Rescattering Contributions to rare B-Meson Decays

Abstract

Several $B$ and $B_s$ decays have been observed which have been cited as evidence for exchange ($E$), penguin annihilation ($PA$) and annihilation ($A$) processes, such as $\bar{b}d\to \bar{u}u$, $\bar{b}s\to \bar{u}u$ and $\bar{b}u\to W^{\ast }\to \bar{c}s$, respectively. These amplitudes are normally thought to be suppressed, as they involve the spectator quark in the weak interaction and thus should be proportional to the $B$-meson decay constant $f_B$. However, as pointed out a number of years ago, they can also be generated by rescattering from processes whose amplitudes do not involve $f_B$, such as color-favored tree amplitudes. In this paper we investigate a number of processes such as $B^0\to K^{+}{K}^{-}$, $B_s\to {\pi }^{+}{\pi }^{-}$, and $B^{+}\to D_s^{+}\varphi$, and identify promising states from which they can be generated by rescattering. We find that $E$ and $PA$-type processes are characterized respectively by amplitudes ranging from 5% to 10% and from 15% to 20% with respect to the largest amplitude from which they can rescatter. Based on this regularity, using approximate flavor SU(3) symmetry in some cases and time-reversal invariance in others, we predict the branching fractions for a large number of as-yet-unseen $B$ and $B_s$ decays in an extensive range from order $10^{-9}$ to $10^{-4}$.

Note, two references and acknowledgement added

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• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Measurements of Branching Fractions and Direct CP Asymmetries for B -> K pi, B->pi pi and B->to KK Decays
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• First evidence for the annihilation decay mode $B^{+}\to D_s^{+}\varphi$

Cited by in corpus (19)

• U-spin breaking in CP asymmetries in B decays
• CP violation in the B system
• Standard Model Predictions and New Physics Sensitivity in B->DD Decays
• Flavor dependence of annihilation parameters in QCD factorization
• Observation of the annihilation decay mode $B^0\to K^{+}{K}^{-}$
• First observations of ${\bar{B}}_s^0\to D^{+}{D}^{-}$, $D_s^{+}{D}^{-}$ and $D^0{\bar{D}}^0$ decays
• Study of $CP$ Violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays in the QCD factorization approach
• Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization
• Charm Penguin in $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$: partonic and hadronic loops
• Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays
• Non-leptonic decays of Charmed mesons into two Pseudoscalars
• Fits of Weak Annihilation and Hard Spectator Scattering Corrections in $B_{u,d}\to VV$ Decays
• Estimating $r_B^{D\pi }$ as an input to the determination of the CKM angle $\gamma$
• Search for the decay Bs -> D*-+ π+-
• Study of localized $CP$ violation in $B^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}$ and the branching ratio of $B^{-}\to \sigma (600){\pi }^{-}$ in the QCD factorization approach
• Revisiting Final State Interaction in Charmless $B_q\to PP$ Decays
• Charm rescattering contribution in rare $B_c^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decay
• Observation of the $B_s^0\to D^{\ast \pm }{D}^{\mp }$ decay
• Search for the decay $B_s^0\to {\pi }^0{\pi }^0$ at Belle