Impact of ADC non-linearities on the sensitivity to sterile keV neutrinos with a KATRIN-like experiment

ADC non-linearities are a major systematic effect in the search for keV-scale sterile neutrinos with tritium $\beta$-decay experiments like KATRIN. They can significantly distort the spectral shape and thereby obscure the tiny kink-like signature of a sterile neutrino. In this work we demonstrate various mitigation techniques to reduce the impact of ADC non-linearities on the tritium $\beta$-decay spectrum to a level of $<$ ppm. The best results are achieved with a multi-pixel ($\ge {10}^4$ pixels) detector using full waveform digitization. In this case, active-to-sterile mixing angles of the order of ${\sin }^2\theta ={10}^{-7}$ would be accessible from the viewpoint of ADC non-linearities. With purely peak-sensing ADCs a comparable sensitivity could be reached with highly linear ADCs, sufficient non-linearity corrections or by increasing the number of pixels to $\ge {10}^5$.