Neutralino decay of MSSM neutral Higgs bosons

We compute the one loop corrected effective Lagrangian for the neutralino-neutralino-neutral Higgs interactions $\chi^{0}_{\ell} \chi^{0}_kH^{0}_m$. The analysis completes the previous analyses where similar corrections were computed for the $\bar{f} f H^{0}_m$ couplings, where $f$ stands for Standard Model quarks and leptons and for the chargino-chargino-neutral Higgs couplings $\chi^{+}_l \chi^{-}_kH^{0}_m$ within the minimal supersymmetric standard model MSSM. The effective one loop Lagrangian is then applied to the computation of the neutral Higgs decays. The sizes of the supersymmetric loop corrections of the neutral Higgs decay widths into $\chi^{0}_{\ell} \chi^{0}_k$ (${\ell}=1,2,3,4$; $k=1,2,3,4$) are investigated and the supersymmetric loop correction is found to be in the range of $\sim 10%$ in significant regions of the parameter space. By including the loop corrections of the other decay channels $\bar{b} b$, $\bar{t} t$, $\bar{\tau} \tau$, $\bar{c} c$, and $\chi^{-}_i \chi^{+}_j$ ($i=1,2$; $j=1,2$), the corrections to branching ratios for $H^{0}_m\to \chi^{0}_{\ell} \chi^{0}_k$ can reach as high as 50%. The effects of CP phases on the branching ratio are also investigated. A discussion of the implications of the analysis for colliders is given.