Isospin-breaking in $\varepsilon'/\varepsilon$: Impact of $\eta_0$ at the Dawn of the 2020s
| Autor: | Buras, Andrzej J., Gerard, Jean-Marc |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1140/epjc/s10052-020-8299-6 |
| Popis: | For direct CP-violation in $K\to\pi\pi$ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $\Delta I=1/2$ rule and conventionally encoded in $\Omega_{\rm IB}$ parameters. The updated prediction $\Omega_{\rm IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$ of the Chiral Perturbation Theory for the strong isospin-breaking due to $\pi_3-\eta_8$ mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $\eta_0$ exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $\eta_8-\eta_0$ mixing as a probe for the non-negligible flavour-singlet component of the physical $\eta$ pole to find $\Omega_{\rm IB}^{(9)}=(35\pm7)\times 10^{-2}$ in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $\pi^+-\pi^0$ mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $\epsilon'/\epsilon$ an improved result $\hat\Omega_{\rm eff}^{(9)}=(29\pm7)\times 10^{-2}$ to be compared with $\hat\Omega_{\rm eff}^{(8)}=(17\pm9)\times 10^{-2}$ used in recent analyses of $\epsilon'/\epsilon$. Accordingly, we get a reduction from $(\epsilon'/\epsilon)_{\rm SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$ to $(\epsilon'/\epsilon)_{\rm SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$ and thereby an effective suppression of $(\epsilon'/\epsilon)_{\rm SM}$ by isospin-breaking corrections as large as $40\%$ relative to the recent RBC-UKQCD value. Comment: 18 pages, no figures, typos removed, additional clarifying comments and one reference added, results unchanged. Version to appear in EPJC |
| Databáze: | arXiv |
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