Implications of general lepton mass matrices in the standard model on mee

Abstract

Within the framework of the standard model (SM), using the facility of weak basis (WB) transformations, the general Dirac neutrino mass matrix and the charged lepton mass matrix can essentially be considered as texture two zero mass matrices. Using type I seesaw formula for Majorana neutrino mass matrix, our analysis yields lower bounds ${m}_{ee}\ensuremath{\gtrsim}0.001\text{ }\text{ }\mathrm{eV}$ for normal mass ordering and ${m}_{ee}\ensuremath{\gtrsim}0.08\text{ }\text{ }\mathrm{eV}$ for inverted mass ordering, the latter being tantalizingly close to the expected outcome of the ongoing experiments. Interestingly, for inverted mass ordering, ${m}_{ee}$ is largely independent of variation of mass ${m}_{3}$, whereas, for normal mass ordering with ${m}_{1}$ in the range 0.0001 eV--0.01 eV, the bound on parameter ${m}_{ee}$ gets further sharpened and one obtains ${m}_{ee}$ within the band 0.014--0.042 eV. Further, noting that a particular set of texture four zero quark mass matrices has been shown to be a unique viable option for the description of quark mixing data, an analysis of similar mass matrices in the lepton sector has also been carried out to obtain bounds for the parameter ${m}_{ee}$ with interesting consequences.