Studies of transiting Neptune-size planets orbiting close to nearby bright stars can inform theories of planet formation because mass and radius and therefore mean density can be accurately estimated and compared with interior models. The distributio
n of such planets with stellar mass and orbital period relative to their Jovian-mass counterparts can test scenarios of orbital migration, and whether hot (period < 10d) Neptunes evolved from hot Jupiters as a result of mass loss. We searched 1763 late K and early M dwarf stars for transiting Neptunes by analyzing photometry from the Wide Angle Search for Planets and obtaining high-precision ($<10^{-3}$) follow-up photometry of stars with candidate transit signals. One star in our sample (GJ 436) hosts a previously reported hot Neptune. We identified 92 candidate signals among 80 other stars and carried out 148 observations of predicted candidate transits with 1-2 m telescopes. Data on 70 WASP signals rules out transits for 39 of them; 28 other signals are ambiguous and/or require more data. Three systems have transit-like events in follow-up photometry and we plan additional follow-up observations. On the basis of no confirmed detections in our survey, we place an upper limit of 10.25% on the occurrence of hot Neptunes around late K and early M dwarfs (95% confidence). A single confirmed detection would translate to an occurrence of 5.3$pm$4.4%. The latter figure is similar to that from Doppler surveys, suggesting that GJ 436b may be the only transiting hot Neptune in our sample. Our analysis of Kepler data for similar but more distant late-type dwarfs yields an occurrence of 0.32$pm$0.21%. Depending on which occurrence is applicable, we estimate that the Next Generation Transit Survey will discover either ~60 or ~1000 hot Neptunes around late K and early M-type dwarfs.
