Neutrino Mass Spectrum for Co-Bimaximal Mixings from Quantum Gravity

TL;DR

This paper explores how quantum gravity effects at the Planck scale perturb the neutrino mass matrix, leading to specific corrections in neutrino masses and mixing angles consistent with observed oscillation data.

Contribution

It introduces a model where quantum gravitational interactions perturb the GUT-scale co-bimaximal neutrino mass matrix, providing predictions for neutrino masses and mixing parameters.

Findings

Neutrino masses are nearly degenerate at high scale.

Quantum gravity induces specific corrections to neutrino mixing angles.

Predicted neutrino mass ranges align with oscillation data.

Abstract

We consider non-renormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective $SU(2)_L\times U(1)$ invariant dimension-5 Lagrangian involving neutrino and Higgs fields,On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. The gravitational interaction $M_X=M_{pl}$ which gives rise to additional terms in neutrino mass matrix. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is Co-bimaximal mixing by assuming mixing angle $\theta_{13}\neq0 = 10^{o}$, $\theta_{23}=\frac{\pi}{4}$, $\tan\theta_{12}^ 2 = \frac{1-3sin\theta_{13}^2}{2} = 34^{o}$ and Dirac phase $\delta=\pm\frac{\pi}{2}$.There additional term can be considered to be perturbation of the GUT scale Co-bimaximal neutrino mass matrix. The relation consider with solar and atmospheric neutrino oscillation data predicted above GUT scale $m_1' \simeq 0.00001eV-0.00003eV$, $m_2' \simeq 0.00008eV-0.00012$, and $m_3' \simeq 0.000207eV-000320eV$.