The stau exchange contribution to muon g − 2 in the decoupling solution

We study the possibility that the lepton-flavor changing process can induce the suitable magnitude of the muon anomalous magnetic moment (gμ − 2) in the decoupling solution to the flavor problem in the minimal supersymmetric standard model. Our analyses introduce the flavor mixings of leftand right-handed stau and smuon phenomenologically. It is found that if both the leftand right-handed sleptons have sizable flavor mixings, the correction to gμ − 2 from the lighter slepton can reach to 10 −9 while the correction to the branching ratio of τ → μγ satisfies the current experimental bound. On the other hand, when only the left-handed or right-handed sleptons have the large flavor mixing, the suitable magnitude of the correction to gμ−2 is not realized owing to the experimental bound of τ → μγ. While the minimal supersymmetric (SUSY) standard model (MSSM) is one of the promising candidates beyond the standard model (SM), introduction of the SUSY breaking terms may lead to the flavor changing neutral current (FCNC) and CP problems. The decoupling solution (sometime called as “effective SUSY”) [1] has been proposed to solve these problems. In this solution, the squarks and sleptons in the first and second generations are heavy enough so that their contributions to the FCNC or CP violating processes are sufficiently suppressed. On the other hand, the gauginos, higgsinos and the sfermions in the third generation are appropriately light to satisfy the naturalness condition on the Higgs boson mass. In other words, the sfermions whose fermionic partners have the large Yukawa couplings belong to the “lighter group” because they are responsible for the quantum corrections to the Higgs boson mass. The muon anomalous magnetic moment, conventionally parameterized as aμ ≡ (gμ−2)/2, has been measured precisely by the E821 experiment at the Brookhaven National Laboratory. The current world average of aμ is about 2.6-σ away from the SM prediction [2]: aμ(exp)− aμ(SM) = 426(165)× 10 , (1) which may suggest that new physics exists around the TeV scale [3]. After the announcement, the many works to understand the implication of (1) to physics beyond the SM have been done [4]. It will take more time to confirm if (1) is really a signal of new physics from theoretical and experimental points of view. However, once it is confirmed, the constraint on models beyond the SM will be stronger. It has been considered that the decoupling solution is disfavored from this observation, since the smuon and the muon-sneutrino are too heavy to give a sizable contribution to gμ−2. However, if the stau and the tau-sneutrino have the couplings to the muon in this model, their mediation may be able to enhance gμ−2 suitably. When tanβ is small, the Yukawa coupling of tau lepton is also small, and it is model dependent whether the stau is classified to the lighter or heavier group in the decoupling solution. In the case, even if one slepton belongs to the lighter group, the slepton may not necessarily correspond to the scalar component of the tau-lepton superfield and may be some mixture of the stau and the smuon. The neutrino oscillation data [5] may suggest the left-handed stau and smuon have a large mixing [6]. If the energy scale of the SUSY-breaking mediation to the MSSM is higher than the mass scale of the right-handed neutrino, this spectrum should be realized so that the tau-neutrino Yukawa coupling does not destabilize