# Theory and Phenomenology of Leptonic CP Violation

Serguey Petcov (see picture, left) gave a theoretical talk discussing CP violation in connection with neutrino phenomenology. He started by discussing the standard parametrization of the PMNS matrix, which enshrines our knowledge of how neutrinos mix. One very specific interest in the phases of the matrix is that the possibility that they contribute to CP violation and the baryon asymmetry in the universe.

There is a message in the value of the neutrino mixing angles, CP violation phases and masses. The message, though, can have two opposite contents: anarchy or symmetry. Based on the symmetry approach one can make predictions on the pattern of these values. The most interesting aspect of this approach is that the delta turns out to be a function of the mixing angles and a number of other fixed parameters that depends on the symmetry used to understand the pattern of neutrino mixing. The measurement of the Dirac phase in the PMNS matrix, together with an improvement of the precision on the mixing angles, can provide unique information.

The observed values of neutrino mixing angles are close to ones one could infer from symmetry considerations, up to perturbative corrections. There is a vast literature on this. The symmetry groups used in this approach are non-Abelian, discrete groups. The tribimaximal mixing can be obtained from a group of permutation A4, or T'(S4). Other mixing matrices can be obtained from still other discrete groups. All these symmetry forms give theta_13=0, so its value needs to be corrected, like other parameters.

The reason for invoking these discrete symmetries is that they refer to rotation of large mixing angles whose value is similar to those of the PMNS elements. The remarkable prediction of this approach is a sum rule of cos(delta) which is expressed as a function of the mixing angles. By measuring cos(delta) with sufficient precision one can distinguish between the possibilities put forth. The same approach can be extended to obtain predictions for the Majorana phases. Many cases have been considered, and they yield non-degenerate predictions.

Petcov then touched on some aspects of leptogenesis theory. This is based on the see-saw mechanism, which explains the smallness of neutrino masses, and links the generation of nu masses to baryon asymmetry in the universe. An integral part of this is right-handed fields, that have masses of several orders of magnitude smaller than the GUT scale. It is experimentally impossible to test this mechanism; the only thing one can hope to do is to have a self-consistent theory of quark masses, charged lepton masses, CP violation, mixing, etcetera. In this theory if neutrinos get mass from the see-saw mechanism, you can test the low-energy part of the theory, to see if the approach is correct.

There are TeV-scale versions of leptogenesis that give more chances to test these ideas experimentally, through the production of Majorana neutrinos. One of the most important questions in the context of leptogenesis is, can the CP violation necessary in the universe be provided exclusively by the Dirac and/or majorana CPV phases ? The answer is positive. However, it is difficult or impossible to prove this within the GUT leptogenesis, it is more possible to do so in the context of TeV-scale leptogenesis.

Petcov concluded by saying that the measurement of the Dirac phase in the PMNS mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information about the possible existence of new fundamental symmetry in the lepton sector.