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Probing the $γ γ^{*} \to η^{(')}$ transition form factors with newly derived $η^{(')}$ -meson light-cone distribution amplitudes

Dan-Dan Hu^1,*, Xing-Gang Wu ^1,†, Yu-Jie Zhang^1,‡, Hai-Bing Fu ^2,§, and Tao Zhong^2,∥

¹Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China
²Department of Physics, Guizhou Minzu University, Guiyang 550025, People’s Republic of China

^*Contact author: hudd@stu.cqu.edu.cn
^†Contact author: wuxg@cqu.edu.cn
^‡Contact author: zhangyj@stu.cqu.edu.cn
^§Contact author: fuhb@gzmu.edu.cn
^∥Contact author: zhongtao@gzmu.edu.cn

Phys. Rev. D 114, 016003 – Published 6 July, 2026

DOI: https://doi.org/10.1103/ycq4-t1my

Abstract

In the present work, we analyze the properties of the transition form factors (TFFs) for the $γ γ^{*} \to η^{(')}$ process, employing the $η^{(')}$ -meson light-cone distribution amplitude (LCDA) derived within the light-cone sum rule framework. To this end, we adopt the quark-flavor mixing scheme for the $η^{(')}$ meson, and compute the TFFs by systematically incorporating transverse-momentum corrections and contributions beyond the leading Fock state. We utilize light-cone harmonic oscillator models to parametrize the longitudinal and transverse behavior of the leading-twist light-cone wave function, for which the corresponding LCDA exhibits a unimodal profile. We further examine the potential contributions of intrinsic charm components to the scaled TFFs $Q^{2} F_{η γ} (Q^{2})$ and $Q^{2} F_{η^{'} γ} (Q^{2})$ . Leveraging a range of values for the decay constant $f_{η_{c_{0}}}$ and implementing the $η - η^{'} - η_{c}$ and $η - η^{'} - G − η_{c}$ mixing mechanisms accordingly, together with the recently updated mixing angles, we investigate the impact of the intrinsic $c \bar{c}$ and gluonic component on these observables. In the high- $Q^{2}$ regime, $Q^{2} F_{η^{'} γ} (Q^{2})$ exhibits a marked increase in sensitivity to the charm quark component, whereas $Q^{2} F_{η γ} (Q^{2})$ becomes notably stabilized. A detailed discussion of $χ^{2} / d . o . f .$ (chi-squared per degree of freedom) and $p$ values indicates that the intrinsic charm quark component is important and yields a substantial, non-negligible contribution across the entire $Q^{2}$ range.

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Phys. Rev. D 114, 016003– Published 6 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 31 January 2026
Accepted 22 May 2026

DOI: https://doi.org/10.1103/ycq4-t1my

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Probing the $γ γ^{*} \to η^{(')}$ transition form factors with newly derived $η^{(')}$ -meson light-cone distribution amplitudes

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Probing the γγ*→η(′) transition form factors with newly derived η(′)-meson light-cone distribution amplitudes

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Probing the $γ γ^{*} \to η^{(')}$ transition form factors with newly derived $η^{(')}$ -meson light-cone distribution amplitudes