Renormalisation of the Higgs sector of the NMSSM. Application to Higgs decays

I will first recollect some memories of my collaboration with Shimizu-sensei, a collaboration that mainly covered the topic of renormalisation and loop corrections. I will then describe the renormalisation of the Higgs sector of the NMSSM, this work could be seen as a natural continuation of the long collaboration I have had with the Minami-Tateya group. This study has been done with Genevieve Belanger, Guillaume Chalons and Vincent Bizouard. Several on-shell renormalisation schemes as well as a mixed on-shell (DR) over bar scheme are analysed. Using SloopS, a code that can perform automatic computation of one-loop corrections, the one loop electroweak corrections to the partial widths of the pseudoscalar and scalar Higgses into lighter Higgses and/or neutralino/charginos are computed.