Search for the antineutrino rest mass in the tritium beta decay

Status and results of the tritium beta spectrum measurement on the "Troitsk nu-mass" set-up are discussed. Measurements carried out in 1994 to 1997 provided the lowest upper limit for electron antineutrino rest mass in the direct kinematics approach. Analysis of the spectrum revealed a narrow (less than 5 eV wide) bump-like structure located 5 to 12 eV below the end point with integral intensity similar to 7.10(-11) of the total decay rate. A specific feature of this structure proved to be a drift of the position of the bump during 3 years of measurement. No other visible anomalies in the measured part of the spectrum were found after introduction of a correction for an effect of electron trapping in the source. After accounting for the bump, the shape of the whole measured part of the beta spectrum agrees with zero m(nu)(2), thus eliminating the problem of "negative m(nu)(2)". The combined result of the 94 and 96 runs without the 97 run data is: m(nu)(2) = 1.5 +/- 5.9(stat) +/- 3.6(syst) eV(2)/c(4). From here most conservative limit for the neutrino mass is : m(nu) < 3.8 eV/c(2) at 95 % C.L. A new type of differential spectrometer, based on adiabatisity principle is proposed.