Abstract
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.
Highlights
Where δ is the Dirac CP-phase and P0=diag(e−iφ1/2, e−iφ2/2, 1) is a diagonal matrix containing the two Majorana phases φ1,2
We have presented the first explicit and systematic study of the effect that radiative corrections have on the validity of neutrino mass sum rules
After briefly reviewing the most general form of a neutrino mass sum rule and a discussion of the general effect of renormalisation group running, we have explicitly computed the resulting allowed regions for all neutrino mass sum rules known if we assume the rules to hold exactly only at the seesaw scale, while correction terms appear when going to lower energies
Summary
We want to briefly review how neutrino mass sum rules can be parametrised and how they can be interpreted as a prediction for the Majorana phases as a function of the (physical) neutrino masses. The most generic example is again a type I seesaw mechanism [29,30,31,32,33,34,35], where the light neutrino mass matrix mν = −mDMR−1mTD is generated from a multiplication of the Dirac mass matrix mD and the heavy neutrino mass matrix MR If, in this product, the structure of mD is generated by two flavon couplings, whereas the scale√of MR√can be fa√ctored out, this would lead to a sum rules featuring a square root, such as m 1 ± m 3 = 2 m 2. If the structure of MR is generated by two flavon couplings, whereas mD only features a single scale, the resulting sum rule would feature an inverse power of one, like 2/m 2 = 1/m 1 + 1/m 3 or 1/m 1 + 1/m 2 = 1/m 3 This scheme extends to basically all kinds of neutrino mass models, see ref. In table 1 we have collected all the sum rules we found in the
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
