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

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 $\mathrm{\mid }{m}_{ee}\mathrm{\mid }$. The error of the predicted value of effective Majorana mass $\sigma (\mathrm{\mid }{m}_{ee}\mathrm{\mid })$ due to the error $\sigma (m_0)$ is obtained by use of the propagation of errors. We investigate in detail how $\sigma (\mathrm{\mid }{m}_{ee}\mathrm{\mid })$ behaves when the Majorana phases $\beta$ and $\alpha$ change, and also when the size of the lightest neutrino mass changes. It is shown that $\sigma (\mathrm{\mid }{m}_{ee}\mathrm{\mid })$ does not exceed $\sigma (m_0)$, and that the minimum value of $ \sigma ( \vert m_{ee} \vert ) $inthe$ \beta - \alpha $planecanbezeroifthesizeof$ m_0 $israthersmall\mathrm{.}Inthenormalmassorderingcase,themaximumvalueof$ \sigma ( \vert m_{ee} \vert ) $inthe$ \beta - \alpha $planebecomesabout$ 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 $\sigma (\mathrm{\mid }{m}_{ee}\mathrm{\mid })$, 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 $\alpha$.