W-mass prediction in the complex NMSSM

In this work, we present our recent calculation of the $W$ boson mass in the complex NMSSM, which includes all state-of-the-art higher-order supersymmetric corrections to $\Delta r$. In particular, we include the full one-loop corrections and the leading andsub-leading two-loop corrections $\mathcal{O}(\alpha + \alpha_t\alpha_s +\left(\alpha_t+\alpha_\lambda+\alpha_\kappa\right)^2)$ from the $\rho$ parameter.We show some numerical investigations of the dependence of $\Delta\rho$ on the renormalization schemes and of the dependence of $M_W$ on some selected parameters. We also discuss comparisons between some public tools which compute $M_W$ in the NMSSM.Finally we present a new version of the public Fortran code, {\tt NMSSMCALC}, including a new $M_W$ prediction.