Measurement of the K± → π+π-e±νe form factors and of the ππ scattering length a00

The quark condensate is a fundamental free parameter of Chiral Perturbation Theory (χPT), since it determines the relative size of the mass and momentum terms in the power expansion. In order to confirm or contradict the assumption of a large quark condensate, on which χPT is based, experimental tests are needed. In particular, the S-wave ππ scattering lengths a00 and a02 can be predicted precisely within χPT as a function of this parameter and can be measured very cleanly in the decay K±→π+π-e±νe (Ke4). About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were analysed and 342,859 K±→π+π-e±νe (Ke4) candidates were selected. The background contamination in the sample could be reduced down to 0.3% and it could be estimated directly from the data, by selecting events with the same signature as Ke4, but requiring for the electron the opposite charge with respect to the kaon, the so-called 'wrong sign' events. This is a clean background sample, since the kaon decay with ΔS=-ΔQ, that would be the only source of signal, can only take place through two weak decays and is therefore strongly suppressed. The Cabibbo-Maksymowicz variables, used to describe the kinematics of the decay, were computed under the assumption of a fixed kaon momentum of 60 GeV/c along the z axis, so that the neutrino momentum could be obtained without ambiguity. The measurement of the form factors and of the ππ scattering length a00 was performed in a single step by comparing the five-dimensional distributions of data and MC in the kinematic variables. (orig.)