Constraints on supersymmetric soft phases from renormalization group relations

Abstract

By using relations derived from renormalization group equations (RGEs), we find that strong indirect constraints can be placed on the top squark mixing phase in A t from the electric dipole moment of the neutron (d n ). Since m t is large, any GUT-scale phase in A t feeds into other weak scale phases through RGEs, which in turn contribute to d n . Thus CP -violating effects due to a weak-scale A t are strongly constrained. We find that |ImA EW t | must be smaller than or of order |ImB EW |, making the electric dipole moment of the top quark unobservably small in most models. Quantitative estimates of the contributions to d n from A u , A d and B show that substantial fine-tuning is still required to satisfy the experimental bound on d n . While the low energy phases of the A's are not as strongly constrained as the phase of B EW , we note that the phase of a universal A GU T induces large contributions in the phase of B EW through RGEs, and is thus still strongly constrained in most models with squark masses below a TeV.

CP violation in top physics

“…We will demonstrate that the prediction made in [123] depends on the GUT-scale boundary conditions, and therefore may be significantly relaxed to yield a large CP-violating phase in the A t term compatible with the existing experimental limit on the NEDM. This should encourage SUSY CP violation studies in top quark systems as they may well be the only venue for constraining arg(A t ) in high energy experiments at colliders in the foreseeable future.…”

“…However, in a more constrained SUSY version, one can reduce the number of the physical CP-odd phases in the theory. In this case the RGE given above are crucial for determining the SUSY CP-violating phases at the EW-scale [123]. We will return to this point later when we discuss the N = 1 minimal low energy SUGRA -GUT model.…”

“…Instead of studying the RGE for the full theory, one needs only consider a complete subset of the RGE of the complex parameters in the effective theory. Taking only the top and bottom Yukawa couplings and neglecting small effects from the other Yukawa couplings, such a complete subset was given in [123]: …”

“…It was stated in [123] that using the relations obtained from the Renormalization Group Equations (RGE) of the imaginary parts in the SUSY Lagrangian, combined with the severe constraint on the low energy phase of the Higgs mass parameter, µ, from the present experimental limit [124] on the NEDM, the phase in A t at low energy scales is likely to be very small provided one imposes some definite boundary conditions for the SUSY soft breaking terms. As a consequence, at high energies, any CP-nonconserving effect that is driven by arg(A t ) will then be suppressed leaving top quark reactions almost insensitive to CP-violating effects of a SUSY origin in models with these assumptions.…”

Rare kaon decays in SUSY with non-universalAterms

“…According to the results of Eqs. (9) and (11) and the constraints in Table 1, the BRs of relevant rare kaon decays are found as follows:…”