On Soft Breaking and CP Phases in the Supersymmetric Standard Model

We consider a class of N=1 supersymmetric extensions of the Standard Model in which the soft breaking sector is CP conserving at the GUT scale. We study the question of whether the presence of explicit CP violation in the Yukawa sector of the theory induces through renormalization effects CP violating phases in the soft terms, which could lead to observable effects. A clear pattern appears in the structure of phases in the soft sector. In particular, the inclusion of intergenerational mixing induces large phases in the flavour mixing entries of the trilinear soft breaking terms, whereas the diagonal entries remain real. A mechanism is proposed for generating through chargino exchange a contribution to the neutron electric dipole moment which can be a few orders of magnitude larger that that of the Standard Model, although still out of reach of experimental tests. We comment on the possible relevance of these phases for baryogenesis at the weak scale in minimal supersymetric scenarios, recently considered in the literature. Introduction In this letter we reconsider the problem of CP violation in supersymmetric extensions of the standard Glashow-Weinberg-Salam model (SM) of the electroweak interactions. In particular, we want to address the question of whether the presence of a CP violating phase (δKM) in the Yukawa sector of the supersymmetric theory may induce, through the running of the relevant parameters from the GUT scale to the Fermi scale, CP violation in the soft breaking sector. In general, it is well known that additional phases may appear in the minimal supersymmetric version of the SM (MSSM) due to the complexity of the soft SUSY breaking couplings. On the other hand, it is also well known that the presence of these extra phases (collectively δsoft) would induce a 1–loop contribution to the electric dipole moment (EDM) of the neutron, which for squarks and gluino masses of O(100 GeV ) is too large and requires δsoft < 0.01 [1]. From this point of view it may be natural demanding the absence of these phases altogether by assuming that the soft breaking sector, as derived from the flat limit (MP lanck → ∞) of an underlying supergravity theory, is CP conserving. However, the presence of an explicit CP violation in the Yukawa sector of the “effective” theory at the GUT scale may reintroduce some CP violation in the soft breaking sector at the Fermi scale, thus posing again the question of its relevance for present day CP odd observables. As a matter of fact, the presence of a small explicit CP violation δsoft ≃ 10 −10 in the trilinear component of the soft breaking potential has been advocated by the authors of ref. [2] in order to trigger the baryon–antibaryon asymmetry in the early universe in a finite temperature MSSM scenario. It is worth stressing that the correct sign of the baryon–antibaryon asymmetry depends crucially on the sign of the explicit soft breaking phase. It is therefore interesting to study whether the δKM induced phases previously mentioned have the correct size and sign to support such a scenario. Our main conclusion is that within the simplified approach of ref. [2], where flavour mixing in the effective potential is neglected, no appreciable phases are induced in the relevant soft breaking parameters. It turns out, however, that due to the presence of flavour mixing large CP violating phases may be induced in the off–diagonal components of the trilinear soft breaking couplings. We study the implications of such a large phases for the EDM of the neutron and find that they induce a contribution consistent with the present upper bound, although it can be as much as four orders of magnitude larger than the SM contribution to the elementary EDM of the quarks. The relevance of these off-diagonal components for the analysis of ref. [2] deserves a separate discussion.