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arXiv · 2506.08576

Measurement of the $\eta$ transition form factor through $\eta' \rightarrow \pi^+\pi^-\eta$ decay

BESIII Collaboration·M. Ablikim·M. N. Achasov·P. Adlarson·X. C. Ai·R. Aliberti·A. Amoroso·Q. An·Y. Bai·O. Bakina·Y. Ban·H. -R. Bao·V. Batozskaya·K. Begzsuren·N. Berger·M. Berlowski·M. Bertani·D. Bettoni·F. Bianchi·E. Bianco·A. Bortone·I. Boyko·R. A. Briere·A. Brueggemann·H. Cai·M. H. Cai·X. Cai·A. Calcaterra·G. F. Cao·N. Cao·S. A. Cetin·X. Y. Chai·J. F. Chang·G. R. Che·Y. Z. Che·G. Chelkov·C. Chen·C. H. Chen·Chao Chen·G. Chen·H. S. Chen·H. Y. Chen·M. L. Chen·S. J. Chen·S. L. Chen·S. M. Chen·T. Chen·X. R. Chen·X. T. Chen·Y. B. Chen·Y. Q. Chen·Z. J. Chen·Z. K. Chen·S. K. Choi·X. Chu·G. Cibinetto·F. Cossio·J. J. Cui·H. L. Dai·J. P. Dai·A. Dbeyssi·R. E. de Boer·D. Dedovich·C. Q. Deng·Z. Y. Deng·A. Denig·I. Denysenko·M. Destefanis·F. De Mori·B. Ding·X. X. Ding·Y. Ding·Y. X. Ding·J. Dong·L. Y. Dong·M. Y. Dong·X. Dong·M. C. Du·S. X. Du·Y. Y. Duan·Z. H. Duan·P. Egorov·G. F. Fan·J. J. Fan·Y. H. Fan·J. Fang·S. S. Fang·W. X. Fang·Y. Q. Fang·R. Farinelli·L. Fava·F. Feldbauer·G. Felici·C. Q. Feng·J. H. Feng·Y. T. Feng·M. Fritsch·C. D. Fu·J. L. Fu·Y. W. Fu
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Abstract

Based on a sample of $(1.0087\pm0.0044)\times10^{10}$ $J/\psi$ events collected at BESIII, the transition form factor of the $\eta$ meson is extracted by analyzing $J/\psi\to\gamma\eta',~\eta'\to\pi^+\pi^-\eta,~\eta\to\gamma l^+l^-$ ($l$=$e$, $\mu$) events. The measured slope of the transition form factor is $\Lambda^{-2}=1.645\pm0.093_{\rm stat.}\pm {0.024_{\rm sys.}}$ (GeV/$c^2$)$^{-2}$ for the di-electron channel and $\Lambda^{-2}=1.645\pm0.343_{\rm stat.}\pm0.017_{\rm sys.}$ (GeV/$c^2$)$^{-2}$ for the di-muon channel. The branching fractions for $\eta\rightarrow\gamma e^+e^-$ and $\eta\rightarrow\gamma\mu^+\mu^-$ are measured to be $\mathcal{B}(\eta\to\gamma e^+e^-)=(6.79\pm0.04_{\rm stat.}\pm0.36_{\rm sys.})\times 10^{-3}$ and $\mathcal{B}(\eta\to\gamma\mu^+\mu^-)=(2.97\pm0.11_{\rm stat.}\pm0.07_{\rm sys.})\times 10^{-4}$. By combining with the results based on the $J/\psi\to\gamma\eta,~\eta\to\gamma e^+e^-$ events from the previous BESIII measurement, we determine $\Lambda^{-2}=1.707\pm0.076_{\rm stat.}\pm0.029_{\rm sys.}$ (GeV/$c^2$)$^{-2}$ and $\mathcal{B}(\eta\to\gamma e^+e^-)=(6.93\pm0.28_{\rm tot.})\times 10^{-3}$. In addition, we search for the dark photon ($A'$) using the combined events. No significant signal is observed, and the upper limits on $\mathcal{B}(\eta\to\gamma A',~A'\to e^+e^-)$ are set at 90\% confidence level for different $A'$ mass hypotheses.

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BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, X. C. Ai, R. Aliberti, A. Amoroso, Q. An, Y. Bai, O. Bakina, Y. Ban, H. -R. Bao, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. Bertani, D. Bettoni, F. Bianchi, E. Bianco, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, M. H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, X. Y. Chai, J. F. Chang, G. R. Che, Y. Z. Che, G. Chelkov, C. Chen, C. H. Chen, Chao Chen, G. Chen, H. S. Chen, H. Y. Chen, M. L. Chen, S. J. Chen, S. L. Chen, S. M. Chen, T. Chen, X. R. Chen, X. T. Chen, Y. B. Chen, Y. Q. Chen, Z. J. Chen, Z. K. Chen, S. K. Choi, X. Chu, G. Cibinetto, F. Cossio, J. J. Cui, H. L. Dai, J. P. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, C. Q. Deng, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, B. Ding, X. X. Ding, Y. Ding, Y. X. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, M. C. Du, S. X. Du, Y. Y. Duan, Z. H. Duan, P. Egorov, G. F. Fan, J. J. Fan, Y. H. Fan, J. Fang, S. S. Fang, W. X. Fang, Y. Q. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, Y. T. Feng, M. Fritsch, C. D. Fu, J. L. Fu, Y. W. Fu. 2025-06-10. Measurement of the $\eta$ transition form factor through $\eta' \rightarrow \pi^+\pi^-\eta$ decay. https://doi.org/10.1103/5k2q-zgyz

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