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Two nearby states in the $X (3872)$ region: Resolving the radiative-decay ratio tension with $η_{c 2}$

Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China

^*Contact author: satoshi@sdu.edu.cn

Phys. Rev. D 113, 114031 – Published 17 June, 2026

DOI: https://doi.org/10.1103/rr8b-j4nw

Abstract

Recently, LHCb reported the radiative-decay ratio $R^{ψ γ} \equiv B [X (3872) \to ψ^{'} γ] / B [X (3872) \to J / ψ γ] = 1.67 \pm 0.25$ extracted from $B^{+} \to K^{+} (J / ψ γ, ψ^{'} γ)$ . This result differs markedly ( $\sim 4.6 σ$ ) from the BESIII value obtained from $e^{+} e^{-} \to γ (J / ψ γ, ψ^{'} γ)$ , $R^{ψ γ} = - 0.04 \pm 0.28$ . Such a significant tension suggests that more than one state in the $X (3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{* 0} {\bar{D}}^{0}$ bound state with $J^{P C} = 1^{+ +}$ and a $2^{- +}$ charmonium candidate, $η_{c 2}$ , slightly above the $D^{* 0} {\bar{D}}^{0}$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and line shapes across multiple processes. By contrast, fits without the $η_{c 2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivate the future experiments to test the two-state hypothesis and search for the so-far missing $η_{c 2}$ .

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Phys. Rev. D 113, 114031– Published 17 June, 2026

Vol. 113, Iss. 11 — 1 June 2026

Received 2 March 2026
Accepted 6 May 2026

DOI: https://doi.org/10.1103/rr8b-j4nw

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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Two nearby states in the $X (3872)$ region: Resolving the radiative-decay ratio tension with $η_{c 2}$

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Two nearby states in the X(3872) region: Resolving the radiative-decay ratio tension with ηc2

Abstract

Physics Subject Headings (PhySH)

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References (69)

Two nearby states in the $X (3872)$ region: Resolving the radiative-decay ratio tension with $η_{c 2}$