Probing Lorentz violation in $2\nu\beta\beta$ using single electron spectra and angular correlations

We show that current investigations of Lorentz invariance violation (LIV) in $2\nu\beta\beta$ decay could be complemented by searches in the single electron spectra and angular correlations between emitted electrons. We find that the angular correlation and the ratio between the spectrum including contribution and the Standard Model one diverge near $Q$-value. We find that both the sign and magnitude of the strength coefficient ($\mathring{a}_{\text{of}}^{(3)}$) play a paramount role in the identification of LIV signatures. We also raise the issue of negative decay rates in case of negative $\mathring{a}_{\text{of}}^{(3)}$ values.