Detailed study of the K ± → π 0 π 0 e ± ν (K e4 00 ) decay properties

A sample of 65210 K-+/- -> pi(0) pi(0)e(+/-)nu (K-e4(00)) decay candidates with 1% background contamination has been collected in 2003-2004 by the NA48/2 collaboration at the CERN SPS. A study of the differential rate provides the first measurement of the hadronic form factor variation in the plane (M-pi pi(2), M-e nu(2)) and brings evidence for a cusp-like structure in the distribution of the squared pi(0)pi(0) invariant mass around . Exploiting a model independent description of this form factor, the branching ratio, inclusive of radiative decays, is obtained using the K-+/- -> pi(0)pi(0)pi(+/-) decay mode as normalization. It is measured to be BR(K-e4(00)) = (2.552 +/- 0.010(stat) +/- 0.010(syst) +/- 0.032(ext)) x 10(-5), which improves the current world average precision by an order of magnitude while the 1.4% relative precision is dominated by the external uncertainty from the normalization mode. A comparison with the properties of the corresponding mode involving a pi(+)pi(-) pair (K-e4(+-)) is also presented.