Abstract
We study a predictive model for explaining the apparent deviation of the muon anomalous magnetic moment from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Higgs; the only new particles at the TeV scale are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g − 2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g − 2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g − 2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizeable portion of parameter space already covered by direct searches at the LHC. The viable parameter space free of fine-tuning for the muon mass will be fully covered by future direct LHC searches, and all of the parameter space can be probed by precision measurements at planned future lepton colliders.
Highlights
If ∆mμ is a perturbative correction to the tree-level muon Yukawa coupling, ∆mμ ∼ α2mμ/(4π), the expected new particle masses are around M ∼ 100 GeV
We study a predictive model for explaining the apparent deviation of the muon anomalous magnetic moment from the Standard Model expectation
While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g − 2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR
Summary
We extend the SM by vector-like leptons L, Lc, S, and Sc. L/Lc have the same/opposite gauge charge as/to the SM lepton doublets and SSc are gauge singlets. We introduce the following Yukawa couplings and Dirac masses,. Where H is the SM Higgs, is the doublet containing the left-handed muon, and ec is the right-handed muon. One-loop quantum corrections given by figure 1 without the external photon lines generate a muon Yukawa coupling,. Where Λ is the cut-off scale of the theory. We describe the embedding of the setup into a “minimally split” supersymmetric theory with scalar masses around 100–1000 TeV scales, where the muon mass (together with the electron and tau masses) may be fully radiatively generated, but turn to the computation of (g − 2)μ
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