Anomalous Neutrino Interaction, Muon g-2, and Atomic Parity Nonconservation

We propose a simple unified description of two recent precision measurements which suggest new physics beyond the Standard Model of particle interactions, i.e. the deviation of sin θW in deep inelastic neutrino-nucleon scattering and that of the anomalous magnetic moment of the muon. Our proposal is also consistent with a third precision measurement, i.e. that of parity nonconservation in atomic Cesium, which agrees with the Standard Model. The minimal Standard Model (SM) of particle interactions is consistent with all present experimental data with only a few possible exceptions. One such is a recent measurement [1] of the electroweak parameter sin θW from νμ and ν̄μ interactions with nucleons, which claims a three-standard-deviation departure from the SM prediction. Another is the measurement [2] of the anomalous magnetic moment of the muon, which originally claimed a value higher than the SM prediction by 2.6 standard deviations [3], but is now revised down to only 1.6σ after a theoretical sign error has been corrected [4]. A third important constraint comes from the measurement [5] of parity nonconservation in atomic Cesium, which was thought to be in disagreement with the SM, but subsequent improved theoretical calculations [6] have shown it to be in good agreement. In addition, the phenomonena of neutrino oscillations are now well-established [7, 8] which suggest strongly that neutrinos have mass and mix with one another. In this paper we propose a simple unified description of all the above effects by extending the SM to include the gauge symmetry Lμ − Lτ [9]. The relevance of this symmetry to the muon g − 2 value and neutrino mass has been discussed by us in a previous paper [10, 11]. Here we focus on how it can also explain the NuTeV result [1] and its other possible experimental consequences. Our model assumes the anomaly-free gauge symmetry U(1)X with gauge boson X which couples to (νμ, μ)L, μR with charge +1 and to (ντ , τ)L, τR with charge −1, but not to any other fermion. This means that it has the contribution ∆aμ = g Xm 2 μ 12π2M X (1) to the muon anomalous magnetic moment. It also contributes to νμ and ν̄μ interactions, but since X does not couple to quarks, the NuTeV result [1] is only affected if X mixes with the Z boson of the SM. This also applies to atomic parity nonconservation. In our previous paper [10], we assume for simplicity that X − Z mixing is zero by the 2 imposition of an interchange symmetry in the Higgs sector, but we also mention that this symmetry cannot be maintained for the entire theory, so that a small deviation is to be expected. This small deviation (corresponding to a mixing angle of order 10) turns out to be just what is needed to explain the NuTeV result, as shown below. The Higgs sector of our model consists of three doublets: Φ = (φ, φ) with charge 0 and η1,2 = (η + 1,2, η 0 1,2) with charge ±1 under U(1)X . The mass matrix spanning X and Z is then given by MXZ =   2g X(v 2 1 + v 2 2) gXgZ(v 2 1 − v 2) gXgZ(v 2 1 − v 2) (g Z/2)(v2 0 + v 1 + v 2)   , (2) where v0 ≡ 〈φ0〉 and v 1,2 ≡ 〈η0 1,2〉 with v 0 + v 1 + v 2 = (2 √ 2GF ) . Assuming that v1 ≃ v2 so that the X − Z mixing is small, we then have M Z ≃ 1 2 g Z(v 2 0 + 2v 2 1), M 2 X ≃ 4g Xv2 1, (3) with the X − Z mixing angle given by sin θ ≃ gXgX(v 2 1 − v 2) M X −M2 Z . (4) The effective νμ and ν̄μ interactions with quarks has the same structure as the SM, but the effective strength is changed from g Z/M 2 Z to g Z ( cos θ M Z + sin θ M X ) − 2gXgZ sin θ cos θ (