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Hep-Ex/0510008V1 4 Oct 2005 Eateto Hsc N Srnm,Nrhetr Univers Northwestern Astronomy, and Physics of Department .Bhe,K Pad .Eppard M EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN-PH-EP/2005-037 13 July 2005 A measurement of the CP-conserving component of the decay K0 π+π−π0 S → J.R. Batley, C. Lazzeroni, D.J. Munday, M. Patel1), M.W. Slater, S.A. Wotton Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, U.K.2) R. Arcidiacono, G. Bocquet, A. Ceccucci, D. Cundy3), N. Doble, V. Falaleev, L. Gatignon, A. Gonidec, P. Grafstr¨om, W. Kubischta, F. Marchetto4), I. Mikulec5), A. Norton, B. Panzer-Steindel, P. Rubin6), H. Wahl7) CERN, CH-1211 Gen`eve 23, Switzerland E. Goudzovski, D. Gurev, P. Hristov1), V. Kekelidze, L. Litov, D. Madigozhin, N. Molokanova, Yu. Potrebenikov, S. Stoynev, A. Zinchenko Joint Institute for Nuclear Research, Dubna, Russian Federation E. Monnier8), E. Swallow, R. Winston The Enrico fermi Institute, The University of Chicago, Chicago, Illinois, 60126, U.S.A. R. Sacco9), A. Walker Department of Physics and Astronomy, University of Edinburgh, JCMB King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, U.K. W. Baldini, P. Dalpiaz, P.L. Frabetti, A. Gianoli, M. Martini, F. Petrucci, M. Scarpa, M. Savri´e Dipartimento di Fisica dell’Universit`ae Sezione dell’INFN di Ferrara, I-44100 Ferrara, Italy A. Bizzeti10), M. Calvetti, G. Collazuol11), G. Graziani, E. Iacopini, M. Lenti, F. Martelli12), G. Ruggiero1), M. Veltri12) arXiv:hep-ex/0510008v1 4 Oct 2005 Dipartimento di Fisica dell’Universit`ae Sezione dell’INFN di Firenze, I-50125 Firenze, Italy M. Behler, K. Eppard, M. Eppard1), A. Hirstius1), K. Kleinknecht, U. Koch, L. Masetti, P. Marouelli, U. Moosbrugger, C. Morales Morales, A. Peters1), M. Wache, R. Wanke, A. Winhart Institut f¨ur Physik, Universit¨at Mainz, D-55099 Mainz, Germany13) A. Dabrowski, T. Fonseca Martin, M. Velasco Department of Physics and Astronomy, Northwestern University, Evanston Illinois 60208-3112, U.S.A. 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’Universit`ae 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. Cheshkov1), 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, Universit¨at Siegen, D-57068 Siegen, Germany14) C. Biino, N. Cartiglia, M. Clemencic, S. Goy Lopez, E. Menichetti, N. Pastrone Dipartimento di Fisica Sperimentale dell’Universit`ae 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, Poland15) H. Dibon, M. Jeitler, M. Markytan, G. Neuhofer, L. Widhalm Osterreichische¨ Akademie der Wissenschaften, Institut f¨ur Hochenergiephysik, A-1050 Wien, Austria16) Submitted to Physics Letters B 1) Present address: CERN, CH-1211 Gen`eve 23, Switzerland 2) Funded by the U.K. Particle Physics and Astronomy Research Council 3) Present address: Istituto di Cosmogeofisica del CNR di Torino, I-10133 Torino, Italy 4) On leave from Sezione dell’INFN di Torino, I-10125 Torino, Italy 5) On leave from Osterreichische¨ Akademie der Wissenschaften, Institut f¨ur Hochenergiephysik, A-1050 Wien, Austria 6) On leave from University of Richmond, Richmond, VA, 23173, USA; supported in part by the US NSF under award #0140230 7) Also at Dipartimento di Fisica dell’Universit`ae Sezione dell’INFN di Ferrara, I-44100 Ferrara, Italy 8) Also at Centre de Physique des Particules de Marseille, IN2P3-CNRS, Universit´ede la M´editerran´e, Marseille, France 9) Present address: Department of Physics, Queen Mary College, University of London, Mile End Road, London E1 4NS, UK 10) Dipartimento di Fisica dell’Universita’ di Modena e Reggio Emilia, via G. Campi 213/A I-41100, Modena, Italy 11) Present address: Scuola Normale Superiore e Sezione dell’INFN di Pisa, I-56100 Pisa, Italy 12) Istituto di Fisica, Universita’ di Urbino, I-61029 Urbino, Italy 13) Funded by the German Federal Minister for Research and Technology (BMBF) under contract 7MZ18P(4)-TP2 14) Funded by the German Federal Minister for Research and Technology (BMBF) under contract 056SI74 15) Supported by the Committee for Scientific Research grants 5P03B10120, SPUB- M/CERN/P03/DZ210/2000 and SPB/CERN/P03/DZ146/2002 16) Funded by the Austrian Ministry for Traffic and Research under contract GZ 616.360/2-IV GZ 616.363/2-VIII, and by the Fonds f¨ur Wissenschaft und Forschung FWF Nr. P08929-PHY Abstract The NA48 collaboration has measured the amplitude of the CP-conserving component of the decay K0 π+π−π0 relative to K0 π+π−π0. For the characteristic parameter λ, the S → L → values Re λ = 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. 1 Introduction 0 + − 0 The KS π π π decay amplitude is dominated by two angular momentum com- ponents, l = 0→ and l =1(l is the angular momentum of the neutral pion with respect to the system of the two charged pions); higher angular momentum states are suppressed because the kaon mass is close to the three pion mass. In this analysis we have measured the CP conserving transition to the l = 1 state through its interference with the domi- 0 + − 0 nant KL π π π decay. We neglect any effects from CP violation in mixing and decay, which are→ totally negligeable at our level of sensitivity. 3π 0 The amplitudes for the decays of neutral kaons into three pions (AL for KL and 3π 0 AS for KS) can be parameterized in terms of the Dalitz variables X and Y , which are defined as sπ− sπ+ sπ0 s0 X = −2 , Y = −2 (1) mπ± mπ± 2 1 with sπ = (pK pπ) , s = (s + + s − + s 0 ), and pK and pπ being the 4-momenta of − 0 3 π π π the kaon and the pion respectively. The Dalitz variable X is a measure of the difference of the energies of the two charged pions in the kaon’s rest system while Y is a measure of the energy of the neutral pion in the kaon’s rest system. 0 + − 0 The l = 1 and the l = 0 components of the decay KS π π π can be separated by the fact that the amplitude of the l = 1 process is antisymmetric→ in X while the l = 0 process is symmetric in X. Therefore the l = 1 contribution can be extracted by separately integrating over the regions X > 0 and X < 0 and subtracting the results from each other. We consider the distribution X>0 X<0 N3π (t) N3π (t) V (t)= X>0 − X<0 (2) N3π (t)+ N3π (t) X>0 X<0 + − 0 where N3π (t)[N3π (t)] is the number of decays of neutral kaons into π π π at time t with a value of the Dalitz variable X larger [smaller] than zero [1, 2]. 0 0 In the NA48 set-up, where KS and KL are produced in equal amounts at a fixed 0 + − 0 target, the interference of the l = 1 component of KS π π π with the l = 0 component of the dominant K0 π+π−π0 decay can be observed.→ It can be described by a complex L → parameter [3] ∞ ∞ ∗ 3π(l=0) 3π(l=1) R−∞ dY R0 dX AL (X,Y )AS (X,Y ) λ = ∞ ∞ π l , (3) R dY R dX A3 ( =0)(X,Y ) 2 −∞ 0 | L | which has been extracted by fitting the distribution defined above: t − ( 1 + 1 ) 2D(E)[Re(λ)cos(∆mt) Im(λ)sin(∆mt)]e 2 τS τL V (t) −− t . (4) ≈ e τL 0 0 ∆m is the mass difference between KL and KS, τL and τS are the respective lifetimes, and the energy-dependent “dilution” D(E) is the difference in the relative abundances of 1 0 K0 and K at production for a kaon energy of E: 0 K0 K D(E)= − 0 (5) K0 + K 2 Experimental setup The data presented here were taken in a high-intensity neutral beam at the CERN Super Proton Synchrotron during 89 days in 2002. Protons of 400 GeV with an average intensity of 5 1010 per 4.8 s spill (within a cycle of 16.2 s) impinged on a beryllium × target, where secondary particles were produced. Charged particles were removed by a sweeping magnet and a 5.1 m long collimator, which selected a beam of neutral particles at an angle of 4.2 mrad with respect to the proton beam. After the collimator, the neutral beam and the decay products propagated in an 0 89 m long vacuum tank, where most of the short-lived kaons (KS) and neutral hyperons 0 0 0 (Λ , Ξ ) as well as a small fraction of the long-lived neutral kaons (KL) decayed. Undecayed 0 particles (KL, neutrons) continued to a beam dump via a vacuum pipe that passed through all of the downstream detectors. Downstream of the vacuum tank there was a magnetic spectrometer consisting of four drift chambers inside a helium-filled tank and a magnet with a horizontal transverse momentum kick of 265 MeV/c. The spatial resolution was 120 µm per view, and the momentum resolution was δp/p = (0.48 0.015 p)%, with momentum p in GeV/c. After the spectrometer there was⊕ a scintillator hodoscope, for the accurate timing of charged particles (yielding a time resolution on single tracks of 250 ps), and a liquid- krypton electromagnetic calorimeter, for the measurement of photons and electrons, with an energy resolution of σ(E)/E = (3.2/√E 9/E 0.42)% (E in GeV).
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