Anomalous $WWZ$ couplings and $K_L\rightarrow \mu^+ \mu^-$

We study contributions to $K_L \rightarrow \mu^+\mu^-$ from anomalous $WWZ$ interactions. There are, in general, seven anomalous couplings. Among the seven anomalous couplings, only two of them contribute significantly. The others are suppressed by factors like $m_s^2/M_W^2$, $m_d^2$, or $m_K^2/M_W^2$. Using the experimental data on $K_L\rightarrow \mu^+\mu^-$, we obtain strong bounds on the two anomalous couplings.