Muon g–2 and Neutrino Mass in a New Minimal Extension of the MSSM

If the one term (ν̂eμ̂ − êν̂μ)τ̂ c is added to the MSSM (Minimal Supersymmetric Standard Model) superpotential, the recently observed muon g–2 (anomalous magnetic moment) excess can be explained very simply by a light ν̃e. If the soft symmetrybreaking terms ν̂αĥ 0 2 − l̂αĥ2 are also added, realistic neutrino masses (with bimaximal mixing) are generated as well. ————– Talk given at the 7th Hellenic School and Workshops on Elementary Particle Physics, Corfu, Greece (September 2001). 1 Lepton numbers in supersymmetry The particle content of the Standard Model with two Higgs doublets as required in supersymmetry is given by L = (ν, l)L ∼ (1, 2,−1/2), Ē = l L ∼ (1, 1, 1), (1) Q = (u, d)L ∼ (3, 2, 1/6), Ū = uL ∼ (3∗, 1,−2/3), D̄ = dL ∼ (3∗, 1, 1/3), (2) Φ1 = (φ 0 1, φ − 1 )L ∼ (1, 2,−1/2), Φ2 = (φ2 , φ2)L ∼ (1, 2, 1/2), (3) under SU(3)×SU(2)L ×U(1)Y . In the Standard Model without supersymmetry, the global quantum numbers Le, Lμ, Lτ and B are separately conserved automatically. In the Minimal Supersymmetric Standard Model (MSSM), they are conserved by assumption, i.e. by the removal of the allowed terms λLLĒ, λLQD̄, λŪD̄D̄, and μ′LΦ2. In that case, the wellknown R parity, i.e. R ≡ (−1)3B+L+2J , is conserved. On the other hand, these terms need not all be forbidden. In particular, the really important restriction is only for the product λλ to be very small or zero to prevent rapid proton decay. Hence a class of R-parity violating models has been widely discussed in the literature which assumes λ = 0, but allows nonzero values of λ, λ, and μ. This means that B is conserved, but L is not, so that there can be neutrino mass and lepton-flavor violation, etc. Actually, there are 17 well-defined models of lepton numbers in supersymmetry, as pointed out already many years ago [1]. Consider the following sets of terms in the superpotential: W (1) = hiΦ1LiĒi + h d ijΦ1QiD̄j + h u ijΦ2QiŪj + μ0Φ1Φ2, (4) W (2) = feL3L1Ē1 + fμL3L2Ē2 + μ3L3Φ2 + fijL3QiD̄j , (5) W (3) = feμτL1L2Ē3, (6) 2 W (4) = feμL3L1Ē2 + fμeL3L2Ē1, (7) W (5) = f ′ eL2L1Ē1 + f ′ τL2L3Ē3 + μ2L2Φ2 + f ′ ijL2QiD̄j . (8) Five models can then be defined with lepton numbers for (e, μ, τ) as shown below. Model 1 : W = W (1) +W , [(1, 0), (0, 1), (0, 0)] (9) Model 2 : W = W (1) +W , [(1, 0), (0, 1), (1, 1)] (10) Model 3 : W = W (1) +W (2) +W , [1, − 1, 0] (11) Model 4 : W = W (1) +W (2) +W , [1, 1, 0] (12) Model 5 : W = W (1) +W (2) +W , [1, 0, 0]. (13) Models 1 and 2 have two conserved lepton numbers. Models 3, 4, and 5 have one conserved lepton number. Each model has also 3 permutations, hence there are 1 + 5 × 3 + 1 = 17 models, ranging from the MSSM with conserved R parity to the most general R parity violating model which conserves B. 2 Muon anomalous magnetic moment In the presence of supersymmetric particles, there are certainly additional contributions [2] to the muon anomalous magnetic moment [3]. To obtain an excess ∆aμ ∼ 10, light ν̃μ, μ̃, and large tan β are required, thereby restricting the MSSM parameter space. In this talk I will present a new minimal extension [4] of the MSSM based on Model 2 of the last section, such that ∆aμ is explained entirely by the single new term we add to the superpotential, i.e. ∆Ŵ = h(ν̂eμ̂− êν̂μ)τ̂ . (14) The new interaction terms of the resulting Lagrangian are then given by Lint = h(νeμ− eνμ)τ̃ c + h(νeτ μ̃− eτ ν̃μ) + h(μτ ν̃e − νμτ ẽ) +H.c. (15) 3 Hence there are 2 contributions to the muon anomalous magnetic moment from ν̃e and τ̃ c exchange. They are easily evaluated [5] and we obtain ∆aμ = hmμ 96π2 (