Lessons from LHCb and Belle II measurements of $B\to J/ψπ$ and $B\to J/ψK$ decays

TL;DR

The paper uses flavor-$SU(3)$ relations with first-order breaking to relate six $B_q\to J/\psi P$ decay amplitudes, enabling predictions for yet-unmeasured CP-violating observables once CKM inputs are fixed. By combining recent LHCb and Belle II measurements with the $SU(3)$ framework, it derives predictions for direct and indirect CP asymmetries, decay-rate ratios, and a lower bound on $\mathcal{B}(B_s\to J/\psi\pi^0)$, as well as a consistency check on $\sin2\beta$ via multiple relations. The results show current data are broadly consistent with the SM CKM mechanism and aim to sharpen CKM determinations, while highlighting where improved measurements—especially of $S^s_{\psi K_S}$, $C^s_{\psi K_S}$, and $S^d_{\psi K_S}$—could reveal higher-order effects or tensions. The work provides a roadmap for leveraging the six decay channels to perform high-precision tests of CP violation and SM flavor dynamics as experimental precision advances.

Abstract

The LHCb collaboration has recently measured the CP asymmetry in $B^+\to J/ψπ^+$ decay, while the Belle II collaboration has recently measured the CP asymmetries in $B^0\to J/ψπ^0$ 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 $B^+\to J/ψK^+$ and $B_s\to J/ψ\overline{K}{}^0$ decays, the difference between $S_{ψK_S}$ and $\sin2β$, and the rate and CP asymmetries in $B_s\to J/ψπ^0$ decay.