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Studies of the decays $D^{0} \to K_{S}^{0} K^{-} π^{+}$ and $D^{0} \to K_{S}^{0} K^{+} π^{-}$

J. Insler¹, H. Muramatsu¹, C. S. Park¹, L. J. Pearson¹, E. H. Thorndike¹, S. Ricciardi², C. Thomas^2,3, M. Artuso⁴, S. Blusk⁴ et al. (CLEO Collaboration)

S. Blusk⁴, R. Mountain⁴, T. Skwarnicki⁴, S. Stone⁴, J. C. Wang⁴, L. M. Zhang⁴, G. Bonvicini⁵, D. Cinabro⁵, M. J. Smith⁵, P. Zhou⁵, T. Gershon⁶, P. Naik⁷, J. Rademacker⁷, K. W. Edwards⁸, K. Randrianarivony⁸, R. A. Briere⁹, H. Vogel⁹, P. U. E. Onyisi¹⁰, J. L. Rosner¹⁰, J. P. Alexander¹¹, D. G. Cassel¹¹, S. Das¹¹, R. Ehrlich¹¹, L. Gibbons¹¹, S. W. Gray¹¹, D. L. Hartill¹¹, D. L. Kreinick¹¹, V. E. Kuznetsov¹¹, J. R. Patterson¹¹, D. Peterson¹¹, D. Riley¹¹, A. Ryd¹¹, A. J. Sadoff¹¹, X. Shi¹¹, W. M. Sun¹¹, J. Yelton¹², P. Rubin¹³, N. Lowrey¹⁴, S. Mehrabyan¹⁴, M. Selen¹⁴, J. Wiss¹⁴, J. Libby¹⁵, M. Kornicer¹⁶, R. E. Mitchell¹⁶, D. Besson¹⁷, T. K. Pedlar¹⁸, D. Cronin-Hennessy¹⁹, J. Hietala¹⁹, S. Dobbs²⁰, Z. Metreveli²⁰, K. K. Seth²⁰, A. Tomaradze²⁰, T. Xiao²⁰, D. Johnson³, S. Malde³, L. Martin³, A. Powell³, G. Wilkinson³, D. M. Asner²¹, G. Tatishvili²¹, J. Y. Ge²², D. H. Miller²², I. P. J. Shipsey²², B. Xin²², G. S. Adams²³, J. Napolitano²³, and K. M. Ecklund²⁴ (CLEO Collaboration)

¹University of Rochester, Rochester, New York 14627, USA
²STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
³University of Oxford, Oxford OX1 3RH, United Kingdom
⁴Syracuse University, Syracuse, New York 13244, USA
⁵Wayne State University, Detroit, Michigan 48202, USA
⁶University of Warwick, Coventry CV4 7AL, United Kingdom
⁷University of Bristol, Bristol BS8 1TL, United Kingdom
⁸Carleton University, Ottawa, Ontario, Canada K1S 5B6
⁹Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
¹⁰University of Chicago, Chicago, Illinois 60637, USA
¹¹Cornell University, Ithaca, New York 14853, USA
¹²University of Florida, Gainesville, Florida 32611, USA
¹³George Mason University, Fairfax, Virginia 22030, USA
¹⁴University of Illinois, Urbana-Champaign, Illinois 61801, USA
¹⁵Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
¹⁶Indiana University, Bloomington, Indiana 47405, USA
¹⁷University of Kansas, Lawrence, Kansas 66045, USA
¹⁸Luther College, Decorah, Iowa 52101, USA
¹⁹University of Minnesota, Minneapolis, Minnesota 55455, USA
²⁰Northwestern University, Evanston, Illinois 60208, USA
²¹Pacific Northwest National Laboratory, Richland, Washington 99352, USA
²²Purdue University, West Lafayette, Indiana 47907, USA
²³Rensselaer Polytechnic Institute, Troy, New York 12180, USA
²⁴Rice University, Houston, Texas 77005, USA

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Phys. Rev. D 85, 092016 – Published 29 May, 2012Erratum Phys. Rev. D 94, 099905 (2016)

DOI: https://doi.org/10.1103/PhysRevD.85.092016

Abstract

The first measurements of the coherence factor $R_{K_{S}^{0} K π}$ and the average strong-phase difference $δ_{D}^{K_{S}^{0} K π}$ in $D^{0} \to K_{S}^{0} K^{\mp} π^{\pm}$ decays are reported. These parameters can be used to improve the determination of the unitary triangle angle $γ$ in $B^{-} \to \tilde{D} K^{-}$ decays, where $\tilde{D}$ is either a $D^{0}$ or a ${\bar{D}}^{0}$ meson decaying to the same final state, and also in studies of charm mixing. The measurements of the coherence factor and strong-phase difference are made using quantum-correlated, fully reconstructed $D^{0} {\bar{D}}^{0}$ pairs produced in $e^{+} e^{-}$ collisions at the $ψ (3770)$ resonance. The measured values are $R_{K_{S}^{0} K π} = 0.73 \pm 0.08$ and $δ_{D}^{K_{S}^{0} K π} = (8.3 \pm 15.2) °$ for an unrestricted kinematic region and $R_{K^{*} K} = 1.00 \pm 0.16$ and $δ_{D}^{K^{*} K} = (26.5 \pm 15.8) °$ for a region where the combined $K_{S}^{0} π^{\pm}$ invariant mass is within $100 MeV / c^{2}$ of the $K^{*} (892)^{\pm}$ mass. These results indicate a significant level of coherence in the decay. In addition, isobar models are presented for the two decays, which show the dominance of the $K^{*} (892)^{\pm}$ resonance. The branching ratio $B (D^{0} \to K_{S}^{0} K^{+} π^{-}) / B (D^{0} \to K_{S}^{0} K^{-} π^{+})$ is determined to be $0.592 \pm 0.044 (stat) \pm 0.018 (syst)$ , which is more precise than previous measurements.