The symmetry approach to quark and lepton masses and mixing
arxiv(2024)
Abstract
The Standard Model lacks an organizing principle to describe quark and lepton
“flavours”. We review the impact of neutrino oscillation experiments, which
show that leptons mix very differently from quarks, placing a major challenge,
but also providing a key input to the flavour puzzle. We briefly sketch the
seesaw and “scotogenic” approaches to neutrino mass, the latter including
also WIMP dark matter. 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 family
and/or CP symmetries can generate novel viable and predictive mixing patterns.
We review the model-independent ways to predict lepton mixing and test both
mixing predictions as well as mass sum rules. We also discuss UV-complete
flavour theories in four and more space-time dimensions, and their predictions.
Benchmarks given include an A_4 scotogenic construction with trimaximal
mixing pattern TM2. Higher-dimensional completions are also reviewed, such as
5-D warped flavordynamics. We present a T^' warped flavordynamics theory
with TM1 mixing pattern, detectable neutrinoless double beta decay rates and
providing a very good fit of flavour observables, including quarks. We also
review how 6-D orbifolds offer a way to determine the structure of the 4-D
family symmetry from the symmetries between the extra-D branes. We describe a
scotogenic A_4 orbifold predicting the “golden” quark-lepton mass relation,
large neutrino mass with normal ordering, higher atmospheric octant, restricted
reactor angle, 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.
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