Beyond the MSSM Higgs with d=6 effective operators

We continue a previous study of the MSSM Higgs Lagrangian extended by all effective operators of dimension d=6 that can be present beyond the MSSM, consistent with its symmetries. By supersymmetry, such operators also extend the neutralino and chargino sectors, and the corresponding component fields Lagrangian is computed onshell. The corrections to the neutralino and chargino masses, due to these operators, are computed analytically in function of the MSSM corresponding values. For individual operators, the corrections are small, of few GeV for the constrained MSSM (CMSSM) viable parameter space. We investigate the correction to the lightest Higgs mass, which receives, from individual operators, a supersymmetric correction of up to 4 (6) GeV above the 2-loop leading-log CMSSM value, from those CMSSM phase space points with: EW fine tuning Delta<200, consistent with WMAP relic density (3$\sigma$), and for a scale of the operators of M=10 (8) TeV, respectively. Applied to the CMSSM point of minimal fine tuning (Delta=18), such increase gives an upper limit $m_h=120(122)\pm 2$ GeV, respectively. The increase of m_h from individual operators can be larger ($\sim$ 10-30 GeV) for those CMSSM phase space points with Delta>200; these can now be phenomenologically viable, with reduced Delta, and this includes those points that would have otherwise violated the LEP2 bound by this value. The neutralino/chargino Lagrangian extended by the effective operators can be used in studies of dark matter relic density within extensions of the MSSM, by implementing it in public codes like micrOMEGAs.