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

The lightest neutralino ($\tilde{\chi}_1^0$) is a promising dark matter (DM) candidate in the R-parity conserving minimal supersymmetric standard model (MSSM). In this work, we focus on dominantly Higgsino-like and Wino-like $\tilde{\chi}_1^0$ DM, with small admixtures of gauginos and Higgsinos, respectively. In particular, we explore large one-loop corrections to the $\tilde{\chi}_1^0 \tilde{\chi}_1^0Z$ vertex, which can significantly affect the estimation of the spin-dependent $\tilde{\chi}_1^0$-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 $\tilde{\chi}_1^0$ is dominantly Higgsino-like, the radiative corrections (including the contributions from the respective counterterms) are substantial and can enhance the $\tilde{\chi}_1^0\tilde{\chi}_1^0Z$ vertex by up to $\sim 120\%$ for the benchmark scenarios we have considered. Further, for an almost pure Wino-like $\tilde{\chi}_1^0$, the increment in the $\tilde{\chi}_1^0\tilde{\chi}_1^0Z$ 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 $\tilde{\chi}_1^0$.