On the neutral scalar sector of the general R-parity violating MSSM

Starting out from the most general, gauge invariant and renormalisable scalar potential of the R-parity violating MSSM and performing a calculable rotation to the scalar fields we arrive at a basis where the sneutrino VEVs are zero. The advantage of our rotation is that, in addition, we obtain diagonal soft supersymmetry breaking sneutrino masses and all potential parameters and VEVs real, proving that the MSSM scalar potential does not exhibit spontaneous or explicit CP-violation at tree level. The model has five CP-even and four CP-odd physical neutral scalars, with at least one CP-even scalar lighter than MZ. We parametrise the neutral scalar sector in a way that resembles the parametrisation of the R-parity conserving MSSM, analyse its mass spectrum, the coupling to the gauge sector and the stability of the potential.