Exploring CP Violation and $\eta$-$\eta'$ Mixing with the $B^0_{s,d} \to J/\psi \eta^{(\prime)}$ Systems

The $B^0_{s,d} \to J/\psi \eta^{(\prime)}$ decays provide new terrain for exploring CP violation. After briefly discussing $\eta$-$\eta'$ mixing, we analyse the effective lifetimes and CP-violating observables of the $B_s$ channels, which allow us to probe New-Physics effects in $B^0_s$-$\bar B^0_s$ mixing. We have a critical look at these observables and show how hadronic corrections can be controlled by means of the $B_d$ decays. Using measurements of the $B^0_{s,d}\to J/\psi \eta^{(\prime)}$ branching ratios by the Belle collaboration, we discuss tests of the $SU(3)_F$ flavour symmetry of strong interactions, obtain the first constraints on the hadronic parameters entering the $B^0_{s,d} \to J/\psi \eta$ system, and predict the $B^0_d\to J/\psi \eta'$ branching ratio at the $5\times10^{-6}$ level. Furthermore, we present strategies for the determination of the $\eta$-$\eta'$ mixing parameters from the $B^0_{s,d} \to J/\psi \eta^{(\prime)}$ observables. We also observe that the $B^0_{s,d} \to J/\psi \eta$ and $B^0_{s,d} \to J/\psi \eta'$ decays are - from a formal point of view - analogous to the quark-antiquark and tetraquark descriptions of the $f_0(980)$ in the $B^0_{s,d} \to J/\psi f_0(980)$ channels, respectively.