Cornering (3+1) sterile neutrino schemes

Using the most recent atmospheric neutrino data, as well as short-baseline, long-baseline and tritium $\beta$-decay data we show that the joint interpretation of the LSND, solar and atmospheric neutrino anomalies in (3+1) sterile neutrino schemes is severely disfavored, in contrast to the theoretically favored (2+2) schemes.Comment: 14 pages, 4 figures, v3: extended tritium decay analysis, small corrections in Fig. 2 and Eq.(4), version accepted for publication in Phys. Lett.