Anatomy of $B^0_{s,d} \to J/\psi f_0(980)$

The $B^0_s\to J/\psi f_0(980)$ decay offers an interesting experimental alternative to the well-known $B^0_s\to J/\psi \phi$ channel for the search of CP-violating New-Physics contributions to $B^0_s$--$\bar B^0_s$ mixing. As the hadronic structure of the $f_0(980)$ has not yet been settled, we take a critical look at the implications for the relevant observables and address recent experimental data. It turns out that the effective lifetime of $B^0_s\to J/\psi f_0(980)$ and its mixing-induced CP asymmetry $S$ are quite robust with respect to hadronic effects and thereby allow us to search for a large CP-violating $B^0_s$--$\bar B^0_s$ mixing phase $\phi_s$, which is tiny in the Standard Model. However, should small CP violation, i.e. in the range $-0.1\lsim S\lsim 0$, be found in $B^0_s\to J/\psi f_0(980)$, it will be crucial to constrain hadronic corrections in order to distinguish possible New-Physics effects from the Standard Model. We point out that $B^0_d\to J/\psi f_0(980)$, which has not yet been measured, is a key channel in this respect and discuss the physics potential of this decay.