Penguin contributions to CP phases in $B_{d,s}$ decays to charmonium

Abstract

The precision of the CP phases $2\beta$ and $2{\beta }_s$ determined from the mixing-induced CP asymmetries in $B_d\to J/\psi K_S$ and $B_s\to J/\psi \varphi$, respectively, is limited by the unknown long-distance contribution of a penguin diagram involving up quarks. The penguin contribution is expected to be comparable in size to the precision of the LHCb and Belle II experiments and therefore limits the sensitivity of the measured quantities to new physics. We analyze the infrared QCD structure of this contribution and find that all soft and collinear divergences either cancel between different diagrams or factorize into matrix elements of local four-quark operators up to terms suppressed by ${\Lambda }_{QCD}/m_{\psi }$, where $m_{\psi }$ denotes the $J/\psi$ mass. Our results, which are based on an operator product expansion, allow us to calculate the penguin-to-tree ratio $P/T$ in terms of the matrix elements of these operators and to constrain the penguin contribution to the phase $2\beta$ as $|\Delta {\varphi }_d|\le {0.68}^{\circ }$. The penguin contribution to $2{\beta }_s$ is bounded as $|\Delta {\varphi }_s^0|\le {0.97}^{\circ }$, $|\Delta {\varphi }_s^{\parallel }|\le {1.22}^{\circ }$, and $|\Delta {\varphi }_s^{\perp }|\le {0.99}^{\circ }$ for the case of longitudinal, parallel, and perpendicular $\varphi$ and $J/\psi$ polarizations, respectively. We further place bounds on $|\Delta {\varphi }_d|$ for $B_d\to \psi (2S)K_S$ and the polarization amplitudes in $B_d\to J/\psi K^{\ast }$. In our approach it is further possible to constrain $P/T$ for decays in which $P/T$ is Cabibbo-unsuppressed and we derive upper limits on the penguin contribution to the mixing-induced CP asymmetries in $B_d\to J/\psi {\pi }^0$, $B_d\to J/\psi {\rho }^0$, $B_s\to J/\psi K_S$, and $B_s\to J/\psi K^{\ast }$. For all studied decay modes we also constrain the sizes of the direct CP asymmetries.

typo in Eqs. (2) and (3) corrected, references updated.Matches version published in PRL

References in corpus (9)

• Branching Ratio Measurements of $B_s$ Decays
• Measurement of the resonant and CP components in ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• The Golden Modes B^0 -> J/psi K_{S,L} in the Era of Precision Flavour Physics
• Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes
• B, Bs -> K form factors: an update of light-cone sum rule results
• Measurement of the CP-violating phase $\beta$ in $B^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays and limits on penguin effects
• Extrapolation and unitarity bounds for the $B\to \pi$ form factor
• Measurement of the $B_s^0\to J/\psi K^{\ast 0}$ branching fraction and angular amplitudes
• $B\to \rho$ semileptonic decays and $|V_{ub}|$

Cited by in corpus (36)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Patterns of Flavour Violation in Models with Vector-Like Quarks
• Yukawa enhancement of $Z$-mediated New Physics in $\Delta S=2$ and $\Delta B=2$ Processes
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• Direct and indirect signals of natural composite Higgs models
• CP Violation in $D^0\to K_S{K}_S$
• Hadronic effects and observables in $B\to \pi {\ell }^{+}{\ell }^{-}$ decay at large recoil
• The CKM Parameters
• 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
• CP violation in the B system
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• Measurement of $CP$ violation parameters and polarisation fractions in $B_s^0\to J/\psi {\overline{K}}^{\ast 0}$ decays
• Towards more precise determinations of the CKM phase $\beta$
• Measurement of CP violation in $B^0\to \psi (\to {\ell }^{+}{\ell }^{-})K_S^0(\to {\pi }^{+}{\pi }^{-})$ decays
• Measurement of $CP$ violation in $B^0\to D^{+}{D}^{-}$ decays
• Branching ratios, $CP$ asymmetries and polarizations of $B\to \psi (2S)V$ decays
• Measurement of the branching fraction and $CP$ asymmetry in $B^{+}\to J/\psi {\rho }^{+}$ decays
• Measurement of the branching fraction and time-dependent $CP$ asymmetry for $B^0\to J/\psi {\pi }^0$ decays
• Theoretical Prospects for B Physics
• Experimental Status of the CKM Matrix
• Prospect for measurement of the CP-violating phase ${\varphi }_s$ in the $B_s\to J/\psi \varphi$ channel at a future Z factory
• How to tame penguins: Advancing to high-precision measurements of ${\varphi }_d$ and ${\varphi }_s$
• Impact of systematic and amplitude model correlations within and between systems of combined input: A case study with ${\varphi }_2$ ($\alpha$)
• Probing quantum decoherence at Belle II and LHCb
• Mixing and mixing-related CP violation in the B system
• CP violation and CKM studies (and first LHCb Run II results)
• Measurement of the B${}_{\mathrm{s}}^0$ $\to$ J/$\psi$K${}_{\mathrm{S}}^0$ effective lifetime from proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Theory Motivation: What measurements are needed?
• $CP$ violation in heavy-flavour hadrons
• Measurement of $CP$ violation in $B^0\to J/\psi K_{\mathrm{S}}^0$ and $B^0\to \psi (2S)K_{\mathrm{S}}^0$ decays
• Summary of CKM 2016 Working Group 4 : mixing and mixing-related $CP$ violation in the $B$ system
• $B^0-{\bar{B}}^0$ entanglement for an ideal experiment on the direct CP violation ${\varphi }_3/\gamma$ phase
• Observation of $CP$ violation in $B^0\to J/\psi \rho (770{)}^0$ decays
• CP Violation in the $B_s^0$ system