E787: a search for the rare decay K{sup +}

Recent results from the first phase of the E787 experiment and an update on the current status are presented. From the first phase the limit on the K{sup +} {r_arrow} {pi}{sup +}{nu}{ovr {nu}} branching ratio is BR( K{sup +} {r_arrow} {pi}{sup +}{nu}{ovr {nu}}) < 2.4 x 10{sup -9}. An observation of the decay K{sup +} {r_arrow} {pi}{sup +}{mu}{sup +}{mu}{sup -} has been made using two separate techniques. An observation of the decay K{sup +} {r_arrow} {pi}{sup +}{gamma}{gamma} has been made and the distribution of two photon invariant mass is inconsistent with phase space but consistent with chiral perturbation theory. A description of recent upgrades to the detector follows. With the upgraded detector the K{sup +} {r_arrow} {pi}{sup +}{nu}{ovr {nu}} decay should soon be observable. A discussion of the expected sensitivity for K{sup +} {r_arrow} {pi}{sup +}{nu}{ovr {nu}} during the current running period is presented. Possible improvements, in order to make a significant measurement of {vert_bar}V{sub td}{vert_bar}, are discussed. One result from the upgraded detector is a measurement of the structure dependent part (SD{sup +}) of the decay K{sup +} {r_arrow} {mu}{sup +}{nu}{sub {mu}}{gamma} with a branching ratio of BR(SD{sup +}) = (1. 33 {+-} 0.12 {+-} 0.18) X 10{sup -5}.