How to tame penguins: Advancing to high-precision measurements of ${\varphi }_d$ and ${\varphi }_s$

Abstract

The complex phases ${\varphi }_d$ and ${\varphi }_s$, associated with the mixing between neutral $B_q^0$ and ${\bar{B}}_q^0$ mesons ($q\in \{d,s\}$), are key observables to test the Standard Model and search for contributions from new physics. They are conventionally determined from the measurements of mixing-induced CP violation in the decays $B_d^0\to J/\psi K^0$, $B_s^0\to J/\psi \varphi$ and $B_s^0\to D_s^{+}{D}_s^{-}$. To reach the highest possible precision on ${\varphi }_d$ and ${\varphi }_s$, it is crucial that corrections from next-to-leading order effects - primarily associated with penguin decay topologies - are accounted for. The strategy adopted in this paper uses the $SU(3)$ flavour symmetry of QCD to relate the unknown contributions from penguin topologies to their counterparts in suitably-chosen control modes, where their effects are enhanced. Utilising new CP asymmetry measurements from LHCb on the decays $B_s^0\to D_s^{+}{D}_s^{-}$, $B_d^0\to D^{+}{D}^{-}$, $B^{+}\to J/\psi K^{+}$ and $B^{+}\to J/\psi {\pi }^{+}$, as well as from Belle-II on the decay $B_d^0\to J/\psi {\pi }^0$, we present the current state-of-the-art picture on controlling the penguin contributions and extract ${\varphi }_d$ and ${\varphi }_s$ from the corresponding observables. We explore the prospects for the end of the Belle-II and HL-LHC flavour physics programmes, and demonstrate the importance of measuring the control modes with future data.

35 pages, 13 figures, published version

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