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Model-independent determination of the strong-phase difference between ${D}^{0}$ and ${\overline{D}}^{0}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays

2024    CERN İşbirliği

Measurements of the strong-phase difference between ${D}^{0}$ and ${\overline{D}}^{0}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ are performed in bins of phase space. The study exploits a sample of quantum-correlated $D\overline{D}$ mesons collected by the BESIII experiment in ${e}^{+}{e}^{-}$ collisions at a center-of-mass energy of 3.773 GeV, corresponding to an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$. Here, $D$ denotes a neutral charm meson in a superposition of flavor eigenstates. The reported results are valuable for measurements of the $CP$-violating phase $\gamma $ (also denoted ${\varphi }_{3}$) in ${B}^{±}\to D{K}^{±}$, $D\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays, and the binning schemes are designed to provide good statistical sensitivity to this parameter. The expected uncertainty on $\gamma $ arising from the precision of the strong-phase measurements, when applied to very large samples of $B$-meson decays, is around 1.5° or 2°, depending on the binning scheme. The binned strong-phase parameters are combined to give a value of ${F}_{+}^{4\pi }=0.746±0.010±0.004$ for the $CP$-even fraction of ${D}^{0}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays, which is around 30% more precise than the previous best measurement of this quantity.