Investigation of the Lorentz invariance violation in two-neutrino double-beta decay

We make a comprehensive investigation of the Lorentz invariance violation (LIV) effects that may occur in two-neutrino double-beta ($2\nu \beta \beta$) decay for all the experimentally interesting nuclei. We deduce the formulas for the LIV deviations and provide single and summed energy electron spectra and angular correlation between electrons with and without LIV contributions to be used for constraining the LIV coefficient ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$. First, we confirm the shifting of the electron spectra to higher electron energies due to LIV for all nuclei. Next, we analyze other LIV signatures that can be used in LIV investigations. Thus, from the comparison of the electron and angular correlation spectra calculated with the inclusion of the LIV contributions, with their standard forms, information can be obtained about the strength versus observability of the LIV effects in the current experimental statistics. Then, we present the alternative method of constraining ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$ from the measurement of the angular correlation coefficient and estimate the statistics that different double-beta decay experiments should reach to constrain the LIV coefficient at the level of the current beta decay experiments. We hope that our work will improve the theoretical support and further stimulate the search for LIV in double-beta decay.

Figure 1

Normalized $2\nu \beta \beta$ single-electron spectra within the SM with the solid line, and the first order contribution in ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$ due to LIV with the dashed line. See text for the assumption on the hypothesis used.

Figure 2

Normalized single-electron spectra within the SM with the solid line, and the first order contribution in ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$ due to LIV with the dashed line for $2\nu \beta \beta$ decay of ${}^{150}\mathrm{Nd}$. We assumed the SSD hypothesis in the left panel and HSD in the right panel.

Figure 3

The quantity ${\chi }^{(1)}({ϵ}_1)$ depicted for current limits of ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$ (dashed for upper limit and dot-dashed for lower limit). The solid line at ${\chi }^{(1)}({\epsilon }_1)=0$ represents the SM prediction.

Figure 4

The quantity ${\chi }^{(+)}(K)$ depicted for current limits of ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$. The same conventions as in Fig. 3 are used.

Figure 5

The angular correlation spectrum plotted for the current limits of ${\stackrel{\circ }{a}}_{\mathrm{of}}^{(3)}$. The same conventions as in Fig. 3 are used.