# Quantum-correlated measurements of $D^{0} \to K^{0}_{\rm S}\pi^{+}\pi^{-}\pi^{0}$ and consequences for the determination of $\gamma$

## TL;DR

This study measures quantum correlations in a specific D meson decay to improve the precision of the CKM angle gamma determination, providing new data on decay fractions and phase differences relevant for CP violation studies.

## Contribution

It presents the first measurement of the CP-even fraction and strong-phase differences in the decay D0 to K0_S pi+ pi- pi0, aiding gamma angle extraction.

## Key findings

- Measured F+ as 0.246 ± 0.018
- Binned strong-phase differences across phase space
- Potential impact on gamma determination from B decays

## Abstract

Quantum-correlated measurements of the decay $D^{0} \to K^{0}_{\rm S}\pi^{+}\pi^{-}\pi^{0}$ are performed using a data sample corresponding to an integrated luminosity of 818 pb$^{-1}$ collected at the $\psi(3770)$ resonance by the CLEO-c detector. Preliminary results are presented for the $CP$-even fraction $F_{+}$ and the strong-phase differences of this decay. The value of $F_{+}$ is measured to be 0.246 $\pm$ 0.018. The strong-phase differences are measured in different regions of $K^{0}_{\rm S}\pi^{+}\pi^{-}\pi^{0}$ phase space by binning around the intermediate resonances present. The potential sensitivity of the results for determining the CKM angle $\gamma$ from $B^{\pm}~\to~D(K^{0}_{\mathrm S}\pi^{+}\pi^{-}\pi^{0})K^{\pm}$ decay using the data collected by the Belle detector is also shown.