Clarifying the puzzling mass shift of the ψ(4160) via a reanalysis of R-value data with unquenched charmonium spectroscopy
Abstract
The long-standing upward shift of the extracted ψ(4160) mass, from about $4.16$~GeV to $4.19$~GeV in later analyses, remains a puzzling issue in charmonium spectroscopy. In our previous study, this problem was investigated through the B+→ K+μ+μ- process within an unquenched charmonium framework, where the lower-mass ψ(4160) assignment was found to be compatible with the data. Here we revisit the BESII R-value data, which played an important role in the historical extraction of the higher ψ(4160) mass, and provide an independent examination. In contrast to the conventional quenched picture with ψ(4040), ψ(4160), and ψ(4415), the unquenched vector-charmonium spectrum contains six states: ψ(4040), ψ(4160), ψ(4220), ψ(4380), ψ(4415), and ψ(4500). Including these states together with the near-threshold ψ(3770), we find that the BESII R-value line shape can be well reproduced over the full energy range while retaining the lower-mass ψ(4160) assignment. The enhancement around $4.19$~GeV then arises from the coherent interplay among the nearby ψ(4040), ψ(4160), and ψ(4220) amplitudes, rather than requiring an upward shift of the ψ(4160) mass itself. The additional higher states also naturally describe the line-shape structure in the $4.4$~GeV region. We further show that the seven-resonance coherent amplitude contains six complex zeros, yielding 26=64 mathematically equivalent solutions with identical line shapes but substantially different di-electron widths and relative phases. Comparing these solutions with available experimental information and representative unquenched charmonium predictions, we provide a qualitative assessment of their phenomenological consistency and highlight several solutions that appear more compatible with present information.
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BibTeX
@misc{peng2026clarifying,
title = {{Clarifying the puzzling mass shift of the $ψ(4160)$ via a reanalysis of $R$-value data with unquenched charmonium spectroscopy}},
author = {Tian-Cai Peng and Xiang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19673},
eprint = {2609.19673},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19673},
note = {CC0},
}
RIS
TY - UNPB
TI - Clarifying the puzzling mass shift of the ψ(4160) via a reanalysis of R-value data with unquenched charmonium spectroscopy
AU - Tian-Cai Peng
AU - Xiang Liu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19673
UR - https://arxiv.org/abs/2609.19673
AB - The long-standing upward shift of the extracted ψ(4160) mass, from about $4.16$~GeV to $4.19$~GeV in later analyses, remains a puzzling issue in charmonium spectroscopy. In our previous study, this problem was investigated through the B^+→ K^+μ^+μ^- process within an unquenched charmonium framework, where the lower-mass ψ(4160) assignment was found to be compatible with the data. Here we revisit the BESII R-value data, which played an important role in the historical extraction of the higher ψ(4160) mass, and provide an independent examination. In contrast to the conventional quenched picture with ψ(4040), ψ(4160), and ψ(4415), the unquenched vector-charmonium spectrum contains six states: ψ(4040), ψ(4160), ψ(4220), ψ(4380), ψ(4415), and ψ(4500). Including these states together with the near-threshold ψ(3770), we find that the BESII R-value line shape can be well reproduced over the full energy range while retaining the lower-mass ψ(4160) assignment. The enhancement around $4.19$~GeV then arises from the coherent interplay among the nearby ψ(4040), ψ(4160), and ψ(4220) amplitudes, rather than requiring an upward shift of the ψ(4160) mass itself. The additional higher states also naturally describe the line-shape structure in the $4.4$~GeV region. We further show that the seven-resonance coherent amplitude contains six complex zeros, yielding 2^6=64 mathematically equivalent solutions with identical line shapes but substantially different di-electron widths and relative phases. Comparing these solutions with available experimental information and representative unquenched charmonium predictions, we provide a qualitative assessment of their phenomenological consistency and highlight several solutions that appear more compatible with present information.
ER -