| Summary: | Abstract There are two sources that help to explain the $$\text {R}_\text {K}$$ R K , $$\text {R}_{\text {K}^*}$$ R K ∗ anomalies in the MF331 model. The first is non-LFUV couplings of the new neutral gauge boson $$\text {Z}^{\prime }$$ Z ′ with leptons, $$\text {g}^{\text {Z}^\prime }(e)\ne \text {g}^{\text {Z}^\prime }(\mu ,\tau )$$ g Z ′ ( e ) ≠ g Z ′ ( μ , τ ) , which causes the $$\text {R}_\text {K}$$ R K , $$\text {R}_{\text {K}^*}$$ R K ∗ anomalies via $$\text {Z}^\prime $$ Z ′ -penguin diagrams involving newly charged gauge bosons $$\text {X}^{\pm }_{\mu }$$ X μ ± , and exotic U-quarks. The second is the contribution from the box diagram only for the first generation of leptons. We show that the penguin diagrams can not explain $$\text {R}_\text {K}$$ R K , $$\text {R}_{\text {K}^*}$$ R K ∗ anomalies, and that the box diagram is required. The experimental constraints for $$\text {R}_\text {K}$$ R K and $$\text {R}_{\text {K}^*}$$ R K ∗ result in new particle mass degeneracy. The contributions of NP to the branching ratios $$\text {Br}(\text {B}_{\text {s}}\rightarrow \mu ^+ \mu ^-), \text {Br}(\text {b}\rightarrow s \gamma )$$ Br ( B s → μ + μ - ) , Br ( b → s γ ) predict results that agree with the experimental limits in the allowed region of the NP scale.
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