Vacuum stability and the hierarchy problem in a fermionic dark matter model

We consider an extension to the Standard Model (SM) with four new fields, including scalar( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> </a:math> ), spinor ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>ψ</c:mi> <c:mrow> <c:mn>1</c:mn> <c:mo>,</c:mo> <c:mn>2</c:mn> </c:mrow> </c:msup> </c:math> ), and vector( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>V</e:mi> <e:mi>μ</e:mi> </e:msub> </e:math> ), under a new <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:mo stretchy="false">)</g:mo> </g:math> gauge group in the hidden sector. The scalar particle interacts with the SM Higgs particle and is an intermediary between the dark and the SM parts. Our dark matter (DM) candidate is the spinor particle. We show that the model successfully explains the relic density of the DM in the universe and evades the strong bounds from direct detection experiments while respecting the theoretical constraints and the vacuum stability conditions. In addition, we study the hierarchy problem within the Veltman approach by solving the renormalization group equations at one-loop. We demonstrate that the addition of the new fields contributes to the Veltman parameters, which, in turn, results in satisfying the Veltman conditions much lower than the Planck scale. For our DM model, we find one representative point in the viable parameter space which satisfies also the Veltman conditions at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi mathvariant="normal">Λ</k:mi> <k:mo>=</k:mo> <k:mn>1</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>TeV</k:mi> </k:math> . Therefore, the presence of the extra particle solves the fine-tuning problem of the Higgs mass.