CP Violation in $B_{(s)}\toφK$ Decays: Standard Model Benchmarks and Isospin-Breaking New Physics

Abstract

The penguin loop-suppressed $B\toφK$ decays are highly sensitive to contributions of hypothetical heavy new particles. Particularly interesting probes for testing the Standard Model and revealing such phenomena are provided by CP violation in the $B^0_d\toφK_{\rm S}$ decay. Standard-Model estimates for the corresponding CP-violating observables are theoretically limited by doubly Cabibbo-suppressed penguin contributions. We study these effects using a factorization approach, and provide predictions for CP asymmetries, to be contrasted with future measurements. To gain additional insight into these hadronic effects, we propose the $B_s^0\toφK_{\rm S}$ decay as a new channel. We predict the observables for this decay for which currently no measurements exist. By comparing $B^0_d\toφK_{\rm S}$ and $B^+ \to φK^+$, we further derive state-of-the-art constraints on isospin observables within the Standard Model. The same framework enables probing of possible New-Physics contributions, including general effects and those with non-trivial isospin structure. Interesting prospects arise for the high-precision era of flavour physics ahead.

Figures (9)

• Figure 1: SM topologies contributing to $B\to\phi K$ processes via $b\to s$ quark transitions, where $B=B^+,B_d^0$ and $K=K^+,K^0$ for $q=u,d$, respectively.
• Figure 2: Illustration of penguin matrix elements of the $\mathcal{O}_2^q$ current--current operator contributions to the $B_d^0\to\phi K^0$ decay.
• Figure 3: Contributions to the $B_s^0 \to \phi K_S$ decay in which the $B_s^0$ meson hadronizes into a $\phi$ meson: QCD penguin topology in the full SM (left) and penguin contraction of the current$–-$current operator $\mathcal{O}_2^q$ in the low-energy effective Hamiltonian (right).
• Figure 4: Hadronic parameters $b|_{\rm incl}$ and $\theta$ as functions of the squared momentum of the virtual gluon or photon. The red-shaded regions cover the allowed parameter ranges associated with the physical momentum range $1/4<k^2/m_b^2<1/2$Gerard:1988jj.
• Figure 5: Correlations between the $B_d^0 \to \phi K_S$ hadronic penguin parameters (left), and the direct CP asymmetry with the hadronic phase shift (right), obtained by varying the virtual gluon and photon momenta over the range $0<k^2<m_b^2$. The red regions indicate the physical range $1/4<k^2/m_b^2<1/2$, while the green stars denote momentum fractions $k^2/m_b^2 = \{1,0.5, 0.4, 0.35, 0.25, 0.15\}$, as indicated.