Scotogenic model from an extended electroweak symmetry

We argue that the higher weak isospin <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>3</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mi>L</a:mi></a:msub></a:math> manifestly unifies dark matter and normal matter in its isomultiplets for which dark matter carries a conserved dark charge while normal matter does not. The resultant gauge symmetry is given by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>3</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>C</e:mi></e:msub><e:mo stretchy="false">⊗</e:mo><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>3</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>L</e:mi></e:msub><e:mo stretchy="false">⊗</e:mo><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>X</e:mi></e:msub><e:mo stretchy="false">⊗</e:mo><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>G</e:mi></e:msub></e:math>, where the first factor is the color group, while the rest defines a scotoelectroweak theory in which <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>X</r:mi></r:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>G</t:mi></t:math> determine electric charge <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>Q</v:mi><v:mo>=</v:mo><v:msub><v:mi>T</v:mi><v:mn>3</v:mn></v:msub><v:mo>−</v:mo><v:mn>1</v:mn><v:mo>/</v:mo><v:msqrt><v:mn>3</v:mn></v:msqrt><v:msub><v:mi>T</v:mi><v:mn>8</v:mn></v:msub><v:mo>+</v:mo><v:mi>X</v:mi></v:math> and dark charge <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>D</x:mi><x:mo>=</x:mo><x:mo>−</x:mo><x:mn>2</x:mn><x:mo>/</x:mo><x:msqrt><x:mn>3</x:mn></x:msqrt><x:msub><x:mi>T</x:mi><x:mn>8</x:mn></x:msub><x:mo>+</x:mo><x:mi>G</x:mi></x:math>. This setup provides both appropriate scotogenic neutrino masses and dark matter stability as preserved by a residual dark parity <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>P</z:mi><z:mi>D</z:mi></z:msub><z:mo>=</z:mo><z:mo stretchy="false">(</z:mo><z:mo>−</z:mo><z:mn>1</z:mn><z:msup><z:mo stretchy="false">)</z:mo><z:mi>D</z:mi></z:msup></z:math>. Interpretation of the dark charge is further discussed, given that <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>S</db:mi><db:mi>U</db:mi><db:mo stretchy="false">(</db:mo><db:mn>3</db:mn><db:msub><db:mo stretchy="false">)</db:mo><db:mi>L</db:mi></db:msub></db:math> is broken at very high energy scale. Published by the American Physical Society 2024