Left-right symmetry just beyond the MSSM, electric dipole moment of neutron and HERA leptoquarks

The supersymmetric left-right (SUSYLR) models solve several of the unnaturalness problems of the MSSM such as the R-parity and SUSY CP problems. If further the $W_R$ mass is in the TeV range, then it also provides a solution to the strong CP problem without the need for an axion. A crucial prediction of this model is the electric dipole moment of the neutron $\simeq 10^{-25}-10^{-26}$ ecm arising from the one loop contribution to the strong CP parameter $\bar{theta}$. Other predictions of the model are a light doubly charged Higgs boson and its fermionic partner with masses in the several hundred GeV range. We then show this model can be extended to include the leptoquarks that can explain the HERA high $Q^2$ anomaly without giving up R-parity conservation.