SEARCH FOR THE RARE KAON DECAY K+ → π+ ν(bar ν)

This thesis describes the search for the rare decay K+ → π+ ν(bar ν) in the pion momentum region 140 MeV/c ≤ Pπ+ ≤ 195 MeV/c. This is a Flavor Changing Neutral Current (FCNC) decay which is forbidden to the first order in the Standard Model (SM) by the GIM mechanism. However, this decay mode is allowed in the second order by two Z-Penguin and one box diagram and is expected to have a branching ratio of (0.72 ± 0.21) x 10-10. This decay mode is sensitive to the coupling of top to down quark and therefore a measurement of the branching ratio for this decay mode provides a measurement of the Cabibbo-Kobayashi-Maskawa matrix element Vtd. The recent observation of two events in the pion momentum region 211 MeV/c ≤ Pπ+ ≤ 229 MeV/c estimates a branching ratio of 1.57-0.82+1.75 x 10-10 for the same decay mode. We have extended the search for this decay to the lower pion momentum region. Data collected by the Experiment E787 at Brookhaven National Laboratory during the 1996 and 1997 run were analyzed in this thesis