Flavor dependence of annihilation parameters in QCD factorization

TL;DR

This paper investigates the flavor dependence of annihilation parameters in QCD factorization for B meson decays, highlighting potential large symmetry breaking effects that impact new physics searches.

Contribution

It challenges the assumption of universal annihilation parameters across different decay modes, emphasizing the importance of flavor symmetry breaking effects in B meson decay analyses.

Findings

Flavor symmetry breaking effects are small in $B_{d,s} o ext{pseudoscalar} ext{pseudoscalar}$ decays.

Large flavor symmetry breaking effects are possible in $B_{d,s} o ext{vector} ext{vector}$ decays.

Careful consideration of flavor symmetry breaking is crucial in new physics searches in B decays.

Abstract

For $B_{d,s} \to \pi^\mp K^\pm$ and $K^{(\ast)} K^{(\ast)}$ decays, the flavor symmetry breaking effects may be particularly small since the final state interactions should be the same between the corresponding $B_d$ and $B_s$ decays due to the charge conjugation symmetry of the final states. This is consistent with the newly measured direct CP asymmetry of $B_s \to \pi^+ K^-$. These decays are thus supposed to be important in testing the Standard Model and in probing new physics effects. However, the observation of pure annihilation decay $B_s \to \pi^+ \pi^-$ appears to imply a large annihilation scenario with $\rho_A \sim 3$, in contrast to the case of $\rho_A \sim 1$ in $B_{u,d}$ decays in the framework of QCD factorization. This seems to indicate unexpectedly large flavor symmetry breaking effects between the annihilation amplitudes of $B_s$ and $B_{u,d}$ decays. This apparent contradiction could be resolved by noticing that there is a priori no reason to justify the common practice of assuming the universality of annihilation parameters for different Dirac structures of effective operators. We then argue that, for $B_{d,s} \to \pi^\mp K^\pm$ decays, the flavor symmetry breaking effects of annihilation amplitudes have all been included in the initial state decay constants and are thus small. But the flavor symmetry breaking effects in $B_{d,s} \to K^{(\ast)} K^{(\ast)}$ decays are likely to be much larger, as part of the annihilation topologies of $B_s \to K K$ decay could be related to $B_s \to \pi^+ \pi^-$ decay. Therefore when new physics effects are searched for in these decay channels, care must be taken to consider the potentially large flavor symmetry breaking effects in more details.