Gauging lepton flavor SU(3) for the muon g − 2

Abstract

Gauging a specific difference of lepton numbers such as Lμ− Lτ is a popular model-building option, which gives rise to economical explanations for the muon anomalous magnetic moment. However, this choice of gauge group seems rather arbitrary, and additional physics is required to reproduce the observed neutrino masses and mixings. We address these shortcomings by embedding Lμ− Lτ in the vectorial SU(3) gauge symmetry of lepton flavor. The vacuum expectation values (VEVs) of scalar fields in the fundamental, six-dimensional and adjoint representations allow for phenomenologically viable lepton and gauge boson masses. The octet scalar gives rise to charged lepton masses, and together with the triplet scalar generates masses for all the leptophilic gauge bosons except for the Lμ− Lτ one. The latter gets its smaller mass from the sextet VEVs, which also generate the neutrino masses, and are determined up to an overall scaling by the observed masses and mixings. The model predicts three heavy neutral leptons at the GeV-TeV scale as well as vectorlike charged lepton partners; it requires the mass of the lightest active neutrino to exceed 10−4 eV, and it naturally provides a resolution of the Cabibbo angle anomaly.

Snowmass White Paper: Flavor Model Building

“…The constraints on the Z depend on how it couples to the other SM fermions. The gauged L µ − L τ in general faces the least severe constraints [166,[178][179][180][244][245][246][247][248][249]. Other examples include flavor violating ALPs [250], from photonic couplings of ALPs [251][252][253], or from ALP with a dark photon [254].…”

Snowmass White Paper: New flavors and rich structures in dark sectors

“…2 shows current bounds on the two models discussed, above, i.e., the vector and scalar mediated models that can explain ∆a µ . The left panel shows constraints on the gauged L µ − L τ model in the parameter space of the Z (commonly denote also as X) gauge boson mass, m X , and the gauge coupling g X [69,[123][124][125][126][127][128][129][130][131]. The parameter region that leads to the explanation of (g − 2) µ is within solid green lines, with the dashed line denoting the central value.…”

“…The next generations of experiments (dotted lines) are expected to explore fully the parameter space relevant for (g − 2) µ . Note that there are other anomaly free gauged U (1) X models that can explain the (g − 2) µ anomaly, however, L µ − L τ is the least constrained [69,119,[123][124][125][126][127][128][129][130][131].…”