Charmless Hadronic B Decays into a Tensor Meson

Abstract

Two-body charmless hadronic B decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Due to the G-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and anti-quark in the SU(3) limit. Our main results are: (i) In the naive factorization approach, the decays such as $B^{-}\to {\bar{K}}_2^{\ast 0}{\pi }^{-}$ and ${\bar{B}}^0\to K_2^{\ast -}{\pi }^{+}$ with a tensor meson emitted are prohibited owing to the fact that a tensor meson cannot be created from the local V-A or tensor current. Nevertheless, they receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of $B^{-}\to {\bar{K}}_2^{\ast 0}{\pi }^{-}$ indicates the importance of nonfactorizable effects. (ii) For penguin-dominated $B\to TP$ and $TV$ decays, the predicted rates in naive factorization are usually too small by one to two orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions.(iii) The dominant penguin contributions to $B\to K_2^{\ast }{\eta }^{{(}^{\prime })}$ arise from the processes: (a) $b\to ss\bar{s}\to s{\eta }_s$ and (b) $b\to sq\bar{q}\to q{\bar{K}}_2^{\ast }$ with ${\eta }_q=(u\bar{u}+d\bar{d})/\sqrt{2}$ and ${\eta }_s=s\bar{s}$. The interference, constructive for $K_2^{\ast }{\eta }^{\prime }$ and destructive for $K_2^{\ast }\eta$, explains why $\Gamma (B\to K_2^{\ast }{\eta }^{\prime })\gg \Gamma (B\to K_2^{\ast }\eta )$.

43 pages, 1 figure

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