Constrain the non-isospin-zero rescattering parameters

Constrain the rescattering parameters \(|\Omega_{11}^{(0)}|\sin(\phi_{11}-\phi_2)\), \(|\Omega_{12}^{(0)}|\sin(\phi_{12}-\phi_2)\), and \(|\Omega_{21}^{(0)}|\sin(\phi_1-\phi_{21})\) that determine the isospin-2/isospin-0 pion and isospin-1/isospin-0 kaon CP-asymmetry contributions within the charm-meson two-body decay framework.

Background

The paper derives bounds on the pure isospin-zero CP-asymmetry contributions using the determinant of the isospin-zero Muskhelishvili–Omnès matrix, which depends on a comparatively well-determined scattering phase. The remaining CP-asymmetry terms involve interference between isospin-zero and isospin-two pion amplitudes or between isospin-zero and isospin-one kaon amplitudes.

These terms depend on individual elements of the coupled-channel dispersive matrix and on strong-phase differences. Unlike the determinant, those individual quantities are strongly affected by poorly known inelasticity and other scattering inputs. Consequently, the minimal-input approach used in the paper does not determine them, limiting quantitative predictions for the contributions that could account for the observed pion CP asymmetry.

References

The question whether the observed effect can be accommodated in the SM or requires NP has yet to be answered.

— Theoretical Perspectives on Flavour Physics  (2609.29314 - Fleischer, 24 Sep 2026) in Section 1, Setting the Stage

Within the currently discussed approach that only implements a minimal set of dispersive inputs, we cannot constrain those parameters.

— Implications of two-channel rescattering for charm CP violation from precise dispersive data  (2608.21212 - Pich et al., 21 Aug 2026) in Section 4, Unconstrained CP asymmetries