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

The method of quasi-optimal weights is applied to constructing (quasi-)optimal criteria for various anomalous contributions in experimental spectra. Anomalies in the spectra could indicate physics beyond the Standard Model (additional interactions and neutrino flavours, Lorenz violation etc.). In particular the cumulative tritium $beta$-decay spectrum (for instance, in Troitsk-$ u$-mass, Mainz Neutrino Mass and KATRIN experiments) is analysed using the derived special criteria. Using the power functions we show that the derived quasi-optimal criteria are efficient statistical instruments for detecting the anomalous contributions in the spectra.