Disentangling the seesaw mechanism in the left-right model: An algorithm for the general case

Senjanović and Tello have analyzed how one could determine the neutrino Dirac mass matrix in the minimal left-right model, assuming that the mass matrices for the light and heavy neutrinos could be taken as inputs. They provided an analytical solution for the Dirac mass matrix in the case that the left-right symmetry is implemented via a generalized parity symmetry and that this symmetry remains unbroken in the Dirac-Yukawa sector. We extend the work of Senjanović and Tello to the case in which the generalized parity symmetry is broken in the Dirac-Yukawa sector. In this case, the elegant method outlined by Senjanović and Tello breaks down and we need to adopt a numerical approach. Several iterative approaches are described; these are found to work in some cases but to be highly unstable in others. A stable, prescriptive numerical algorithm is described that works in all but a vanishingly small number of cases. We apply this algorithm to numerical datasets that are consistent with current experimental constraints on neutrino masses and mixings. We also provide some additional context and supporting explanations for the case in which the parity symmetry is unbroken.

Figure 1

$|\mathrm{\Delta }{|}^2$ vs $\mathrm{Im}({\eta }_2)$ for the parity-conserving scenario.

Figure 2

$|\mathrm{\Delta }{|}^2$ vs $\mathrm{Im}({\eta }_2)$ for parity-violating scenario I. Note that the horizontal and vertical scales are different than those of Fig. 1.

Figure 3

$|\mathrm{\Delta }{|}^2$ vs $\mathrm{Im}({\eta }_2)$ for parity-violating scenario II.

Figure 4

Convergence plot for $U_e$ (left panel) and $M_D$ (right panel) for parity-violating scenario II. See Eq. (57) for the definitions of ${\delta }_l^{(1)}$ and ${\delta }_l^{(2)}$, with $l=U_e,M_D$.