⚛️ high-energy experiments

Evidence for $\eta_{c}(2S)\to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$ and observation of $\chi_{cJ} \to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$

Using a large sample of $\psi(3686)$ events collected by the BESIII detector, this study reports evidence for the decay $\eta_{c}(2S)\to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$ and provides the first observation of $\chi_{cJ} \to p\bar{p}\pi^{+}\pi^{-}\pi^{0}$ decays with significantly improved precision measurements of their branching fractions and those of the intermediate $\chi_{cJ}\to p\bar{p}\omega$ processes.

Original authors: BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. Barbagiovanni, V. BatozskayaBESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. Barbagiovanni, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, D. Cabiati, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, W. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. K. Chen, J. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, E. Di Fiore, X. X. Ding, Y. Ding, Y. X. Ding, Yi. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, Z. J. Dong, M. C. Du, S. X. Du, Shaoxu Du, X. L. Du, Y. Q. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, Y. H. Fan, J. Fang, Jin Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, L. Feng, Q. X. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu, H. Gao, Xu Gao, Y. Gao, Y. N. Gao, Y. Y. Gao, Yunong Gao, Z. Gao, S. Garbolino, I. Garzia, L. Ge, P. T. Ge, Z. W. Ge, C. Geng, E. M. Gersabeck, A. Gilman, K. Goetzen, J. Gollub, J. B. Gong, J. D. Gong, L. Gong, W. X. Gong, W. Gradl, S. Gramigna, M. Greco, M. D. Gu, M. H. Gu, C. Y. Guan, A. Q. Guo, H. Guo, J. N. Guo, L. B. Guo, M. J. Guo, R. P. Guo, X. Guo, Y. P. Guo, Z. Guo, A. Guskov, J. Gutierrez, J. Y. Han, T. T. Han, X. Han, F. Hanisch, K. D. Hao, X. Q. Hao, F. A. Harris, C. Z. He, K. K. He, K. L. He, F. H. Heinsius, C. H. Heinz, Y. K. Heng, C. Herold, P. C. Hong, G. Y. Hou, X. T. Hou, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, Q. P. Hu, S. L. Hu, T. Hu, Y. Hu, Y. X. Hu, Z. M. Hu, G. S. Huang, K. X. Huang, L. Q. Huang, P. Huang, X. T. Huang, Y. P. Huang, Y. S. Huang, T. Hussain, N. Hüsken, N. in der Wiesche, J. Jackson, Q. Ji, Q. P. Ji, W. Ji, X. B. Ji, X. L. Ji, Y. Y. Ji, L. K. Jia, X. Q. Jia, D. Jiang, H. B. Jiang, S. J. Jiang, X. S. Jiang, Y. Jiang, J. B. Jiao, J. K. Jiao, Z. Jiao, L. C. L. Jin, S. Jin, Y. Jin, M. Q. Jing, X. M. Jing, T. Johansson, S. Kabana, X. L. Kang, X. S. Kang, B. C. Ke, V. Khachatryan, A. Khoukaz, O. B. Kolcu, B. Kopf, L. Kröger, L. Krümmel, Y. Y. Kuang, M. Kuessner, X. Kui, N. Kumar, A. Kupsc, W. Kühn, Q. Lan, W. N. Lan, T. T. Lei, M. Lellmann, T. Lenz, C. Li, C. H. Li, C. K. Li, Chunkai Li, Cong Li, D. M. Li, F. Li, G. Li, H. B. Li, H. J. Li, H. L. Li, H. N. Li, H. P. Li, Hui Li, J. N. Li, J. S. 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Uman, E. van der Smagt, B. Wang, Bin Wang, Bo Wang, C. Wang, Chao Wang, Cong Wang, D. Y. Wang, F. K. Wang, H. J. Wang, H. R. Wang, J. Wang, J. J. Wang, J. P. Wang, K. Wang, L. L. Wang, L. W. Wang, M. Wang, Mi Wang, N. Y. Wang, P. Wang, S. Wang, Shun Wang, T. Wang, W. Wang, W. P. Wang, X. F. Wang, X. L. Wang, X. N. Wang, Xin Wang, Y. Wang, Y. D. Wang, Y. F. Wang, Y. H. Wang, Y. J. Wang, Y. L. Wang, Y. N. Wang, Yanning Wang, Yaqian Wang, Yi Wang, Yuan Wang, Z. Wang, Z. L. Wang, Z. Q. Wang, Z. Y. Wang, Zhi Wang, Ziyi Wang, D. Wei, D. H. Wei, D. J. Wei, H. R. Wei, F. Weidner, H. R. Wen, S. P. Wen, U. Wiedner, G. Wilkinson, M. Wolke, J. F. Wu, L. H. Wu, L. J. Wu, Lianjie Wu, S. G. Wu, S. M. Wu, X. W. Wu, Z. Wu, H. L. Xia, L. Xia, B. H. Xiang, D. Xiao, G. Y. Xiao, H. Xiao, Y. L. Xiao, Z. J. Xiao, C. Xie, K. J. Xie, Y. Xie, Y. G. Xie, Y. H. Xie, Z. P. Xie, T. Y. Xing, D. B. Xiong, G. F. Xu, H. Y. Xu, Q. J. Xu, Q. N. Xu, T. D. Xu, X. P. Xu, Y. Xu, Y. C. Xu, Z. S. Xu, F. Yan, L. Yan, W. B. 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Published 2026-08-24

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Original authors: BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, C. S. Akondi, R. Aliberti, A. Amoroso, Q. An, Y. H. An, Y. Bai, O. Bakina, H. R. Bao, X. L. Bao, M. Barbagiovanni, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. B. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, D. Cabiati, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, T. T. Chang, G. R. Che, Y. Z. Che, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, W. Chen, X. R. Chen, X. T. Chen, X. Y. Chen, Y. B. Chen, Y. Q. Chen, Z. K. Chen, J. Cheng, L. N. Cheng, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. Cottee-Meldrum, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denisenko, M. Destefanis, F. De Mori, E. Di Fiore, X. X. Ding, Y. Ding, Y. X. Ding, Yi. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, Z. J. Dong, M. C. Du, S. X. Du, Shaoxu Du, X. L. Du, Y. Q. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, Y. H. Fan, J. Fang, Jin Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, L. Feng, Q. X. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu, H. Gao, Xu Gao, Y. Gao, Y. N. Gao, Y. Y. Gao, Yunong Gao, Z. Gao, S. Garbolino, I. Garzia, L. Ge, P. T. Ge, Z. W. Ge, C. Geng, E. M. Gersabeck, A. Gilman, K. Goetzen, J. Gollub, J. B. Gong, J. D. Gong, L. Gong, W. X. Gong, W. Gradl, S. Gramigna, M. Greco, M. D. Gu, M. H. Gu, C. Y. Guan, A. Q. Guo, H. Guo, J. N. Guo, L. B. Guo, M. J. Guo, R. P. Guo, X. Guo, Y. P. Guo, Z. Guo, A. Guskov, J. Gutierrez, J. Y. Han, T. T. Han, X. Han, F. Hanisch, K. D. Hao, X. Q. Hao, F. A. Harris, C. Z. He, K. K. He, K. L. He, F. H. Heinsius, C. H. Heinz, Y. K. Heng, C. Herold, P. C. Hong, G. Y. Hou, X. T. Hou, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, Q. P. Hu, S. 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Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the heart of matter, protons and neutrons are not solid, indivisible spheres but are instead built from smaller, more fundamental particles called quarks. These quarks are bound together by a powerful force known as the strong interaction, which acts like an invisible glue holding the atomic nucleus together. Physicists study this force by creating short-lived, heavy particles called charmonia, which are made of a charm quark and its antimatter twin, an anti-charm quark. These particles are like tiny, fleeting laboratories where scientists can test the rules of quantum chromodynamics, the theory that describes how the strong force works. While some of these particles are well understood, others remain mysterious, particularly those in a state called a "spin-singlet," where the internal spins of the quarks cancel each other out. Understanding how these specific particles decay into other forms of matter is crucial for checking if our current theories of the universe are complete or if there are hidden rules we have yet to discover.

A team of researchers using the BESIII detector at the BEPCII collider in Beijing has recently peered into one of these mysterious decays. They analyzed a massive collection of data containing over two billion events of a specific particle called the $\psi(3686)$ , which is a type of charmonium. When this particle decays, it often emits a flash of light, or a photon, and transforms into a lighter charmonium particle. The scientists were looking for a specific outcome: the transformation of the $\psi(3686)$ into a photon and a particle called the $\eta_c(2S)$ , which then immediately breaks apart into a proton, an antiproton, and three pions (two charged and one neutral). This final group of particles is complex, and finding the $\eta_c(2S)$ hiding within it is like spotting a specific, rare flower in a dense, chaotic garden.

After sifting through the data with rigorous statistical methods, the team found evidence that this rare decay does indeed happen. They observed a signal for the $\eta_c(2S)$ decaying into a proton, an antiproton, and three pions with a level of certainty that scientists call 3.3 sigma. In the world of particle physics, this is a strong hint that the event is real, though it falls just short of the highest standard of proof required to claim a definitive discovery. The researchers calculated that the probability of this specific chain of events occurring is roughly 3.4 in one billion. This measurement provides the first direct look at how the $\eta_c(2S)$ breaks down into these specific particles, offering a new piece of the puzzle for understanding the behavior of these elusive spin-singlet states.

In the same study, the team also examined the decays of three related particles known as the $\chi_{cJ}$ family. Unlike the $\eta_c(2S)$ , these particles had been seen before, but the researchers were able to measure their decay rates into the same group of particles with much greater precision than ever before. They found that the $\chi_{c0}$ particle decays into a proton, an antiproton, and three pions about 4.79 times out of every thousand decays. The $\chi_{c1}$ does so about 2.13 times out of a thousand, and the $\chi_{c2}$ about 3.72 times out of a thousand. These numbers are significantly more accurate than previous estimates, reducing the margin of error by about 30 to 50 percent. This improved precision helps physicists refine their models of how these particles interact and decay.

Furthermore, the team looked at an intermediate step in these decays, where the particles briefly form a short-lived particle called an omega meson before breaking apart further. They measured the rates at which the $\chi_{cJ}$ particles decay into a proton, an antiproton, and this omega meson. The results showed that the $\chi_{c0}$ produces this combination about 5.76 times out of every ten thousand decays, the $\chi_{c1}$ about 1.85 times, and the $\chi_{c2}$ about 4.51 times. These measurements align closely with what was previously known but with a much tighter range of uncertainty. By confirming these rates and finding the first evidence for the $\eta_c(2S)$ decay, the study enriches the experimental knowledge of how charmonium particles behave below the energy threshold where they can break apart into open charm particles. This work helps to test the theoretical predictions that govern the strong force and brings scientists one step closer to a coherent understanding of the subatomic world.

Technical Summary: Evidence for $\eta_c(2S) \to p\bar{p}\pi^+\pi^-\pi^0$ and Observation of $\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$

Problem and Motivation
The properties of charmonium states below the open-charm threshold, particularly the spin-singlet $\eta_c(2S)$ and the spin-triplet $\chi_{cJ}$ ( $J=0,1,2$ ) states, remain incompletely understood. While the $\psi(3686)$ (the first radial excitation of $J/\psi$ ) is well-measured, the $\eta_c(2S)$ suffers from poorly determined properties, with measured partial widths accounting for less than 10% of its total width. Investigating new decay modes of $\eta_c(2S)$ is crucial for testing Quantum Chromodynamics (QCD) predictions, specifically the "12% rule" regarding the ratio of decay widths between spin-singlet and spin-triplet charmonia. Furthermore, precise measurements of hadronic decays such as $\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$ and $\chi_{cJ} \to p\bar{p}\omega$ are necessary inputs for calculating charmonium production cross sections in $p\bar{p}$ collisions. Prior to this work, the non-resonant process $\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$ had not been measured.

Methodology
The analysis utilizes a data sample of $(2.712 \pm 0.014) \times 10^9$ $\psi(3686)$ events collected by the BESIII detector at the BEPCII collider. The study focuses on the radiative transition $\psi(3686) \to \gamma \eta_c(2S)/\chi_{cJ}$ , followed by the hadronic decays $\eta_c(2S)/\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$ and $\pi^0 \to \gamma\gamma$ .

Event Selection: Events are selected requiring exactly four charged tracks (identified as protons/antiprotons and pions) and at least three photon candidates. Kinematic fits are applied: a 1-constraint fit for $\pi^0$ reconstruction, a 4-constraint (4C) fit constraining the final state to the $\psi(3686)$ four-momentum, and a 3-constraint (3C) fit where the radiative photon energy is unconstrained to suppress backgrounds from final-state radiation (FSR) and fake photons.
Background Suppression: Dominant backgrounds from $\psi(3686) \to \pi^+\pi^- J/\psi$ and $\pi^0\pi^0 J/\psi$ are rejected using recoil mass and invariant mass vetoes. Hyperon-related backgrounds ( $\Lambda, \Sigma$ ) are suppressed by vetting specific invariant mass combinations. Continuum backgrounds are estimated using a dataset collected at $\sqrt{s} = 3.650$ GeV.
Signal Extraction: Signal yields are extracted via an unbinned maximum likelihood fit to the $p\bar{p}\pi^+\pi^-\pi^0$ invariant mass spectrum ( $M_{3C}$ ). The signal lineshape is modeled by a Breit-Wigner function convolved with a Gaussian resolution, modified by an $E_\gamma^3$ term and a damping factor. For the intermediate $\chi_{cJ} \to p\bar{p}\omega$ process, a two-dimensional (2D) unbinned likelihood fit is performed on the distributions of $M(p\bar{p}\pi^+\pi^-\pi^0)$ versus $M(\pi^+\pi^-\pi^0)$ .
Systematic Uncertainties: Sources include tracking efficiency, particle identification (PID), photon reconstruction, kinematic fit corrections, background veto variations, mass/width parameters, efficiency curve parametrization, and normalization factors. Data-MC discrepancies in momentum distributions are addressed via reweighting for $\chi_{cJ}$ decays, while a conservative estimate is applied for $\eta_c(2S)$ using $\chi_{cJ}$ as a control sample.

Key Contributions and Results

Evidence for $\eta_c(2S) \to p\bar{p}\pi^+\pi^-\pi^0$ : The paper reports the first evidence for this decay mode with a signal significance of $3.3\sigma$ (statistical significance from the fit is $4.1\sigma$ , reduced to $3.3\sigma$ after systematic variations). The product of branching fractions is determined to be:
$B[\psi(3686) \to \gamma \eta_c(2S)] \times B[\eta_c(2S) \to p\bar{p}\pi^+\pi^-\pi^0] = (3.4 \pm 0.5 \pm 0.8) \times 10^{-6}$
where the first uncertainty is statistical and the second is systematic.
Observation of $\chi_{cJ} \to p\bar{p}\pi^+\pi^-\pi^0$ : The hadronic decays for all three $\chi_{cJ}$ states are observed and their branching fractions are measured for the first time:
- $B(\chi_{c0} \to p\bar{p}\pi^+\pi^-\pi^0) = (4.79 \pm 0.01 \pm 0.40) \times 10^{-3}$
- $B(\chi_{c1} \to p\bar{p}\pi^+\pi^-\pi^0) = (2.13 \pm 0.01 \pm 0.17) \times 10^{-3}$
- $B(\chi_{c2} \to p\bar{p}\pi^+\pi^-\pi^0) = (3.72 \pm 0.01 \pm 0.29) \times 10^{-3}$
Improved Measurements of $\chi_{cJ} \to p\bar{p}\omega$ : The branching fractions for the intermediate process $\chi_{cJ} \to p\bar{p}\omega$ (with $\omega \to \pi^+\pi^-\pi^0$ ) are updated with significantly improved precision (30%–50% improvement over world averages):
- $B(\chi_{c0} \to p\bar{p}\omega) = (5.76 \pm 0.01 \pm 0.42) \times 10^{-4}$
- $B(\chi_{c1} \to p\bar{p}\omega) = (1.85 \pm 0.01 \pm 0.13) \times 10^{-4}$
- $B(\chi_{c2} \to p\bar{p}\omega) = (4.51 \pm 0.01 \pm 0.33) \times 10^{-4}$
  The results for $\chi_{c0}$ and $\chi_{c1}$ are consistent with world averages within one standard deviation, while $\chi_{c2}$ agrees within two standard deviations.

Significance
The authors state that these measurements enrich the experimental knowledge of $\eta_c(2S)$ and $\chi_{cJ}$ hadronic decays. Specifically, the observation of $\eta_c(2S) \to p\bar{p}\pi^+\pi^-\pi^0$ provides direct insight into its decay mechanisms, contributing to a more coherent understanding of the charmonium spectrum below the open-charm threshold. Additionally, these results offer valuable experimental data to test theoretical predictions regarding the "12% rule" for $\eta_c(1S)$ and $\eta_c(2S)$ decays. The updated branching fractions for $\chi_{cJ}$ decays serve as key inputs for calculating charmonium production cross sections in $p\bar{p}$ experiments.

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