Neutrino mass sum-rules in flavor symmetry models

Abstract

Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A 4 , S 4 or T ′ , which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be probed in three different ways, using beta decay, neutrino-less double beta decay and cosmology. The general relations between the corresponding three neutrino mass observables are well known. The sum-rules lead to relations between the observables that are different from the general case and therefore only certain regions in parameter space are allowed. Plots of the neutrino mass observables are given for the sum-rules, and analytical expressions for the observables are provided. The case of deviations from the exact sum-rules is also discussed, which can introduce new features. The sum-rules could be used to distinguish some of the many models in the literature, which all lead to the same neutrino oscillation results. *

Large θ 13 in a SUSY SU(5) × T′ model

“…36. For examples of sum rules in models with only two parameters in the neutrino sector, see [38,39].…”

Reactor mixing angle from hybrid neutrino masses

“…With O( ) ∼ 0.01 eV, as required by neutrino mixing data (see figure 1, hatched (orange) vertical stripe), and fixing the heaviest neutrino mass to be O(|m heaviest |) ∼ 0.1 eV one can estimate ε to be order 0.1 − 0.3. Thus, once the hybrid contribution is added the lower limits on the neutrino observables will obey the constraints found in [40] for ε = 0.1 − 0.3, which -for completeness -we summarize in table 2. Note that in the exact TBM limit the inverted spectrum is not allowed, but becomes possible once the deviations are added.…”

“…The dot indicates that the IO is not allowed in the exact TBM limit. The results have been taken from [40].…”

“…As has been discussed at length in [40], neutrino mass sum-rules add further constraints on neutrino observables: the lightest neutrino mass (m light ), the sum of absolute neutrino masses ( m ν i ), the kinematic electron neutrino mass in β decay (m β ) and the effective mass for 0νββ ( m ee ). In the presence of deviations from the TBM structure the sumrules and corresponding constraints change.…”

“…In [40] this type of deviation from the sum rule was parametrized as 19) This means that the results in [40] can be directly translated to our case through the equality ε = 3| |/|m 0 heaviest |. With O( ) ∼ 0.01 eV, as required by neutrino mixing data (see figure 1, hatched (orange) vertical stripe), and fixing the heaviest neutrino mass to be O(|m heaviest |) ∼ 0.1 eV one can estimate ε to be order 0.1 − 0.3.…”