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We present a full one-loop renormalisation of the Higgs sector of theNext-to-Minimal- Supersymmetric-Standard-Model (NMSSM) and its implementationwithin SloopS, a code for the automated computations of one-loop processes intheories beyond the Stan- dard Model. The present work is the sequel to thestudy we performed on the renor- malisation of the sectors of the NMSSMcomprising neutralinos, charginos and sfermions thereby completing the fullone-loop renormalisation of the NMSSM. We have investi- gated severalrenormalisation schemes based on alternative choices (on-shell or DR) of thephysical parameters. Special attention is paid to the issue of the mixingbetween physical fields. To weigh the impact of the different renormalisationschemes, the partial widths for the decays of the Higgs bosons intosupersymmetric particles are computed at one-loop. In many decays largedifferences between the schemes are found. We discuss the origin of thesedifferences. In particular we study two contrasting scenarios. The first modelis MSSM-like with a small value for the mixing between the doublet and sin-glet Higgs superfields while the second model has a moderate value for thismixing. We critically discuss the issue of the reconstruction of the underlyingparameters and their counterterms in the case of a theory with a large numberof parameters, such as the NMSSM, from a set of physical parameters. In thepresent study this set corresponds to the minimum set of masses for theimplementation of the on-shell schemes.

One-loop renormalisation of the NMSSM in SloopS 2: the Higgs sector