Correlating Bq0→μ+μ− and KL→π0νν¯ decays with four generations

The Bs→μ+μ−Bs→μ+μ− mode has finally been observed, albeit at rate 1.2σ   below Standard Model (SM) value, while the rarer Bd0→μ+μ− decay has central value close to 4 times SM expectation but with only 2.2σ significance. The measurement of CP   violating phase ϕsϕs has finally reached SM sensitivity. Concurrent with improved measurements at LHC Run 2, KL→π0νν¯ and K+→π+νν¯ decays are being pursued in a similar time frame. We find, whether Bd0→μ+μ− is enhanced or not, KL→π0νν¯ can be enhanced up to the Grossman–Nir bound in the fourth generation model, correlated with some suppression of Bs→μ+μ−Bs→μ+μ−, and with ϕsϕs remaining small.