Neutralino exchange corrections to the Higgs boson mixings with explicit $\mathrm{CP}$ violation

A calculus for the derivatives of the eigenvalues of the neutralino mass matrix with respect to the $\mathrm{CP}$ violating background fields is developed and used to compute the mixings among the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd Higgs sectors arising from the inclusion of the neutralino sector consisting of the neutralino, the Z boson, and the neutral Higgs bosons $\left({\chi }_i^0-Z-h^0-H^0\right)$ exchange in the loop contribution to the effective potential including the effects of large $\mathrm{CP}$ violating phases. Along with the top squark, bottom squark, tau slepton and chargino–$W$–charged-Higgs-boson $\left({\chi }^{+}-W-H^{+}\right)$ contributions computed previously the present analysis completes the one loop corrections to the Higgs boson mass matrix in the presence of large phases. $\mathrm{CP}$ violation in the neutral Higgs sector is discussed in the above framework with specific focus on the mixings of the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors arising from the neutralino sector. It is shown that numerically the effects of the neutralino exchange contribution on the mixings of the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors are comparable to the effects of the top squark and of the chargino exchange contributions and thus the neutralino exchange contribution must be included for a realistic analysis of mixings in the $\mathrm{CP}$ even and the $\mathrm{CP}$ odd sectors. Phenomenological implications of these results are discussed.