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The symmetry approach to quark and lepton masses and mixing
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abstract
The Standard Model lacks an organizing principle to describe quark and lepton ``flavours''. Neutrino oscillation experiments show that leptons mix very differently from quarks, adding a major challenge to the flavour puzzle. We briefly sketch the seesaw and the dark-matter-mediated ``scotogenic'' neutrino mass generation approaches. We discuss the limitations of popular neutrino mixing patterns and examine the possibility that they arise from symmetry, giving a bottom-up approach to residual flavour and CP symmetries. We show how such family and/or CP symmetries can yield novel, viable and predictive mixing patterns. Model-independent ways to predict lepton mixing and neutrino mass sum rules are reviewed. We also discuss UV-complete flavour theories in four and more space-time dimensions. As benchmark examples we present an $A_4$ scotogenic construction with trimaximal mixing pattern TM2 and another with $S_4$ flavour symmetry and generalized CP symmetry. Higher-dimensional flavour completions are also briefly discussed, such as 5-D warped flavordynamics with a $T^\prime$ symmetry yielding a TM1 mixing pattern, detectable neutrinoless double beta decay rates and a very good global fit of flavour observables. We also mention 6-D orbifolds as a way to fix the structure of the 4-D family symmetry. We give a scotogenic benchmark orbifold model predicting the ``golden'' quark-lepton mass relation, stringent neutrino oscillation parameter regions, and an excellent global flavour fit, including quark observables. Finally, we discuss promising recent progress in tackling the flavor issue through the use of modular symmetries.
Forward citations
Cited by 9 Pith papers
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The $\pi/12$ model: trimaximal first-column lepton mixing with charged-lepton $\mu$--$\tau$ breaking
The pi/12 model fixes the electron row to sin2 theta12 = 0.31811 and sin2 theta13 = 0.02233, and predicts delta about 272 degrees, epsilon2 about -0.066, and sum m nu about 65.6 meV.
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Modulus stabilization of modular flavor models in Jordan frame supergravity
Non-minimal scalar-curvature coupling reshapes the modulus potential, allowing stabilization at i∞ or at CP-breaking points in modular flavor models.
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Modular Flavor Symmetries and Fermion Mass Hierarchies
In modular flavor models, fermion mass hierarchies require the modulus to sit near the critical points i, i∞, or ω; the paper classifies the near-critical mass patterns for reducible 2⊕1 matter assignments.
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Flavor Symmetries and Winding Modes
In the Z3 heterotic orbifold, the modular symmetry of the Kähler modulus is Gamma(3), and the discrete flavor symmetry Delta(27) arises from misaligned U(1) gauge symmetries that become massless at different critical points.
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A Compact Phenomenological Pattern in Fermion Mass Ratios and Mixing Parameters
A hand-built exponent ansatz reproduces the charged-fermion mass ratios and the CKM/PMNS mixing angles at the percent-to-ten-percent level.
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Modular Symmetry with Weighton
A systematic classification of modular weighton models at levels 3, 4 and 5, with two T' benchmark fits that reproduce quark and lepton hierarchies, each requiring one admitted cancellation.
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Heavy neutrino mixing prospects at hadron colliders: a machine learning study
XGBoost applied to simulated same-sign and opposite-sign dilepton events from WR decays in the inverse seesaw left-right model gives projected heavy neutrino mass reaches up to 17.1 and 19.5 TeV at a 100 TeV collider.
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Right-handed neutrinos: seesaw models and signatures
A pedagogical review that explains how adding right-handed neutrinos can generate small neutrino masses through seesaw mechanisms and what experimental signatures such models predict.
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Quark and lepton masses
A review of fermion mass and mixing data and of the main theoretical attempts to explain them, from GUTs to string theory, without claiming a new result.
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