Coxeter groups and the PMNS matrix

Abstract

We discuss the symmetries of the Lagrangian of the leptonic sector. We consider the case when this symmetry group is a Coxeter group. The number of elements of the PMNS matrix predicted by this group structure would depend on the number of generators of this group. We analyze finite Coxeter groups with 2 to 4 generators and even finite subgroups of infinite Coxeter groups with 4 generators and show which of them can give results that are consistent with experimental data.

31 pages, 1 figure and 4 table, minor changes. Matches with publish version

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Cited by in corpus (4)

• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Generalized ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ in Scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis
• Hidden flavor symmetries of SO(10) GUT
• Involution symmetries and the PMNS matrix