Orbifold modular GUT of flavor

We discuss an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>5</a:mn><a:mo stretchy="false">)</a:mo></a:math> grand unified theory based on the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>10</e:mn><e:mi>d</e:mi></e:math> orbifold <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo stretchy="false">(</g:mo><g:msup><g:mi mathvariant="double-struck">T</g:mi><g:mn>2</g:mn></g:msup><g:msup><g:mo stretchy="false">)</g:mo><g:mn>3</g:mn></g:msup><g:mo>/</g:mo><g:mo stretchy="false">(</g:mo><g:msub><g:mi mathvariant="double-struck">Z</g:mi><g:mn>4</g:mn></g:msub><g:mo>×</g:mo><g:msub><g:mi mathvariant="double-struck">Z</g:mi><g:mn>2</g:mn></g:msub><g:mo stretchy="false">)</g:mo></g:math> plus three modular <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>S</p:mi><p:mn>4</p:mn></p:msub></p:math> groups with moduli at respective fixed points <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>i</r:mi><r:mo>,</r:mo><r:mi>i</r:mi><r:mo>+</r:mo><r:mn>2</r:mn><r:mo>,</r:mo><r:mi>ω</r:mi><r:mo>=</r:mo><r:msup><r:mi>e</r:mi><r:mrow><r:mn>2</r:mn><r:mi>i</r:mi><r:mi>π</r:mi><r:mo>/</r:mo><r:mn>3</r:mn></r:mrow></r:msup></r:math>. The resulting model has hierarchical quark and charged-lepton mass matrices, arising from a double weighton mechanism, and reproduces the highly predictive littlest seesaw mechanism in the neutrino sector. The down-quark mass matrix has an upper triangular form, contributing to Cabibbo-Kobayashi-Maskawa mixing, while the charged-lepton mass matrix has a lower-triangular form with suppressed contributions to Pontecorvo-Maki-Nakagawa-Sakata mixing. The orbifold yields successful <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>S</t:mi><t:mi>U</t:mi><t:mo stretchy="false">(</t:mo><t:mn>5</t:mn><t:mo stretchy="false">)</t:mo></t:math> breaking with doublet-triplet splitting of the Higgs multiplets. Published by the American Physical Society 2024