In Pursuit of New Physics with $B_d^0\to J/\psi K^0$ and $B_s^0\to J/\psi \varphi$ Decays at the High-Precision Frontier

Abstract

The decays $B_d^0\to J/\psi K_{\text{S}}^0$and $B_s^0\to J/\psi \varphi$ play a key role for the determination of the $B_q^0$-${\bar{B}}_q^0$ ($q=d,s$) mixing phases ${\varphi }_d$ and ${\varphi }_s$, respectively. The theoretical precision of the extraction of these quantities is limited by doubly Cabibbo-suppressed penguin topologies, which can be included through control channels by means of the $SU(3)$ flavour symmetry of strong interactions. Using the currently available data and a new simultaneous analysis, we discuss the state-of-the-art picture of these effects and include them in the extracted ${\varphi }_q$ values. We have a critical look at the Standard Model predictions of these phases and explore the room left for new physics. Considering future scenarios for the high-precision era of flavour physics, we illustrate that we may obtain signals for physics beyond the Standard Model with a significance well above five standard deviations. We also determine effective colour-suppression factors of $B_d^0\to J/\psi K^0$, $B_d^0\to J/\psi K_{\text{S}}^0$ and $B_d^0\to J/\psi {\pi }^0$ decays, which serve as benchmarks for QCD calculations of the underlying decay dynamics, and present a new method using information from semileptonic $B_d^0\to {\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ and $B_s^0\to K^{-}{\ell }^{+}{\nu }_{\ell }$ decays.

Comments: 33 pages, 13 figures, matches published version