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The method of quasi-optimal weights is applied to constructing(quasi-)optimal criteria for various anomalous contributions in experimentalspectra. Anomalies in the spectra could indicate physics beyond the StandardModel (additional interactions and neutrino flavours, Lorenz violation etc.).In particular the cumulative tritium $\beta$-decay spectrum (for instance, inTroitsk-$\nu$-mass, Mainz Neutrino Mass and KATRIN experiments) is analysedusing the derived special criteria. Using the power functions we show that thederived quasi-optimal criteria are efficient statistical instruments fordetecting the anomalous contributions in the spectra.

Statistical criteria for possible indications of new physics in tritium $\beta$-decay spectrum