Predicted value of $0\nu \beta \beta$-decay effective Majorana mass with error of lightest neutrino mass

Abstract

Assuming that the lightest neutrino mass $m_0$ is measured, we study the influence of error of the measured $m_0$ on the uncertainty of the predicted value of the neutrinoless double beta decay ($0\nu \beta \beta$) effective Majorana mass $|m_{ee}|$. The error of the predicted value of effective Majorana mass $\sigma (|m_{ee}|)$ due to the error $\sigma (m_0)$ is obtained by use of the propagation of errors. We investigate in detail how $\sigma (|m_{ee}|)$ behaves when the Majorana phases $\beta$ and $\alpha$ change, and also when the size of the lightest neutrino mass changes. It is shown that $\sigma (|m_{ee}|)$ does not exceed $\sigma (m_0)$, and that the minimum value of $\sigma (|m_{ee}|)$ in the $\beta -\alpha$ plane can be zero if the size of $m_0$ is rather small. In the normal mass ordering case, the maximum value of $\sigma (|m_{ee}|)$ in the $\beta -\alpha$ plane becomes about $0.68\sigma (m_0)$ if $m_0(=m_1)$ is very small, while in the inverted mass ordering case, it becomes about $0.02\sigma (m_0)$ if $m_0(=m_3)$ is very small. By use of the calculated $\sigma (|m_{ee}|)$, we also discuss the minimum condition for the relative error of the lightest neutrino mass to raise the possibility of obtaining the information on $\beta$ and $\alpha$.

Comments: 21 pages, 1 figure