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

Abstract

The $B_{s,d}^0\to J/\psi {\eta }^{(\prime )}$ decays provide new terrain for exploring CP violation. After briefly discussing $\eta$-${\eta }^{\prime }$ mixing, we analyse the effective lifetimes and CP-violating observables of the $B_s$ channels, which allow us to probe New-Physics effects in $B_s^0$-${\bar{B}}_s^0$ 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 $B_{s,d}^0\to J/\psi {\eta }^{(\prime )}$ 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 $B_{s,d}^0\to J/\psi \eta$ system, and predict the $B_d^0\to J/\psi {\eta }^{\prime }$ branching ratio at the $5\times 10^{-6}$ level. Furthermore, we present strategies for the determination of the $\eta$-${\eta }^{\prime }$ mixing parameters from the $B_{s,d}^0\to J/\psi {\eta }^{(\prime )}$ observables. We also observe that the $B_{s,d}^0\to J/\psi \eta$ and $B_{s,d}^0\to J/\psi {\eta }^{\prime }$ decays are - from a formal point of view - analogous to the quark-antiquark and tetraquark descriptions of the $f_0(980)$ in the $B_{s,d}^0\to J/\psi f_0(980)$ channels, respectively.

Comments: 17 pages, 3 figures