Study of the Jarlskog-Like Parameters for Neutrino Mass Matrix with one Vanishing Minor and Zero Sum of Mass Eigenvalues with the Majorana Phases

In this work we carry out to determine the Jarlskog-like parameters of the neutrino mass matrix with two constraints (a) one vanishing minor and (b) zero-sum of the neutrino mass eigenvalues with the Majorana phases (henceforth, vanishing trace). A neutrino mass matrix has six possible cases of one vanishing minor. Out of them, we choose to study three cases viz., \(C_{11}=0\) , \(C_{12}=0\) and \(C_{13}=0\) with the co-lateral condition of vanishing trace. For each case, the dependence of the Jarlskog-like parameters \(\nu _{\rho \sigma }^{ij}\) on the Dirac CP violating phase \((\delta )\) and the Majorana CP violating phases \(\alpha \) and \(\beta \) is tried to understand by plotting \(\nu _{\rho \sigma }^{ij}\) for the values of \(\delta \) , \(\alpha \) and \(\beta \) constrained on the light of the current \(3\sigma \) neutrino data.