The neutral kaon decays to $\pi^+$ $\pi^-$ $\pi^0$: a detailed analysis of the CPLEAR data

CPLEAR Collaboration:     A. Angelopoulos - et al.

doi:doi:10.1007/s100520050285

2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 5, 389-409
DOI 10.1007/s100529800974

The neutral kaon decays to $\pi^+$ $\pi^-$ $\pi^0$ :
a detailed analysis of the CPLEAR data

CPLEAR Collaboration
A. Angelopoulos¹ - A. Apostolakis¹ - E. Aslanides¹¹ - G. Backenstoss² - P. Bargassa¹³ - O. Behnke¹⁷ - A. Benelli² - V. Bertin¹¹ - F. Blanc⁷ - P. Bloch⁴ - P. Carlson¹⁵ - M. Carroll⁹ - E. Cawley⁹ - M.B. Chertok³ - M. Danielsson¹⁵ - M. Dejardin¹⁴ - J. Derre¹⁴ - A. Ealet¹¹ - C. Eleftheriadis¹⁶ - L. Faravel⁷ - P. Fassnacht¹¹ - W. Fetscher¹⁷ - M. Fidecaro⁴ - A. Filipcic¹⁰ - D. Francis³ - J. Fry⁹ - E. Gabathuler⁹ - R. Gamet⁹ - H.-J. Gerber¹⁷ - A. Go⁴ - A. Haselden⁹ - P.J. Hayman⁹ - F. Henry-Couannier¹¹ - R.W. Hollander⁶ - K. Jon-And¹⁵ - P.-R. Kettle¹³ - P. Kokkas⁴ - R. Kreuger⁶ - R. Le Gac¹¹ - F. Leimgruber² - I. Mandic¹⁰ - N. Manthos⁸ - G. Marel¹⁴ - M. Mikuz¹⁰ - J. Miller³ - F. Montanet¹¹ - T. Nakada¹³ - B. Pagels¹⁷ - I. Papadopoulos¹⁶ - P. Pavlopoulos² - G. Polivka² - R. Rickenbach² - B.L. Roberts³ - T. Ruf⁴ - M. Schäfer¹⁷ - L.A. Schaller⁷ - T. Schietinger² - A. Schopper⁴ - L. Tauscher² - C. Thibault¹² - F. Touchard¹¹ - C. Touramanis⁹ - C.W.E. Van Eijk⁶ - S. Vlachos² - P. Weber¹⁷ - O. Wigger¹³ - M. Wolter¹⁷ - D. Zavrtanik¹⁰ - D. Zimmerman³

¹ University of Athens, Greece
² University of Basle, Switzerland
³ Boston University, USA
⁴ CERN, Geneva, Switzerland
⁵ LIP and University of Coimbra, Portugal
⁶ Delft University of Technology, Netherlands
⁷ University of Fribourg, Switzerland
⁸ University of Ioannina, Greece
⁹ University of Liverpool, UK
¹⁰ J. Stefan Inst. and Phys. Dep., University of Ljubljana, Slovenia
¹¹ CPPM, IN2P3-CNRS et Université d'Aix-Marseille II, France
¹² CSNSM, IN2P3-CNRS, Orsay, France
¹³ Paul Scherrer Institut (PSI), Switzerland
¹⁴ CEA, DSM/DAPNIA, CE-Saclay, France
¹⁵ Royal Institute of Technology, Stockholm, Sweden
¹⁶ University of Thessaloniki, Greece
¹⁷ ETH-IPP Zürich, Switzerland

Received: 13 March 1998 / Published online: 3 September 1998

Abstract
A detailed analysis of neutral kaons decaying to $\pi^{+}\pi^{-}\pi^{0}$ is presented based on the complete data set containing half a million events. Time-dependent decay rate asymmetries are measured between initially tagged ${\mathrm{{K}\mbox{}^0}}$ and ${\mathrm{\overline{K}\mbox{}^0}}$ and for different regions of the phase space. These asymmetries, resulting from the interference between the CP-conserving decay amplitude of ${\mathrm{K_L}}$ and the decay amplitude of ${\mathrm{K_S}}$ - either CP-violating or CP-conserving - allow the determination of the ${\mathrm{K_S}}$ parameters $\eta_{+-0}$ (CP-violating) and $\lambda$ (CP-conserving), and also of the main isospin components of the ${\mathrm{K_S}}$ decay amplitude. The branching ratio of ${\mathrm{K_S}}\rightarrow \pi^{+}\pi^{-}\pi^{0}$ (CP-conserving) is deduced directly from $\lambda$ . In addition, we extract the slope parameters describing the energy dependence of the ${\mathrm{K_L}} \rightarrow \pi^{+}\pi^{-}\pi^{0}$ Dalitz plot. The whole set of our results fits well within the current phenomenological picture of the neutral-kaon system including CP violation and Chiral Perturbation Theory (ChPT).