Possible Deviation from the Tri-bimaximal Neutrino Mixing in a Seesaw Model

We propose a simple but suggestive seesaw model with two phenomenological conjectures: three heavy (right-handed) Majorana neutrinos are degenerate in mass in the symmetry limit and three light Majorana neutrinos have the tri-bimaximal mixing pattern $V^{}_0$. We show that a small mass splitting between the first generation and the other two generations of heavy Majorana neutrinos is responsible for the deviation of the solar neutrino mixing angle $\theta^{}_{12}$ from its initial value $35.3^\circ$ given by $V^{}_0$, and the slight breaking of the mass degeneracy between the second and third generations of heavy Majorana neutrinos results in a small mixing angle $\theta^{}_{13}$ and a tiny departure of the atmospheric neutrino mixing angle $\theta^{}_{23}$ from $45^\circ$. It turns out that a normal hierarchy of the light neutrino mass spectrum is favored in this seesaw scenario.