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

TL;DR

This paper measures the strong-phase difference between $D^0$ and $ar{D}^0$ decays to four pions using quantum-correlated data, providing crucial inputs for precise $CP$ violation studies in $B$ decays.

Contribution

It introduces a model-independent method to determine the strong-phase difference in $D^0 o ourpi$ decays using BESIII data, improving the precision of $CP$-even fraction measurements.

Findings

Strong-phase difference measured in phase space bins.

Expected $oldsymbol{ ext{uncertainty on }oldsymbol{ extgamma}}$ is about 1.5-2 degrees.

$C extbf{P}$-even fraction $F_+^{4 extpi} = 0.746 \

Abstract

Measurements of the strong-phase difference between $D^0$ and $\bar{D}^0\to\pi^+\pi^-\pi^+\pi^-$ are performed in bins of phase space. The study exploits a sample of quantum-correlated $D\bar{D}$ 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~fb$^{-1}$. Here, $D$ denotes a neutral charm meson in a superposition of flavor eigenstates. The reported results are valuable for measurements of the $C\!P$-violating phase $\gamma$ (also denoted $\phi_3$) in $B^\pm \to DK^\pm$, $D \to \pi^+\pi^-\pi^+\pi^-$ 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 $1.5^\circ$ or $2^\circ$, depending on the binning scheme. The binned strong-phase parameters are combined to give a value of $F_+^{4\pi} = 0.746 \pm 0.010 \pm 0.004$ for the $C\!P$-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.