Eur. Phys. J. C (2026) 86: 460
https://doi.org/10.1140/epjc/s10052-026-15663-7

Regular Article - Theoretical Physics

Mass and width of $T_{c\overline{c}}(4020)$ in the developed Bethe–Salpeter theory

¹ Department of Fundamental Courses, Shandong University of Science and Technology, 271019, Taian, China
² Department of Physics, Sichuan University, 610064, Chengdu, China
³ Institute of Theoretical Physics, The Chinese Academy of Sciences, 100080, Beijing, China
⁴ CCAST (World Laboratory), 100080, Beijing, China

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Received: 4 September 2025
Accepted: 2 April 2026
Published online: 3 May 2026

Abstract

In experiments exotic meson resonance $T_{c\overline{c}}(4020)$ lies above the $D_{}^{\ast }{\overline{D}}^{\ast }$ threshold, and in principle one can not explain $T_{c\overline{c}}(4020)$ as a meson-meson bound state because meson-meson bound state must lie below the $D_{}^{\ast }{\overline{D}}^{\ast }$ threshold. In this work, exotic resonance $T_{c\overline{c}}(4020)$ is considered as an unstable meson-meson molecular state $D_{}^{\ast }{\overline{D}}^{\ast }$, and the developed Bethe–Salpeter theory for dealing with unstable state is applied to investigate resonance $T_{c\overline{c}}(4020)$. We calculate the mass and width of unstable meson-meson molecular state $D_{}^{\ast }{\overline{D}}^{\ast }$ in the framework of relativistic quantum field theory and find that this unstable meson-meson molecular state lies above the $D_{}^{\ast }{\overline{D}}^{\ast }$ threshold, which is consistent with experimental values of resonance $T_{c\overline{c}}(4020)$.