Renormalization group evolution of neutrino mixing parameters near $θ_{13} = 0$ and models with vanishing $θ_{13}$ at the high scale

Abstract

Renormalization group (RG) evolution of the neutrino mass matrix may take the value of the mixing angle θ 13 very close to zero, or make it vanish. On the other hand, starting from θ 13 = 0 at the high scale it may be possible to generate a non-zero θ 13 radiatively. In the most general scenario with non-vanishing CP violating Dirac and Majorana phases, we explore the evolution in the vicinity of θ 13 = 0, in terms of its structure in the complex U e3 plane. This allows us to explain the apparent singularity in the evolution of the Dirac CP phase δ at θ 13 = 0. We also introduce a formalism for calculating the RG evolution of neutrino parameters that uses the Jarlskog invariant and naturally avoids this singular behaviour. We find that the parameters need to be extremely fine-tuned in order to get exactly vanishing θ 13 during evolution. For the class of neutrino mass models with θ 13 = 0 at the high scale, we calculate the extent to which RG evolution can generate a nonzero θ 13 , when the low energy effective theory is the standard model or its minimal supersymmetric extension. We find correlated constraints on θ 13 , the lightest neutrino mass m 0 , the effective Majorana mass m ee measured in the neutrinoless double beta decay, and the supersymmetric parameter tan β.

Large U_{e3} and Tri-bimaximal Mixing

“…As is seen, k 13 depends on the Dirac CP phase δ which is unphysical for the case of θ 13 = 0 at the high scale Λ. However as discussed in [27,30], the value of δ at this point depends on the values of the masses and the Majorana phases and RG evolution takes care of that automatically. For analytical estimates, it is convenient to consider the shift of the mixing angles θ ij from their initial values.…”

A review of mu-tau flavor symmetry in neutrino physics

“…Finally it is worth pointing out that a finite and meaningful value of δ will be generated along with a nonzero value of θ 13 after the exact µ-τ permutation symmetry at Λ FS is broken via the RGE running effects. Of course, the real seeds of such a radiative generation of δ must be the nontrivial Majorana phases ρ and σ at Λ FS [143,144].…”

Renormalization Group Evolution of Neutrino Masses and Mixing in Seesaw Models

“…( 91). If the symmetry θ 13 = 0 is implemented at the high scale µ 0 [62], which is the case for many neutrino mass models, the maximum θ 13 value can be achieved with the choice 2φ…”

“…Some generic features of the RG evolution of the light neutrino masses and the mixing parameters in the effective theory have been studied extensively in literature [61,68,69,70,58,71]. These effects can have interesting consequences such as the generation of large mixing angles [72,73,74,75,76,77], small mass splittings for degenerate neutrinos [78,79,80,81,82,83,84,85,86,87], or radiative generation of θ 13 starting from a zero value at the high scale [62,88,89,90]. Some specific features of the RG evolution, like the stability of mixing angles and masses [66,91,92,93,94], possible occurrence of fixed points [95,96,97] have also been studied.…”

“…m i , θ 12 , θ 23 and φ i is independent of δ upto O(θ 0 13 ), and hence will have continuous, non-singular evolution even at θ 13 = 0. This apparent singularity in δ has been explored in [62] by analyzing the evolution of the complex quantity U e3 , which stays continuous throughout the RG evolution and shows that a fine tuning is indeed required, but that is to ensure that θ 13 exactly vanishes. However, if the parameters happen to be tuned such that θ 13 vanishes exactly, then the limiting value of δ as θ 13 → 0 is always the one given by the prescription mentioned in Eq.…”