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

TL;DR

This paper analyzes how errors in measuring the lightest neutrino mass affect the uncertainty in predicting the neutrinoless double beta decay effective Majorana mass, considering phase variations and mass orderings.

Contribution

It provides a detailed error propagation analysis of the predicted Majorana mass with respect to lightest neutrino mass measurement errors, including phase and mass ordering effects.

Findings

The uncertainty in effective Majorana mass does not exceed the error in lightest neutrino mass.

Minimum uncertainty can be zero for small lightest neutrino mass depending on phases.

Maximum uncertainty varies with mass ordering, reaching about 0.68 times the mass error in normal ordering.

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 $ \vert m_{ee} \vert $. The error of the predicted value of effective Majorana mass $ \sigma ( \vert m_{ee} \vert ) $ due to the error $ \sigma (m_0) $ is obtained by use of the propagation of errors. We investigate in detail how $ \sigma ( \vert m_{ee} \vert ) $ 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 ( \vert m_{ee} \vert ) $ does not exceed $ \sigma (m_0) $, and that the minimum value of $ \sigma ( \vert m_{ee} \vert ) $ 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 ( \vert m_{ee} \vert ) $ 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 ( \vert m_{ee} \vert ) $, 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 $.