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

A sample of 65210 K± → π0π0e±ν (K00 e4) 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 (M2 ππ,M2 eν) and brings evidence for a cusp-like structure in the distribution of the squared π0π0 invariant mass around 4m2 π+. Exploiting a model independent description of this form factor, the branching ratio, inclusive of radiative decays, is obtained using the K± → π0π0π± decay mode as normalization. It is measured to be BR(K00 e4) = (2.552 ± 0.010stat ± 0.010syst ± 0.032ext) × 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 π+π− pair (K+− e4 ) is also presented.