Physics Letters B 630 (2005) 31–39 www.elsevier.com/locate/physletb A measurement of the CP-conserving component of the decay 0 → + − 0 KS π π π J.R. Batley, C. Lazzeroni, D.J. Munday, M. Patel 1, M.W. Slater, S.A. Wotton Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK 2 R. Arcidiacono, G. Bocquet, A. Ceccucci, D. Cundy 3, N. Doble, V. Falaleev, L. Gatignon, A. Gonidec, P. Grafström, W. Kubischta, F. Marchetto 4, I. Mikulec 5, A. Norton, B. Panzer-Steindel, P. Rubin 6,H.Wahl7 CERN, CH-1211 Genève 23, Switzerland E. Goudzovski, D. Gurev, P. Hristov 1, V. Kekelidze, L. Litov, D. Madigozhin, N. Molokanova, Yu. Potrebenikov, S. Stoynev, A. Zinchenko Joint Institute for Nuclear Research, Dubna, Russia E. Monnier 8, E. Swallow, R. Winston The Enrico Fermi Institute, The University of Chicago, Chicago, IL 60126, USA R. Sacco 9,A.Walker Department of Physics and Astronomy, University of Edinburgh JCMB King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK W. Baldini, P. Dalpiaz, P.L. Frabetti, A. Gianoli, M. Martini, F. Petrucci, M. Scarpa, M. Savrié Dipartimento di Fisica dell’Università e Sezione dell’INFN di Ferrara, I-44100 Ferrara, Italy A. Bizzeti 10, M. Calvetti, G. Collazuol 11, G. Graziani, E. Iacopini, M. Lenti, F. Martelli 12, G. Ruggiero 1, M. Veltri 12 Dipartimento di Fisica dell’Università e Sezione dell’INFN di Firenze, I-50125 Firenze, Italy 0370-2693 2005 Elsevier B.V. Open access under CC BY license. doi:10.1016/j.physletb.2005.09.077 32 J.R. Batley et al. / Physics Letters B 630 (2005) 31–39 M. Behler, K. Eppard, M. Eppard 1, A. Hirstius 1, K. Kleinknecht, U. Koch, L. Masetti, P. Marouelli, U. Moosbrugger, C. Morales Morales, A. Peters 1, M. Wache, R. Wanke, A. Winhart Institut für Physik, Universität Mainz, D-55099 Mainz, Germany 13 A. Dabrowski, T. Fonseca Martin, M. Velasco Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208-3112, USA G. Anzivino, P. Cenci, E. Imbergamo, G. Lamanna, P. Lubrano, A. Michetti, A. Nappi, M. Pepe, M.C. Petrucci, M. Piccini, M. Valdata Dipartimento di Fisica dell’Università e Sezione dell’INFN di Perugia, I-06100 Perugia, Italy C. Cerri, F. Costantini, R. Fantechi, L. Fiorini, S. Giudici, I. Mannelli, G. Pierazzini, M. Sozzi Dipartimento di Fisica, Scuola Normale Superiore e Sezione dell’INFN di Pisa, I-56100 Pisa, Italy C. Cheshkov 1, J.B. Cheze, M. De Beer, P. Debu, G. Gouge, G. Marel, E. Mazzucato, B. Peyaud, B. Vallage DSM/DAPNIA, CEA Saclay, F-91191 Gif-sur-Yvette, France M. Holder, A. Maier, M. Ziolkowski Fachbereich Physik, Universität Siegen, D-57068 Siegen, Germany 14 C. Biino, N. Cartiglia, M. Clemencic, S. Goy Lopez, E. Menichetti, N. Pastrone Dipartimento di Fisica Sperimentale dell’Università e Sezione dell’INFN di Torino, I-10125 Torino, Italy W. Wislicki Soltan Institute for Nuclear Studies, Laboratory for High Energy Physics, PL-00-681 Warsaw, Poland 15 H. Dibon, M. Jeitler ∗, M. Markytan, G. Neuhofer, L. Widhalm Österreichische Akademie der Wissenschaften, Institut für Hochenergiephysik, A-1050 Wien, Austria 16 Received 13 July 2005; accepted 26 September 2005 Available online 11 October 2005 Editor: W.-D. Schlatter J.R. Batley et al. / Physics Letters B 630 (2005) 31–39 33 Abstract 0 → + − 0 The NA48 Collaboration has measured the amplitude of the CP-conserving component of the decay KS π π π relative 0 → + − 0 = ± =− ± to KL π π π . For the characteristic parameter λ,thevaluesReλ 0.038 0.010 and Im λ 0.013 0.007 have been extracted. These values agree with earlier measurements and with theoretical predictions from chiral perturbation theory. 2005 Elsevier B.V. Open access under CC BY license. 1. Introduction ing transition to the l = 1 state through its interference 0 → + − 0 with the dominant KL π π π decay. We neglect 0 → + − 0 The KS π π π decay amplitude is dominated any effects from CP violation in mixing and decay, by two angular momentum components, l = 0 and which are totally negligible at our level of sensitivity. l = 1(l is the angular momentum of the neutral pion The amplitudes for the decays of neutral kaons into 3π 0 3π 0 with respect to the system of the two charged pions); three pions (AL for KL and AS for KS ) can be pa- higher angular momentum states are suppressed be- rameterized in terms of the Dalitz variables X and Y , cause the kaon mass is close to the three pion mass. which are defined as In this analysis we have measured the CP conserv- s − − s + s 0 − s X = π π ,Y= π 0 (1) * 2 2 Corresponding author. mπ± mπ± E-mail address: [email protected] (M. Jeitler). 1 Present address: CERN, CH-1211 Genève 23, Switzerland. 2 1 with s = (p − p ) , s = (s + + s − + s 0 ) and 2 Funded by the UK Particle Physics and Astronomy Research π K π 0 3 π π π Council. pK and pπ being the 4-momenta of the kaon and the 3 Present address: Istituto di Cosmogeofisica del CNR di Torino, pion, respectively. The Dalitz variable X is a measure I-10133 Torino, Italy. of the difference of the energies of the two charged 4 On leave from Sezione dell’INFN di Torino, I-10125 Torino, pions in the kaon’s rest system while Y is a measure of Italy. 5 the energy of the neutral pion in the kaon’s rest system. On leave from Österreichische Akademie der Wissenschaften, The l = 1 and the l = 0 components of the decay Institut für Hochenergiephysik, A-1050 Wien, Austria. 0 → + − 0 6 On leave from University of Richmond, Richmond, VA 23173, KS π π π can be separated by the fact that the USA; supported in part by the US NSF under award #0140230. amplitude of the l = 1 process is antisymmetric in X 7 Also at Dipartimento di Fisica dell’Università e Sezione while the l = 0 process is symmetric in X. Therefore dell’INFN di Ferrara, I-44100 Ferrara, Italy. the l = 1 contribution can be extracted by separately 8 Also at Centre de Physique des Particules de Marseille, IN2P3- integrating over the regions X>0 and X<0 and sub- CNRS, Université de la Méditerrané, Marseille, France. tracting the results from each other. We consider the 9 Present address: Department of Physics, Queen Mary College, University of London, Mile End Road, London E1 4NS, UK. distribution 10 Dipartimento di Fisica dell’Università di Modena e Reggio Emilia, via G. Campi 213/A I-41100, Modena, Italy. N X>0(t) − N X<0(t) 11 Present address: Scuola Normale Superiore e Sezione dell’INFN V(t)= 3π 3π , (2) X>0 + X<0 di Pisa, I-56100 Pisa, Italy. N3π (t) N3π (t) 12 Istituto di Fisica, Università di Urbino, I-61029 Urbino, Italy. 13 Funded by the German Federal Minister for Research and Tech- where N X>0(t) [N X<0(t)] is the number of decays of nology (BMBF) under contract 7MZ18P(4)-TP2. 3π 3π + − 0 14 Funded by the German Federal Minister for Research and Tech- neutral kaons into π π π at time t with a value of nology (BMBF) under contract 056SI74. the Dalitz variable X larger [smaller] than zero [1,2]. 15 Supported by the Committee for Scientific Research 0 0 In the NA48 set-up, where KS and KL are produced grants 5P03B10120, SPUB-M/CERN/P03/DZ210/2000 and in equal amounts at a fixed target, the interference of SPB/CERN/P03/DZ146/2002. the l = 1 component of K0 → π +π −π 0 with the l = 0 16 Funded by the Austrian Ministry for Traffic and Research under S 0 → + − 0 contract GZ 616.360/2-IV GZ 616.363/2-VIII, and by the Fonds für component of the dominant KL π π π decay Wissenschaft und Forschung FWF No. P08929-PHY. can be observed. It can be described by a complex pa- 34 J.R. Batley et al. / Physics Letters B 630 (2005) 31–39 rameter [3] mentum resolution was δp/p = (0.48 ⊕ 0.015p)%, ∞ ∞ ∗ = = with momentum p in GeV/c. dY dXA 3π(l 0)(X, Y )A3π(l 1)(X, Y ) = −∞ 0 L S After the spectrometer there was a scintillator ho- λ ∞ ∞ , | 3π(l=0) |2 doscope, for the accurate timing of charged particles −∞ dY 0 dX AL (X, Y ) (3) (yielding a time resolution on single tracks of 250 ps), which has been extracted by fitting the distribution de- and a liquid-krypton electromagnetic calorimeter, for fined above: the measurement of photons and electrons,√ with an = ⊕ ⊕ energy resolution of σ(E)/E (3.2/ E 9/E V(t)≈ 2D(E) Re(λ) cos(mt) − Im(λ) sin(mt) 0.42)%(E in GeV). These were followed by a hadron − t 1 + 1 calorimeter and a muon detector. A more detailed de- 2 ( τ τ ) × e S L scription of the detector has been given elsewhere [4]. − t . (4) e τL 0 0 m is the mass difference between KL and KS , τL 3. The trigger and τS are the respective lifetimes, and the energy- dependent “dilution” D(E) is the difference in the + − 0 relative abundances of K0 and K¯ 0 at production for Decays into π π π made up only a small part a kaon energy of E: of the event rate in the detector. This was due to the 0 small expected branching ratio for the KS decay and 0 − ¯ 0 0 K K to the long lifetime of the KL.