Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s
Abstract For direct CP-violation in $$K\rightarrow \pi \pi $$ K→ππ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $$\Delta I=1/2$$ ΔI=1/2 rule and conventionally encoded in $$\Omega _\mathrm{IB}$$ ΩIB parameters. The updated prediction $$\Ome...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-020-8299-6 |
| _version_ | 1818281851472576512 |
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| author | Andrzej J. Buras Jean-Marc Gérard |
| author_facet | Andrzej J. Buras Jean-Marc Gérard |
| author_sort | Andrzej J. Buras |
| collection | DOAJ |
| description | Abstract For direct CP-violation in $$K\rightarrow \pi \pi $$ K→ππ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $$\Delta I=1/2$$ ΔI=1/2 rule and conventionally encoded in $$\Omega _\mathrm{IB}$$ ΩIB parameters. The updated prediction $$\Omega _\mathrm{IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$$ ΩIB(8)=(15.9±8.2)×10-2 of the Chiral Perturbation Theory for the strong isospin-breaking due to $$\pi _3-\eta _8$$ π3-η8 mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $$\eta _0$$ η0 exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $$\eta _8-\eta _0$$ η8-η0 mixing as a probe for the non-negligible flavour-singlet component of the physical $$\eta $$ η pole to find $$\Omega _\mathrm{IB}^{(9)}=(35\pm 7)\times 10^{-2}$$ ΩIB(9)=(35±7)×10-2 in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $$\pi ^+-\pi ^0$$ π+-π0 mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $$\varepsilon '/\varepsilon $$ ε′/ε an improved result $$\hat{\Omega }_\mathrm{eff}^{(9)}=(29\pm 7)\times 10^{-2}$$ Ω^eff(9)=(29±7)×10-2 to be compared with $$\hat{\Omega }_\mathrm{eff}^{(8)}=(17\pm 9)\times 10^{-2}$$ Ω^eff(8)=(17±9)×10-2 used in recent analyses of $$\varepsilon '/\varepsilon $$ ε′/ε . Accordingly, we get a reduction from $$(\varepsilon '/\varepsilon )_\text {SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$$ (ε′/ε)SM(8)=(17.4±6.1)×10-4 to $$(\varepsilon '/\varepsilon )_\text {SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$$ (ε′/ε)SM(9)=(13.9±5.2)×10-4 and thereby an effective suppression of $$(\varepsilon '/\varepsilon )_\text {SM}$$ (ε′/ε)SM by isospin-breaking corrections as large as $$40\%$$ 40% relative to the recent RBC-UKQCD value. |
| first_indexed | 2024-12-13T00:11:41Z |
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| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-13T00:11:41Z |
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| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-c2bb723a87074c739e6e4874013a606d2022-12-22T00:05:56ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-08-0180811010.1140/epjc/s10052-020-8299-6Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020sAndrzej J. Buras0Jean-Marc Gérard1TUM Institute for Advanced StudyCentre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de LouvainAbstract For direct CP-violation in $$K\rightarrow \pi \pi $$ K→ππ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $$\Delta I=1/2$$ ΔI=1/2 rule and conventionally encoded in $$\Omega _\mathrm{IB}$$ ΩIB parameters. The updated prediction $$\Omega _\mathrm{IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$$ ΩIB(8)=(15.9±8.2)×10-2 of the Chiral Perturbation Theory for the strong isospin-breaking due to $$\pi _3-\eta _8$$ π3-η8 mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $$\eta _0$$ η0 exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $$\eta _8-\eta _0$$ η8-η0 mixing as a probe for the non-negligible flavour-singlet component of the physical $$\eta $$ η pole to find $$\Omega _\mathrm{IB}^{(9)}=(35\pm 7)\times 10^{-2}$$ ΩIB(9)=(35±7)×10-2 in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $$\pi ^+-\pi ^0$$ π+-π0 mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $$\varepsilon '/\varepsilon $$ ε′/ε an improved result $$\hat{\Omega }_\mathrm{eff}^{(9)}=(29\pm 7)\times 10^{-2}$$ Ω^eff(9)=(29±7)×10-2 to be compared with $$\hat{\Omega }_\mathrm{eff}^{(8)}=(17\pm 9)\times 10^{-2}$$ Ω^eff(8)=(17±9)×10-2 used in recent analyses of $$\varepsilon '/\varepsilon $$ ε′/ε . Accordingly, we get a reduction from $$(\varepsilon '/\varepsilon )_\text {SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$$ (ε′/ε)SM(8)=(17.4±6.1)×10-4 to $$(\varepsilon '/\varepsilon )_\text {SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$$ (ε′/ε)SM(9)=(13.9±5.2)×10-4 and thereby an effective suppression of $$(\varepsilon '/\varepsilon )_\text {SM}$$ (ε′/ε)SM by isospin-breaking corrections as large as $$40\%$$ 40% relative to the recent RBC-UKQCD value.http://link.springer.com/article/10.1140/epjc/s10052-020-8299-6 |
| spellingShingle | Andrzej J. Buras Jean-Marc Gérard Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s European Physical Journal C: Particles and Fields |
| title | Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s |
| title_full | Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s |
| title_fullStr | Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s |
| title_full_unstemmed | Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s |
| title_short | Isospin-breaking in $$\varepsilon '/\varepsilon $$ ε′/ε : impact of $$\eta _0$$ η0 at the dawn of the 2020s |
| title_sort | isospin breaking in varepsilon varepsilon ε ε impact of eta 0 η0 at the dawn of the 2020s |
| url | http://link.springer.com/article/10.1140/epjc/s10052-020-8299-6 |
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