η→γγ and η′→γγ, respectively. The central values are lower than the corresponding experimental values, indicating that the real-photon point provides a more sensitive test of the absolute TFF normalization.
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BibTeX
@misc{xu2026determination,
title = {{Determination of the $η$-$η^\prime$ Mixing Angle from $F_η^(\prime)γ(Q^2)$ within the Self-consistent Light-front Quark Model}},
author = {Shuai Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00407},
eprint = {2608.00407},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00407},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Determination of the η-η^′ Mixing Angle from F_η^(′)γ(Q^2) within the Self-consistent Light-front Quark Model
AU - Shuai Xu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2608.00407
UR - https://arxiv.org/abs/2608.00407
AB - We study the η-η^′ system in the self-consistent light-front quark model (LFQM) with the quark flavor mixing scheme, where the single mixing angle is constrained by the transition form factors (TFFs) F_η^(′)γ(Q^2). A continuous combined χ^2 fit to the CLEO and BABAR data gives θ=41.55^+0.57_−0.60 ^∘, in close agreement with the recent LHCb result (41.6^+1.0_−1.2)^∘. Using this mixing angle, we calculate the decay constants, light-cone distribution amplitudes (LCDAs), Gegenbauer moments, ξ-moments, transverse momentum moments, electromagnetic interaction radii and two-photon decay widths of the η and η^′ mesons. The predicted a_2^η and ⟨ξ^2⟩_η are consistent with the latest BABAR results, and the electromagnetic interaction radii also agree well with the A2 and BESIII measurements. These results demonstrate that TFF data strongly constrain the light-front description of the nonperturbative properties of the η-η^′ system. After the fit and LFQM-input uncertainties are propagated, the predicted widths are 0.428^+0.038_−0.035 keV and 3.067^+0.190_−0.180 keV for η→γγ and η^′→γγ, respectively. The central values are lower than the corresponding experimental values, indicating that the real-photon point provides a more sensitive test of the absolute TFF normalization.
ER -