Implications of the neutron electric dipole moment for supersymmetric models

Abstract

The electric dipole moment of the neutron in the supersymmetric standard models is reconsidered. Assuming CP-violating phases are not much suppressed, we explore the region of the supersymmetric mass parameters allowed by the experiments. The chargino-loop diagram gives constraints more stringently than the gluino-and neutralino-loop diagrams. It is found that the squark masses should be larger than -1 TeV, while the charginos and the neutralinos could be as light as a few hundred GeV. PACS number(s1: 13.40.Fn, 11.30.Er, 12.15.Ji, 14.80.Ly It was found soon after supersymmetric grand unified models were proposed [I] that the electric dipole moment (EDM) of the neutron could have a large value in the supersymmetric extensions of the standard model [2,3]. If CP-violating phases inherent in these supersymmetric standard models are of order unity and supersymmetric particles have masses of order 100 GeV, then the EDM of the neutron is predicted to be 1 0 -~~-1 0 -~~e cm.From the experimental bounds d , 1 < 1oP2'e cm 141, therefore, it is usually considered that the ~p-violatIng phases would be quite small [2,3,5]. However, the supersymmetric particles might not be as light as 100 GeV, since no signal has been found up to now in high-energy collider experiments. Moreover, the natural magnitudes of the CP-violating phases should be of order unity unless there is some mystic symmetry forcing the phases to vanish. We may have to reconsider what the EDM of the neutron implies for the supersymmetric standard models.In this Brief Report we discuss the EDM of the neutron in a manner alternative to the conventional one. If the supersymmetric particles are heavy enough, the CPviolating phases do not have to be unnaturally small. Assuming that the CP-violating phases are not suppressed, we explore the values of the supersymmetric mass parameters compatible with the experiments [6]. For definiteness, our discussions are based on the standard N = 1 supergravity models [7].There are three operators contributing to the EDM of the neutron: the quark electric dipole operator, the Weinberg gluonic operator, and the quark chromoelectric dipole operator [8,9]. These operators get non-negligible QCD corrections. In this Brief Report, however, we shall discuss only the familiar quark electric dipole operator and shall not take the QCD correction into consideration. This would be justified from the following two points. First, these gluonic contributions would be smaller than that of the quark electric dipole operator contrary to the case in the nonsupersymmetric standard model. Second, we can get at least the necessary conditions of being not contradictory to the experiments because the QCD correction does not reduce the contribu-tion of the quark electric dipole operator.The quark electric dipole operator is contributed to at the one-loop level by the Feynman diagrams in which propagate the squarks and one of the charginos mi, the neutralinos xi, and the gluinos g. These EDM operators change the chirality of the quark. In the chargino...

Constraints on supersymmetric soft phases from renormalization group relations

“…The gluino [11] and chargino [7] contributions appear in the literature. While an expression for the neutralino contribution is given by Kizukuri and Oshimo [7], it is written in terms of 4 × 4 complex unitary matrices which must be determined numerically.…”

The soft supersymmetry-breaking Lagrangian: theory and applications

“…Early references include [310,311,312,313,314,315,316,201,317] and slightly later references include [318,319,320,321,322,323]. Using the rough estimate of the one-loop EDMs for e.g.…”

ConstrainingCPviolating phases of the minimal supersymmetric standard model

“…As previous calculations have shown [12,13,14], the diagrams in Figure 1b lead to EDMs in violation of the current limits of d e < 4.3×10 −27 ecm [25] and d n < 6.3× 10 −25 ecm [26] unless SUSY particles are heavier than O(1)T eV or the CP violating phases are less than O(10 −2 ). However, small phases in fact are not inevitable, for recently it has been pointed out [15,16] that a cancellation can occur among the various SUSY diagrams, allowing O(1) CP violating phases to be consistent with the current EDM experimental limits.…”

“…The simplest SUSY models can not satisfy the experimental EDM bounds without either setting all SUSY CP violating phases to zero or raising SUSY particle masses above 1 T eV [12,13,14]. Recent works have noted, however, that the supergravity-broken MSSM with O(1) phases for the gaugino masses M i , triscalar coupling A, and Higgs coupling parameter µ, and no flavor-mixing beyond the standard CKM matrix can be consistent with existing limits on the electric dipole moments (EDMs) of the electron and neutron [15,16] .…”