Patterns of $C$- and $CP$-violation in hadronic $\eta$ and $\eta'$ three-body decays
| Autor: | Akdag, Hakan, Isken, Tobias, Kubis, Bastian |
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| Rok vydání: | 2021 |
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| Zdroj: | JHEP 02 (2022) 137; JHEP 12 (2022) 156 (erratum) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP02(2022)137 |
| Popis: | We construct hadronic amplitudes for the three-body decays $\eta^{(\prime)}\to\pi^+\pi^-\pi^0$ and $\eta'\to\eta\pi^+\pi^-$ in a non-perturbative fashion, allowing for $C$- and $CP$-violating asymmetries in the $\pi^+\pi^-$ distributions. These amplitudes are consistent with the constraints of analyticity and unitarity. We find that the currently most accurate Dalitz-plot distributions taken by the KLOE-2 and BESIII collaborations confine the patterns of these asymmetries to a relative per mille level. Our dispersive representation allows us to extract the individual coupling strengths of the $C$- and $CP$-violating contributions arising from effective isoscalar and isotensor operators in $\eta^{(\prime)}\to\pi^+\pi^-\pi^0$ and an effective isovector operator in $\eta'\to\eta\pi^+\pi^-$, while the strongly different sensitivities to these operators can be understood from chiral power counting arguments. Comment: 43 pages, 9 figures, 5 tables; v2: discussion extended, version published in JHEP; v3: incorporates an erratum that fixes the phases of the C-violating norms by hermiticity and time reversal |
| Databáze: | arXiv |
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