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TeV scale horizontal gauge symmetry and its implications in B-physics

We propose a gauged $U(1)_{H}$ horizontal symmetry around TeV scale that is a subgroup of a $SU(3)_{H}$ horizontal gauge symmetry broken at ${\cal O}(10^{14}) \GeV$. The breaking generates right-handed Majorana neutrino masses through a $SU(3)_H$ sextet scalar. A particular Majorana right-handed neutrino mass matrix explicitly determines the remnant $U(1)_{H}$ at low energy which only couples to $b-s$ and $μ-τ$ in the gauge eigenstate. The dangerous $K-\bar{K}$, $D-\bar{D}$ mixing and $B_s \rightarrow μ^+ μ^-$ are kept to be safe because the relevant couplings are suppressed through high powers of small mixing angles in the fermion rotation matrix. Our analysis which applies to the general case shows that the Tevatron di-muon anomaly can be explained through the $B_{s}$ and $B_{d}$ mixing while keeping all the other experimental constraints within 90 \% C. L. For the $B$ meson decay, the $B_{s}\to μ^{\pm}τ^{\mp}$ is the leading leptonic decay channel which is several orders of magnitude below current experimental bound.