Direct and Semi-Direct Approaches to Lepton Mixing with a Massless Neutrino

Abstract

We discuss the possibility of enforcing a massless Majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the PMNS matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. We find a phenomenologically viable scheme for the semi-direct approach based on $Q(648)$ which contains $\Delta (27)$ and the quaternion group as subgroups. This leads to novel predictions for the first column of the PMNS matrix corresponding to a normal neutrino mass hierarchy with $m_1=0$, and sum rules for the mixing angles and phase which are characterised by the solar angle being on the low side ${\theta }_{12}\sim 31^{\circ }$ and the Dirac (oscillation) CP phase $\delta$ being either about $\pm 45^{\circ }$ or $\pm \pi$.

18 pages, 1 figure, small comments added in introduction and section 3, one reference added, version matches publication in JHEP

References in corpus (6)

• Updated fit to three neutrino mixing: status of leptonic CP violation
• The Horizontal Symmetry for Neutrino Mixing
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?
• Classification of lepton mixing matrices from finite residual symmetries
• On the finite subgroups of U(3) of order smaller than 512

Cited by in corpus (13)

• Eclectic Flavor Groups
• Simplified Models of Flavourful Leptoquarks
• CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
• The symmetry approach to quark and lepton masses and mixing
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• Informationally complete characters for quark and lepton mixings
• Perspectives for tests of neutrino mass generation at the GeV scale: Experimental reach versus theoretical predictions
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Discrete symmetries and Efficient Counting of Operators
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Group-theoretical search for rows or columns of the lepton mixing matrix