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An analysis of the electric dipole moment (EDM) of the neutron and of the leptons in the minimal supersymmetric standard model (MSSM) with the most general allowed set of CP violating phases without generational mixing is given. The analysis includes the contributions from the gluino, the chargino and the neutralino exchanges to the electric dipole operator, the chromoelectic dipole operator, and the CP violating purely gluonic dimension six operator. It is found that the EDMs depend only on certain combination of the CP phases. The independent set of such phases is classified. The analysis of the EDMs given here provides the framework for the exploration of the effects of large CP violating phases on low energy phenomena such as the search for supersymmetry at colliders, and in the analyses of dark matter consistent with the experimental limits on EDMs via the mechanism of internal cancellations. It is well known that supersymmetric theories contain many new sources of CP violation and can produce large contributions to the electric dipole moments of the neutron and of the electron[1-5]. With normal size CP violating phases, i.e., phases O(1), and with SUSY spectrum in the TeV range, the neutron and the electron EDMs already lie in excess of the current experimental limit, which for the neutron is[6] dn < 1.1× 10 ecm and for the electron is [7] de < 4.3× 10 ecm. Two approaches have usually been adopted to rectify this situation. The first is to make the phases small, i.e. O(10)[1], and the other is to use mass suppression by making the SUSY spectrum heavy, i.e., in the several TeV range[4]. The first case, however, represents fine tuning, while the second violates naturalness and also makes the SUSY spectrum so heavy that it may not be accesssible even at the LHC. Recently, a third possibility was proposed[8], i.e., that of internal cancellations in EDMs reducing them below the experimental limits even for CP violating phases O(1). In recent works the importance of CP violating phases on low energy phenomenona has been recognized[9, 10, 11]. In ref.[10] it is shown that large CP violating phases can affect sparticle searches at colliders and in ref.[11] it is found that large CP violating phases can produce large effects on the neutralino relic density consistent with the experimental constraints on the the neutron and on the electron EDM via the cancellation mechanism[8]. However, as one goes beyond the framework of minimal supergravity to include non-universalities in the soft SUSY breaking parameters one finds that new CP violating phases arise which also affect low energy phenomena. Currently the effect of CP violating phases beyond the two CP phases allowed by the minimal supergravity cannot be investigated because the analytic computations of the EDMs in terms of these phases do not exist in the literature and consequently the EDM constraints arising from experiment cannot be implemented. The purpose of this Letter is to provide the analytic results for the EDMs beyond the minimal supergravity model by inclusion of all CP violating phases in the framework of MSSM. As is conventional we ignore generational mixings whose effects are known to be small. We analyse all one loop diagrams with the gluino, the chargino, and the neutralino exhanges for the electric dipole, and the chromoelectric dipole operators allowing for all phases. We also analyse the two loop diagrams which contribute to the purely gluonic dimension six operator allowing again for all CP violating phases. In MSSM the CP violating phases relevant for the analysis of the EDM’s arise

The Neutron and the Lepton EDMs in MSSM, Large CP violating Phases, and the Cancellation Mechanism