Lessons from LHCb and Belle II measurements of $B\to J/\psi \pi$ and $B\to J/\psi K$ decays

Abstract

The LHCb collaboration has recently measured the CP asymmetry in $B^+\to J/\psi\pi^+$ decay, while the Belle II collaboration has recently measured the CP asymmetries in $B^0\to J/\psi\pi^0$ decay. Within the Standard Model, and using flavor-$SU(3)$ relations including first-order breaking corrections, these measurements lead to new predictions with regard to CP violation in $B^+\to J/\psi K^+$ and $B_s\to J/\psi\overline{K}{}^0$ decays, the difference between $S_{\psi K_S}$ and $\sin2\beta$, and the rate and CP asymmetries in $B_s\to J/\psi\pi^0$ decay.