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.