https://doi.org/10.1140/epjc/s10052-020-8299-6
Regular Article - Theoretical Physics
Isospin-breaking in 
: impact of 
at the dawn of the 2020s
1
TUM Institute for Advanced Study, Lichtenbergstr. 2a, 85748, Garching, Germany
2
Physik Department, TU München, James-Franck-Straße, 85748, Garching, Germany
3
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium
* e-mail: andrzej.buras@tum.de
Received:
27
May
2020
Accepted:
29
July
2020
Published online:
5
August
2020
For direct CP-violation in 
decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the 
rule and conventionally encoded in 
parameters. The updated prediction 
of the Chiral Perturbation Theory for the strong isospin-breaking due to 
mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet exchange contribution in this truncated octet scheme. We rather exploit the phenomenological 
mixing as a probe for the non-negligible flavour-singlet component of the physical 
pole to find 
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 
mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio an improved result 
to be compared with 
used in recent analyses of . Accordingly, we get a reduction from 
to 
and thereby an effective suppression of 
by isospin-breaking corrections as large as 
relative to the recent RBC-UKQCD value.
© The Author(s), 2020
