Power corrections in charmless nonleptonic $B$ decays: Annihilation is factorizable and real
Christian M. Arnesen, Zoltan Ligeti, Ira Z. Rothstein, and Iain W. Stewart

\vspace*{0.2cm} We classify $\Lambda_{\rm QCD}/m_b$ power corrections to nonleptonic $B\to M_1 M_2$ decays, where $M_{1,2}$ are charmless non-isosinglet mesons. Using recent developments in soft-collinear effective theory, we prove that the leading contributions to annihilation amplitudes of order $\alpha_s(m_b) \Lambda_{\rm QCD}/m_b$ are real. The leading annihilation amplitudes depend on twist-2 and the twist-3 three parton distributions. A complex nonperturbative parameter from annihilation first appears at ${\cal O}\big[\alpha_s^2(\sqrt{\Lambda m_b})\Lambda_{\rm QCD}/m_b \big]$. ``Chirally enhanced'' contributions are also factorizable and real at lowest order. Thus, incalculable strong phases are suppressed in annihilation amplitudes, unless the $\alpha_s(\sqrt{\Lambda m_b})$ expansion breaks down. Modeling the distribution functions, we find that $(11\pm 9)\%$ and $(15\pm 11)\%$ of the absolute values of the measured $\bar B^0\to K^-\pi^+$ and $B^-\to K^-K^0$ penguin amplitudes come from annihilation. This is consistent with the expected size of power corrections.

© 2008 The American Physical Society.