Penguin Effects in $\phi_{d,s}$ Determinations

Abstract

The theoretical precision of the measurement of the $B^0_{d,s}$-$\bar B^0_{d,s}$ mixing phases $\phi_{d,s}$ through the benchmark decays $B^0_d\to J/\psi K_S$, $B^0_s\to J/\psi \phi$ and $B^0_s\to J/\psi f_0(980)$ is limited by doubly Cabibbo-suppressed penguin topologies which are usually neglected. However, the search for New-Physics effects in the quark-flavor sector has entered a territory where these effects have to be taken into account, which will be particularly relevant for the LHCb upgrade era. Thanks to their non-perturbative nature, the penguin corrections cannot be calculated but have rather to be controlled through experimental data. An overview of the picture of the penguin parameters originating from the current data for $B_{(s)}\to J/\psi \pi, J/\psi K$ decays and the physics potential of the control channels $B^0_s\to J/\psi K_{\rm S}$, $B^0_s\to J/\psi \bar K^{*0}$ and $B_d^0\to J/\psi f_0(980)$ is given, emphasizing also the usefulness of effective $B_s$ decay lifetimes.