Mass spectrum and decay widths of charmonium-like mesons: A diabatic approach with complex scaling
Abstract
In this work, we extend our previous diabatic framework for the charmonium-like spectrum below $4.3$ GeV by introducing the complex scaling method. Unlike the previous framework, the present approach explicitly incorporates couplings to the meson-meson continuum, comprehensively accounting for its contributions to the physical states. Consequently, it allows bound and resonant states to be treated on an equal footing, enabling the direct extraction of decay widths from complex energy eigenvalues without introducing any additional free parameters. Using the obtained solutions, we calculate the channel weights and complex root-mean-square radii (rscriptscriptstyleRMS ) to elucidate their internal structures. Specifically, we find that the χc1(3872), ψ(4040), and ψ(4230) states exhibit significant molecular characteristics. Furthermore, we propose the X(3940) as a candidate for a JPC=1++ state and discuss the nature of the χc0(2P) resonance in detail.
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BibTeX
@misc{zhang2026mass,
title = {{Mass spectrum and decay widths of charmonium-like mesons: A diabatic approach with complex scaling}},
author = {Zi-Zhao Zhang and Bo-Chao Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29909},
eprint = {2609.29909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29909},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mass spectrum and decay widths of charmonium-like mesons: A diabatic approach with complex scaling
AU - Zi-Zhao Zhang
AU - Bo-Chao Liu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29909
UR - https://arxiv.org/abs/2609.29909
AB - In this work, we extend our previous diabatic framework for the charmonium-like spectrum below $4.3$ GeV by introducing the complex scaling method. Unlike the previous framework, the present approach explicitly incorporates couplings to the meson-meson continuum, comprehensively accounting for its contributions to the physical states. Consequently, it allows bound and resonant states to be treated on an equal footing, enabling the direct extraction of decay widths from complex energy eigenvalues without introducing any additional free parameters. Using the obtained solutions, we calculate the channel weights and complex root-mean-square radii (r_scriptscriptstyleRMS ) to elucidate their internal structures. Specifically, we find that the χ_c1(3872), ψ(4040), and ψ(4230) states exhibit significant molecular characteristics. Furthermore, we propose the X(3940) as a candidate for a J^PC=1^++ state and discuss the nature of the χ_c0(2P) resonance in detail.
ER -