Effective theory of light Dirac neutrino portal dark matter with observable ΔNeff

We study the possibility of light Dirac neutrino portal dark matter (DM) in an effective field theory setup. Dirac nature of light neutrino automatically includes its right chiral part <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>ν</a:mi><a:mi>R</a:mi></a:msub></a:math> which, in our setup, also acts like a portal between DM and the standard model (SM) particles. Considering a Dirac fermion singlet DM stabilized by an unbroken <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>Z</c:mi><c:mn>2</c:mn></c:msub></c:math> symmetry, we write down all possible dimension-6 effective operators involving DM-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>ν</e:mi><e:mi>R</e:mi></e:msub></e:math> as well as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>ν</g:mi><g:mi>R</g:mi></g:msub></g:math>-SM which conserve <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>Z</i:mi><i:mn>2</i:mn></i:msub></i:math>, global lepton number and SM gauge symmetries. DM thermalization also ensures the thermalization of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>ν</k:mi><k:mi>R</k:mi></k:msub></k:math>, leading to enhanced effective relativistic degrees of freedom <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>N</m:mi><m:mi>eff</m:mi></m:msub></m:math>, within reach of future cosmic microwave background (CMB) experiments. We study the complementarity among DM and CMB related observations for different Lorentz structures of effective operators. We also propose a UV complete gauged B-L symmetric model with Dirac neutrino portal dark matter.