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

• Published in: arXiv.org 2017-09
• Main Authors: Harnew, Samuel, Naik, Paras, Prouve, Claire, Rademacker, Jonas, Asner, David
• Format: Article
• Language: English
• Subjects: Amplitudes; Bins; Computer simulation; Decay; Large Hadron Collider; Parameter uncertainty; Phase shift; Superposition (mathematics)
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1709.03467

For the first time, the strong phase difference between \(D^0\) and \(\bar{D}^0\to\pi^+\pi^-\pi^+\pi^-\) amplitudes is determined in bins of the decay phase space. The measurement uses \(818\,\mathrm{pb}^{-1}\) of \(e^+e^-\) collision data that is taken at the \(\psi(3770)\) resonance and collected by the CLEO-c experiment. The measurement is important for the determination of the \(C P\)-violating phase \(\gamma\) in \(B^{\pm}\to D K^{\pm}\) (and similar) decays , where the \(D\) meson (which represents a superposition of \(D^0\) and \(\bar{D}^0\)) subsequently decays to \(\pi^+\pi^-\pi^+\pi^-\). To obtain optimal sensitivity to \(\gamma\), the phase space of the \(D \to \pi^+\pi^-\pi^+\pi^-\) decay is divided into bins based on a recent amplitude model of the decay. Although an amplitude model is used to define the bins, the measurements obtained are model-independent. The \(CP\)-even fraction of the \(D \to \pi^+\pi^-\pi^+\pi^-\) decay is determined to be \(F_{+}^{4\pi} = 0.769 \pm 0.021 \pm 0.010\), where the uncertainties are statistical and systematic, respectively. Using simulated \(B^{\pm}\to D K^{\pm}, D \to \pi^+\pi^-\pi^+\pi^-\) decays, it is estimated that by the end of the current LHC run, the LHCb experiment could determine \(\gamma\) from this decay mode with an uncertainty of \((\pm10\pm7)^\circ\), where the first uncertainty is statistical based on estimated LHCb event yields, and the second is due to the uncertainties on the parameters determined in this paper.