Determine the effect of the four-pion threshold on the scattering phase

Determine the effect of the four-pion threshold and the associated two-to-four interaction on the $(K\pi)_{\mathbf{27}}$ scattering phase, particularly through the cusp and derivative discontinuity near the threshold.

Background

The scattering analysis treats the (Kπ)27(K\pi)_{\mathbf{27}} system as an elastic single-channel problem and excludes the four-pion threshold, although the extracted spectrum extends to energies close to or above that threshold. The authors explain that opening the four-pion channel produces a cusp in the scattering phase, whose derivative discontinuity is controlled by the two-to-four interaction strength.

Because the current dataset is expected to be more strongly affected by other uncertainties, the authors do not quantify this threshold effect in the present work. They explicitly defer a careful treatment to future work, leaving unresolved how the threshold modifies the phase-shift determination and its extrapolation toward the D-meson mass.

References

At the same time it should be emphasised that the four-pion threshold is not included in this step. The threshold is known to introduce a cusp in the scattering phase, with the discontinuity in the derivative set by the two-to-four interaction strength. We expect the effect of this to be subdominant to other sources of uncertainty in the present dataset, and leave a careful consideration of its effect to future work.

— $D \to (K π)_{\mathbf{27}}$ at the SU(3)-flavour-symmetric point I: Methodology and strong phase determination  (2608.30737 - Black et al., 31 Aug 2026) in Section 5, Conclusions and outlook