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Charmless hadronic B decays into a tensor meson

2011; American Physical Society; Volume: 83; Issue: 3 Linguagem: Inglês

10.1103/physrevd.83.034001

1550-7998

Hai-Yang Cheng, Kwei-Chou Yang,

High-Energy Particle Collisions Research

Two-body charmless hadronic $B$ decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Because of 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 antiquark in the SU(3) limit. Our main results are: (i) In the na\"{\i}ve factorization approach, the decays such as ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{K}}_{2}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}_{2}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}$ with a tensor meson emitted are prohibited because a tensor meson cannot be created from the local $V\ensuremath{-}A$ or tensor current. Nevertheless, the decays receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{K}}_{2}^{*0}{\ensuremath{\pi}}^{\ensuremath{-}}$ indicates the importance of nonfactorizable effects. (ii) For penguin-dominated $B\ensuremath{\rightarrow}TP$ and $TV$ decays, the predicted rates in na\"{\i}ve factorization are usually too small by 1 to 2 orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions. (iii) The dominant penguin contributions to $B\ensuremath{\rightarrow}{K}_{2}^{*}{\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}$ arise from the processes: (a) $b\ensuremath{\rightarrow}ss\overline{s}\ensuremath{\rightarrow}s{\ensuremath{\eta}}_{s}$ and (b) $b\ensuremath{\rightarrow}sq\overline{q}\ensuremath{\rightarrow}q{\overline{K}}_{2}^{*}$ with ${\ensuremath{\eta}}_{q}=(u\overline{u}+d\overline{d})/\sqrt{2}$ and ${\ensuremath{\eta}}_{s}=s\overline{s}$. The interference, constructive for ${K}_{2}^{*}{\ensuremath{\eta}}^{\ensuremath{'}}$ and destructive for ${K}_{2}^{*}\ensuremath{\eta}$, explains why $\ensuremath{\Gamma}(B\ensuremath{\rightarrow}{K}_{2}^{*}{\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\gg}\ensuremath{\Gamma}(B\ensuremath{\rightarrow}{K}_{2}^{*}\ensuremath{\eta})$. (iv) We use the measured rates of $B\ensuremath{\rightarrow}{K}_{2}^{*}(\ensuremath{\omega},\ensuremath{\phi})$ to extract the penguin-annihilation parameters ${\ensuremath{\rho}}_{A}^{TV}$ and ${\ensuremath{\rho}}_{A}^{VT}$ and the observed longitudinal polarization fractions ${f}_{L}({K}_{2}^{*}\ensuremath{\omega})$ and ${f}_{L}({K}_{2}^{*}\ensuremath{\phi})$ to fix the phases ${\ensuremath{\phi}}_{A}^{VT}$ and ${\ensuremath{\phi}}_{A}^{TV}$. (v) The experimental observation that ${f}_{T}/{f}_{L}\ensuremath{\ll}1$ for $B\ensuremath{\rightarrow}{K}_{2}^{*}(1430)\ensuremath{\phi}$, whereas ${f}_{T}/{f}_{L}\ensuremath{\sim}1$ for $B\ensuremath{\rightarrow}{K}_{2}^{*}(1430)\ensuremath{\omega}$ with ${f}_{T}$ being the transverse polarization fraction, can be accommodated in QCDF, but it cannot be dynamically explained at first place. For penguin-dominated $B\ensuremath{\rightarrow}TV$ decays, we find ${f}_{L}({K}_{2}^{*}\ensuremath{\rho})\ensuremath{\sim}{f}_{L}({K}_{2}^{*}\ensuremath{\omega})\ensuremath{\sim}0.65$, whereas ${f}_{L}({K}^{*}{f}_{2})\ensuremath{\sim}0.93$. It will be of great interest to measure ${f}_{L}$ for these modes to test QCDF. Theoretically, transverse polarization is expected to be small in tree-dominated $\overline{B}\ensuremath{\rightarrow}TV$ decays except for the ${a}_{2}^{\ensuremath{-}}{\ensuremath{\rho}}^{0}$, ${a}_{2}^{\ensuremath{-}}{\ensuremath{\rho}}^{+}$, ${K}_{2}^{*0}{K}^{*\ensuremath{-}}$ and ${K}_{2}^{*0}{\overline{K}}^{*0}$ modes. (vi) For tree-dominated decays, their rates are usually very small except for the ${a}_{2}^{0}({\ensuremath{\pi}}^{\ensuremath{-}},{\ensuremath{\rho}}^{\ensuremath{-}})$, ${a}_{2}^{+}({\ensuremath{\pi}}^{\ensuremath{-}},{\ensuremath{\rho}}^{\ensuremath{-}})$ and ${f}_{2}({\ensuremath{\pi}}^{\ensuremath{-}},{\ensuremath{\rho}}^{\ensuremath{-}})$ modes with branching fractions of order ${10}^{\ensuremath{-}6}$ or even larger.