Radiative corrections to the direct detection of the Higgsino- and wino-like neutralino dark matter: Spin-dependent interactions

The lightest neutralino (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mover accent="true"><a:mi>χ</a:mi><a:mo stretchy="false">˜</a:mo></a:mover><a:mn>1</a:mn><a:mn>0</a:mn></a:msubsup></a:math>) is a promising dark matter (DM) candidate in the R-parity conserving minimal supersymmetric standard model. In this work, we focus on dominantly Higgsino-like and wino-like <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mover accent="true"><e:mi>χ</e:mi><e:mo stretchy="false">˜</e:mo></e:mover><e:mn>1</e:mn><e:mn>0</e:mn></e:msubsup></e:math> DM, with small admixtures of gauginos and Higgsinos, respectively. In particular, we explore large one-loop corrections to the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mover accent="true"><i:mi>χ</i:mi><i:mo stretchy="false">˜</i:mo></i:mover><i:mn>1</i:mn><i:mn>0</i:mn></i:msubsup><i:msubsup><i:mover accent="true"><i:mi>χ</i:mi><i:mo stretchy="false">˜</i:mo></i:mover><i:mn>1</i:mn><i:mn>0</i:mn></i:msubsup><i:mi>Z</i:mi></i:math> vertex, which can significantly affect the estimation of the spin-dependent <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msubsup><o:mover accent="true"><o:mi>χ</o:mi><o:mo stretchy="false">˜</o:mo></o:mover><o:mn>1</o:mn><o:mn>0</o:mn></o:msubsup></o:math>-nucleon scattering cross section in the regions where such DM candidates are viable. We have used the on-shell renormalization scheme to estimate the relevant counterterm contributions. In the parameter region where <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msubsup><s:mover accent="true"><s:mi>χ</s:mi><s:mo stretchy="false">˜</s:mo></s:mover><s:mn>1</s:mn><s:mn>0</s:mn></s:msubsup></s:math> is dominantly Higgsino-like, the radiative corrections (including the contributions from the respective counterterms) are substantial and can enhance the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msubsup><w:mover accent="true"><w:mi>χ</w:mi><w:mo stretchy="false">˜</w:mo></w:mover><w:mn>1</w:mn><w:mn>0</w:mn></w:msubsup><w:msubsup><w:mover accent="true"><w:mi>χ</w:mi><w:mo stretchy="false">˜</w:mo></w:mover><w:mn>1</w:mn><w:mn>0</w:mn></w:msubsup><w:mi>Z</w:mi></w:math> vertex by up to <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mo>∼</cb:mo><cb:mn>120</cb:mn><cb:mo>%</cb:mo></cb:math> for the benchmark scenarios we have considered. Further, for an almost pure wino-like <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mover accent="true"><eb:mi>χ</eb:mi><eb:mo stretchy="false">˜</eb:mo></eb:mover><eb:mn>1</eb:mn><eb:mn>0</eb:mn></eb:msubsup></eb:math>, the increment in the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msubsup><ib:mover accent="true"><ib:mi>χ</ib:mi><ib:mo stretchy="false">˜</ib:mo></ib:mover><ib:mn>1</ib:mn><ib:mn>0</ib:mn></ib:msubsup><ib:msubsup><ib:mover accent="true"><ib:mi>χ</ib:mi><ib:mo stretchy="false">˜</ib:mo></ib:mover><ib:mn>1</ib:mn><ib:mn>0</ib:mn></ib:msubsup><ib:mi>Z</ib:mi></ib:math> vertex is up to 15%. The corresponding cross sections with the proton and the neutron can be changed by up to about 50%. In addition, including the electroweak box diagrams, the cross sections can be significantly enhanced, in particular, for the wino-like <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msubsup><ob:mover accent="true"><ob:mi>χ</ob:mi><ob:mo stretchy="false">˜</ob:mo></ob:mover><ob:mn>1</ob:mn><ob:mn>0</ob:mn></ob:msubsup></ob:math>.