The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos

TL;DR

This paper explores the $$-$$ reflection symmetry in Majorana neutrinos, analyzing its theoretical foundations, extensions, symmetry breaking effects, and phenomenological consequences in neutrino physics.

Contribution

It provides a comprehensive review of the $$-$$ reflection symmetry, including recent progress, extensions, and implications for neutrino mass models.

Findings

The $$-$$ symmetry constrains neutrino flavor textures.

Radiative corrections can softly break the symmetry.

Phenomenological implications include predictions for neutrino oscillation parameters.

Abstract

The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector -- the effective Majorana neutrino mass term keeps invariant when the three left-handed neutrino fields transform as $\nu^{}_{e \rm L} \to (\nu^{}_{e \rm L})^c$, $\nu^{}_{\mu \rm L} \to (\nu^{}_{\tau \rm L})^c$ and $\nu^{}_{\tau \rm L} \to (\nu^{}_{\mu \rm L})^c$. A direct application of such a $\mu$-$\tau$ reflection symmetry to the canonical seesaw mechanism can help a lot to constrain the flavor textures of active and sterile Majorana neutrinos. The present article is intended to summarize the latest progress made in exploring the properties of this minimal flavor symmetry, its translational and rotational extensions, its soft breaking effects via radiative corrections from a superhigh energy scale to the electroweak scale, and its various phenomenological implications.