Measurement of the Dalitz plot slopes of the K ± → π ± π + π − decay

The distribution of the K± → π±π+π− decays in the Dalitz plot has been measured by the NA48/2 experiment at the CERN SPS with a sample of 4.71×10 fully reconstructed events. With the standard Particle Data Group parameterization the following values of the slope parameters were obtained: g = (−21.134±0.014)%, h = (1.848± 0.039)%, k = (−0.463± 0.012)%. The quality and statistical accuracy of the data have allowed an improvement in precision by more than an order of magnitude, and are such as to warrant a more elaborate theoretical treatment, including pion-pion rescattering, which is in preparation. Funded by the U.K. Particle Physics and Astronomy Research Council Present address: Istituto di Cosmogeofisica del CNR di Torino, I-10133 Torino, Italy Present address: Scuola Normale Superiore, I-56100 Pisa, Italy Present address: CERN, CH-1211 Genève 23, Switzerland Also at Centre de Physique des Particules de Marseille, IN2P3-CNRS, Université de la Méditerranée, Marseille, France Also Istituto di Fisica, Università di Modena, I-41100 Modena, Italy Istituto di Fisica, Università di Urbino, I-61029 Urbino, Italy Funded by the German Federal Minister for Education and research under contract 05HK1UM1/1 Permanent address: SLAC, Stanford University, Menlo Park, CA 94025, U.S.A. Present address: UCLA, Los Angeles, CA 90024, U.S.A. Funded by the German Federal Minister for Research and Technology (BMBF) under contract 056SI74 Funded by the Austrian Ministry for Traffic and Research under the contract GZ 616.360/2-IV GZ 616.363/2-VIII, and by the Fonds für Wissenschaft und Forschung FWF Nr. P08929-PHY Introduction The K → πππ decay can be described [1] in terms of the Lorentz invariant kinematic variables u and v defined as u = s12 − s0 mπ , v = s13 − s23 mπ , (1) sij = (Pi + Pj) , i, j = 1, 2, 3, i < j; s0 = 1 3 (s12 + s13 + s23) ≡ 1 3 m2K +m 2 π. Here mπ is the charged pion mass, mK is the charged kaon mass, Pi are the pion fourmomenta, the indices i, j = 1, 2 correspond to the two pions of the same electric charge (“even” pions), and the index i, j = 3 to the other (“odd”) pion. The experimental Dalitz plot distribution of the K → πππ decay has been up to now experimentally analyzed [2, 3] in terms of a polynomial expansion in powers of u and v: |M(u, v)| ∼ C(u, v) · (1 + gu+ hu + kv). (2) Here g, h, k are the linear and quadratic slope parameters (terms proportional to odd powers of v are forbidden by Bose symmetry, and the variable v is defined only up to a sign), and C(u, v) is the Coulomb factor [4]: