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The long-awaited $B_s\to \mu^+\mu^-$ mode has finally been observed at rateconsistent with Standard Model, albeit lower by 1.2$\sigma$. There is some hintfor New Physics in the rarer $B_d^0 \to \mu^+\mu^-$ decay, especially if thecurrently 2.2$\sigma$-enhanced central value persists with more data. Themeasurement of $CP$ violating phase $\phi_s$, via both $B_s\to J/\psi K\bar K$and $J/\psi\pi\pi$ modes, has reached Standard Model sensitivity. Thesemeasurements stand major improvement when LHC enters Run 2. Concurrently, the$K_L\to\pi^0\nu\bar\nu$ and $K^+\to\pi^+\nu\bar\nu$ modes are being pursued ina similar time frame. We illustrate the possible correlations between NewPhysics effects in these four modes, using the fourth generation as example.While correlations may or may not exist in other New Physics models, the fourgeneration model can accommodate enhancements in both $B_d^0 \to \mu^+\mu^-$and $K_L\to\pi^0\nu\bar\nu$.

Correlating $B_q^0 \to \mu^+\mu^-$ and $K_L \to \pi^0\nu\bar\nu$ Decays with Four Generations