$B\to J/\psi K$ Decays in QCD Factorization

Abstract

The hadronic decays $B\to J/\psi K(K^{\ast })$ are interesting because experimentally they are the only color-suppressed modes which have been measured, and theoretically they are calculable by QCD factorization even the emitted meson $J\psi$ is heavy. We analyze the decay $B\to J\psi K$ within the framework of QCD factorization in the heavy quark limit. We show explicitly the scale and ${\gamma }_5$-scheme independence of decay amplitudes and infrared safety of nonfactorizable corrections at twist-2 order. Leading-twist contributions from the light-cone distribution amplitudes (LCDAs) of the mesons are too small to accommodate the data; the nonfactorizable corrections to naive factorization are small and not significant. We study the twist-3 effects due to the kaon and find that the coefficient $a_2(J\psi K)$ is largely enhanced by the nonfactorizable spectator interactions arising from the twist-3 kaon LCDA ${\varphi }_{\sigma }^K$, which are formally power-suppressed but chirally, logarithmically and kinematically enhanced. Therefore, factorization breaks down at twist-3 order. Higher-twist effects of $J\psi$ are briefly discussed. Our result also resolves the long-standing sign ambiguity of $a_2(J\psi K)$, which turns out to be positive for its real part.

18 pages, 2 figures. Typos in Eqs.(3.4), (3.5), and (3.6) are corrected

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