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

We present a full one-loop renormalisation of the Higgs sector of the Next-to-Minimal- Supersymmetric-Standard-Model (NMSSM) and its implementation within SloopS, a code for the automated computations of one-loop processes in theories beyond the Stan- dard Model. The present work is the sequel to the study we performed on the renor- malisation of the sectors of the NMSSM comprising neutralinos, charginos and sfermions thereby completing the full one-loop renormalisation of the NMSSM. We have investi- gated several renormalisation schemes based on alternative choices (on-shell or DR) of the physical parameters. Special attention is paid to the issue of the mixing between physical fields. To weigh the impact of the different renormalisation schemes, the partial widths for the decays of the Higgs bosons into supersymmetric particles are computed at one-loop. In many decays large differences between the schemes are found. We discuss the origin of these differences. In particular we study two contrasting scenarios. The first model is 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 this mixing. We critically discuss the issue of the reconstruction of the underlying parameters and their counterterms in the case of a theory with a large number of parameters, such as the NMSSM, from a set of physical parameters. In the present study this set corresponds to the minimum set of masses for the implementation of the on-shell schemes.