One-loop calculations of the decay of the next-to-lightest neutralino in the MSSM

We calculate one-loop corrections to the decays of the next-to-lightest neutralino $\tilde{\chi}_2^0$ into the lightest neutralino $\tilde{\chi}_1^0$ and two leptons; this includes diagrams where a real photon is emitted. In cases where two-body decays $\tilde{\chi}_2^0 \to \tilde{l}^\pm_1 l^\mp \to \tilde{\chi}_1^0 l^- l^+$ are kinematically allowed, we calculate these decays both with and without the single-pole approximation, and find consistent results. For example, for the minimal supergravity parameter set SPS1a, the integrated partial widths (the branching ratios) for $\tilde{\chi}_2^0\to \tilde{\chi}_1^0 l^- l^+ (l = e, \mu)$ are enhanced by about 15.5 (13.6) percent by the one-loop corrections. We also study a scenario where $\tilde \chi_2^0$ cannot undergo two-body decays, and find corrections to these branching ratios of about 13.6 percent. Moreover, we study the dilepton invariant mass ($M_{l^+ l^-}$) distribution, whose endpoint is often used in analyses that aim to reconstruct (differences of) supersymmetric particle masses at the LHC. The shape of this distribution is altered significantly by the emission of hard photons. For example, for the SPS1a parameter set the peak of the $M_{l^+ l^-}$ distribution is shifted by several GeV when these contributions are included.