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

The $B^0_{s,d} \to J/ψη^{(\prime)}$ decays provide new terrain for exploring CP violation. After briefly discussing $η$-$η'$ 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 $B^0_{s,d}\to J/ψη^{(\prime)}$ 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 $B^0_{s,d} \to J/ψη$ system, and predict the $B^0_d\to J/ψη'$ branching ratio at the $5\times10^{-6}$ level. Furthermore, we present strategies for the determination of the $η$-$η'$ mixing parameters from the $B^0_{s,d} \to J/ψη^{(\prime)}$ observables. We also observe that the $B^0_{s,d} \to J/ψη$ and $B^0_{s,d} \to J/ψη'$ decays are - from a formal point of view - analogous to the quark-antiquark and tetraquark descriptions of the $f_0(980)$ in the $B^0_{s,d} \to J/ψf_0(980)$ channels, respectively.

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