Paper
Polarization transfer in $ψ'\toψππ$: a complete spin density matrix analysis framework
Authors
Jiabao Gong, Guanyu Wang, Dongyu Yuan, Libo Liao, Yilun Wang, Jiarong Li, Xiaoshen Kang, Lei Zhang, Jin Zhang, Gang Li
Abstract
A theoretical framework based on the Spin Density Matrix (SDM) formalism is developed to describe polarization transfer in the decay chain $e^+e^- \rightarrow ψ^\prime \rightarrow ψππ$. Explicit relations connecting the SDMs of $ψ^\prime$ and $ψ$ are derived, generalizing Cahn's analysis into a complete SDM treatment. For the dominant $S$-wave $ππ$ emission, the SDM is shown to be perfectly preserved, $ρ_ψ= ρ_{ψ^\prime}$, rendering the $ψ$ an ideal probe of the initial polarization state. Deviations arising from $D$-wave contributions are quantified, and a self-consistency experimental test is proposed that simultaneously validates the framework and constrains partial wave amplitudes. This formalism provides a consistent basis for extracting $ψ$ polarization and for amplitude analyses of subsequent $ψ$ decays in a continuum-background-free environment. The framework extends to other hadronic transitions, including $ψ' \to h_cπ^0$ in charmonium and $Υ(nS) \to Υ(mS)ππ$ in bottomonium, as well as to electroweak processes such as $e^+e^- \to Z^\ast \to ZH$, where the same angular-momentum structure governs polarization transfer -- offering a unified probe of dynamics from charmonium to the Higgs sector.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.09858v1</id>\n <title>Polarization transfer in $ψ'\\toψππ$: a complete spin density matrix analysis framework</title>\n <updated>2026-03-10T16:19:30Z</updated>\n <link href='https://arxiv.org/abs/2603.09858v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.09858v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>A theoretical framework based on the Spin Density Matrix (SDM) formalism is developed to describe polarization transfer in the decay chain $e^+e^- \\rightarrow ψ^\\prime \\rightarrow ψππ$. Explicit relations connecting the SDMs of $ψ^\\prime$ and $ψ$ are derived, generalizing Cahn's analysis into a complete SDM treatment. For the dominant $S$-wave $ππ$ emission, the SDM is shown to be perfectly preserved, $ρ_ψ= ρ_{ψ^\\prime}$, rendering the $ψ$ an ideal probe of the initial polarization state. Deviations arising from $D$-wave contributions are quantified, and a self-consistency experimental test is proposed that simultaneously validates the framework and constrains partial wave amplitudes. This formalism provides a consistent basis for extracting $ψ$ polarization and for amplitude analyses of subsequent $ψ$ decays in a continuum-background-free environment. The framework extends to other hadronic transitions, including $ψ' \\to h_cπ^0$ in charmonium and $Υ(nS) \\to Υ(mS)ππ$ in bottomonium, as well as to electroweak processes such as $e^+e^- \\to Z^\\ast \\to ZH$, where the same angular-momentum structure governs polarization transfer -- offering a unified probe of dynamics from charmonium to the Higgs sector.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='hep-ph'/>\n <category scheme='http://arxiv.org/schemas/atom' term='hep-ex'/>\n <published>2026-03-10T16:19:30Z</published>\n <arxiv:comment>13 pages, 5 figures</arxiv:comment>\n <arxiv:primary_category term='hep-ph'/>\n <author>\n <name>Jiabao Gong</name>\n </author>\n <author>\n <name>Guanyu Wang</name>\n </author>\n <author>\n <name>Dongyu Yuan</name>\n </author>\n <author>\n <name>Libo Liao</name>\n </author>\n <author>\n <name>Yilun Wang</name>\n </author>\n <author>\n <name>Jiarong Li</name>\n </author>\n <author>\n <name>Xiaoshen Kang</name>\n </author>\n <author>\n <name>Lei Zhang</name>\n </author>\n <author>\n <name>Jin Zhang</name>\n </author>\n <author>\n <name>Gang Li</name>\n </author>\n </entry>"
}