Vector dark matter with Higgs portal in type II seesaw framework

We study the phenomenology of a vector dark matter (VDM) in a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mi>X</a:mi></a:msub></a:math> gauged extension of the Standard Model (SM), which is set in a type II seesaw framework. When this <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><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:math> symmetry is spontaneously broken by the vacuum expectation value (VEV) of a newly introduced complex scalar singlet, the gauge boson <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>Z</i:mi><i:mo>′</i:mo></i:msup></i:math> becomes massive. The stability of the dark matter (DM) is ensured by the presence of an exact charge conjugation symmetry resulting from the structure of the Lagrangian. On the other hand, the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>S</k:mi><k:mi>U</k:mi><k:mo stretchy="false">(</k:mo><k:mn>2</k:mn><k:msub><k:mo stretchy="false">)</k:mo><k:mi>L</k:mi></k:msub></k:math> triplet scalar facilitates light neutrino masses via the type II seesaw mechanism. We have studied the phenomenology of the usual WIMP DM, considering all possible theoretical and experimental constraints that are applicable. Due to the presence of a triplet scalar, the present framework can also accommodate the observed <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>2</o:mn><o:mi>σ</o:mi></o:math> deviation in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>h</q:mi><q:mo stretchy="false">→</q:mo><q:mi>Z</q:mi><q:mi>γ</q:mi></q:math> decay rate, recently measured at the LHC. The possibility of nonthermal production of DM from the decay of the singlet scalar has also been briefly discussed.