Discrete dark matter with light Dirac neutrinos

We propose a new realization of light Dirac neutrino mass and dark matter (DM) within the framework of a non-Abelian discrete flavor symmetry based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>A</a:mi><a:mn>4</a:mn></a:msub></a:math> group. In addition to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>A</c:mi><c:mn>4</c:mn></c:msub></c:math>, we also consider a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>Z</e:mi><e:mn>2</e:mn></e:msub></e:math> and an unbroken global lepton number symmetry <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:mi>L</g:mi></g:msub></g:math> to keep unwanted terms away while guaranteeing the Dirac nature of light neutrinos. The field content, their transformations, and flavon vacuum alignments are chosen in such a way that the type-I Dirac seesaw generates only one light Dirac neutrino mass while the other two masses arise from scotogenic contributions at one-loop. This leads to the Dirac scoto-seesaw framework, a generalization of the widely studied scoto-seesaw model to Dirac neutrinos. The symmetry breaking of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>A</k:mi><k:mn>4</k:mn></k:msub></k:math> leaves a remnant <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi mathvariant="script">Z</m:mi><m:mn>2</m:mn></m:msub></m:math> symmetry responsible for stabilizing DM. Dirac nature of light neutrinos introduces additional relativistic degrees of freedom <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi mathvariant="normal">Δ</p:mi><p:msub><p:mi>N</p:mi><p:mi>eff</p:mi></p:msub></p:math> within reach of cosmic microwave background experiments.