Dalitz-plot decomposition for the $e^+ e^- \to J/ψ\, π\, π\, (K \bar{K})$ and $e^+ e^- \to h_c \, π\, π$ processes
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| Format: | Preprint |
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2024
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| author | Ermolina, Viktoriia Danilkin, Igor Vanderhaeghen, Marc |
| author_facet | Ermolina, Viktoriia Danilkin, Igor Vanderhaeghen, Marc |
| contents | We present an analysis of the $e^+ e^- \to γ^* \to J/ψ\, π\, π\, (K \bar{K})$ and $e^+ e^- \to γ^* \to h_c \, π\, π$ processes employing the recently proposed Dalitz-plot decomposition approach, which is based on the helicity formalism for three-body decays. For the above reactions, we validate the factorization of the overall rotation for all decay chains and spin alignments, along with the crossing symmetry between final states, using a Lagrangian-based toy model. For the model-dependent factors that describe the subchannel dynamics, we employ the dispersive treatment of the $π\, π\, (K \bar{K})$ final state interaction, which accurately reproduces pole positions and couplings of the $f_0(500)$ and $f_0(980)$ resonances. The constructed amplitudes serve as an essential framework to further constrain the properties of the charged exotic states $Z_c(3900)$ and $Z_c(4020)$, produced in these reactions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dalitz-plot decomposition for the $e^+ e^- \to J/ψ\, π\, π\, (K \bar{K})$ and $e^+ e^- \to h_c \, π\, π$ processes Ermolina, Viktoriia Danilkin, Igor Vanderhaeghen, Marc High Energy Physics - Phenomenology We present an analysis of the $e^+ e^- \to γ^* \to J/ψ\, π\, π\, (K \bar{K})$ and $e^+ e^- \to γ^* \to h_c \, π\, π$ processes employing the recently proposed Dalitz-plot decomposition approach, which is based on the helicity formalism for three-body decays. For the above reactions, we validate the factorization of the overall rotation for all decay chains and spin alignments, along with the crossing symmetry between final states, using a Lagrangian-based toy model. For the model-dependent factors that describe the subchannel dynamics, we employ the dispersive treatment of the $π\, π\, (K \bar{K})$ final state interaction, which accurately reproduces pole positions and couplings of the $f_0(500)$ and $f_0(980)$ resonances. The constructed amplitudes serve as an essential framework to further constrain the properties of the charged exotic states $Z_c(3900)$ and $Z_c(4020)$, produced in these reactions. |
| title | Dalitz-plot decomposition for the $e^+ e^- \to J/ψ\, π\, π\, (K \bar{K})$ and $e^+ e^- \to h_c \, π\, π$ processes |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.19946 |