Supersymmetric Relations Among Electromagnetic Dipole Operators

Supersymmetric contributions to all leptonic electromagnetic dipole operators have essentially identical diagramatic structure. With approximate slepton universality this allows the muon anomalous magnetic moment to be related to the electron electric dipole moment in terms of supersymmetric phases, and to radiative flavor changing lepton decays in terms of small violations of slepton universality. If the current discrepancy between the measured and Standard Model values of the muon anomalous magnetic moment is due to supersymmetry, the current bound on the electron electric dipole moment then implies that the phase of the electric dipole operator is less than 2 × 10−3. Likewise the current bound on μ → eγ decay implies that the fractional selectron–smuon mixing in the left–left mass squared matrix, δmμ̃ẽ/m 2 l̃ , is less than 10−4. These relations and constraints are fairly insensitive to details of the superpartner spectrum for moderate to large tan β. High precision measurements of low energy processes can often provide useful probes of physics beyond the Standard Model. Many processes of this type involve the coupling of a photon to Standard Model fermions, such as anomalous magnetic dipole moments [1], electric dipole moments (EDMs) [2], and rare radiative decays [3]. The effective operators which describe these interactions are all of the electromagnetic dipole form. The magnitude of these operators in general depends on the overall scale and details of the heavy particle mass spectrum as well as the interactions which violate the requisite symmetries. In supersymmetric theories the one-loop contributions to all the electromagnetic dipole operators have very similar diagramatic structure. In this paper we point out that in the lepton sector this similarity allows the muon anomalous magnetic moment to be related to the electron EDM in terms of the phase of the electromagnetic dipole operator, and to the rate for radiative lepton decays, μ → eγ, τ → μγ and τ → eγ, in terms of violations of slepton universality. For moderate to large tanβ and with approximate slepton universality these relations turn out to be fairly insensitive to details of the superpartner mass spectrum. If the discrepancy between the current measured value of the muon anomalous magnetic moment [4] and the Standard Model value is interpreted as arising from supersymmetry, fairly model independent bounds can be obtained on the phase of the dipole operator and fractional flavor violating splitting in the slepton mass squared matrix from the current experimental bounds on the electron EDM and li → ljγ decays respectively. Alternately, an upper limit on the supersymmetric contribution to the muon anomalous magnetic moment provides a lower limit for the most stringent possible bounds arising from the electron EDM and li → ljγ decays. The relations among the supersymmetric electromagnetic dipole operators presented here are particularly interesting and useful in light of the recent high precision measurement of the muon anomalous magnetic moment [4]. The relation between the muon anomalous magnetic moment and radiative flavor changing lepton decays has previously been considered in the context of supersymmetric see-saw models of neutrino masses [5]. In the next section the structure of the various supersymmetric contribu-