Role of unphysical neutrino phases in the phenomenology of consistently defined textures. Case study: traceless neutrino mass matrix

Abstract

We highlight the role played by the unphysical phases in the definition of neutrino mass matrix, showing it does not relate to mere semantics, rather it has an effect on the phenomenology. As a case study, we take the neutrino mass matrix texture characterized by a vanishing trace, and study the effect of the phases, physical and unphysical, in its definition. We undergo a thorough phenomenological analysis, first (second) when the unphysical (CP) phases are vanishing, then move on to the general case where all phases exist. We stress that the effect of the unphysical phases on the phenomenology originates from changing the texture definition upon introducing them, while they are not observable. Finally we present a theoretical realization of the texture based on $A_5$ non-abelian flavor symmetry, which is also related to a consistently defined texture.