Branching ratios and polarization inB→VV,VA,AAdecays

Abstract

We present a detailed study of charmless two-body $B$ decays into final states involving two vector mesons ($VV$) or two axial-vector mesons ($AA$) or one vector and one axial-vector meson ($VA$), within the framework of QCD factorization, where $A$ is either a $^{3}P_{1}$ or $^{1}P_{1}$ axial-vector meson. The main results are as follows. (i) In the presence of next-to-leading-order nonfactorizable corrections, effective Wilson coefficients ${a}_{i}^{h}$ are helicity-dependent. For some penguin-dominated modes, the constructive (destructive) interference in the negative-helicity (longitudinal-helicity) amplitude of the $\overline{B}\ensuremath{\rightarrow}VV$ decay will render the former comparable to the latter and push up the transverse polarization. (ii) In QCD factorization, the transverse polarization fraction can be large for penguin-dominated charmless $VV$ modes by allowing for sizable penguin-annihilation contributions. (iii) Using the measured ${\overline{K}}^{*0}{\ensuremath{\rho}}^{\ensuremath{-}}$ channel as an input, we predict the branching ratios and polarization fractions for other $\overline{B}\ensuremath{\rightarrow}{\overline{K}}^{*}\ensuremath{\rho}$ decays. (iv) The smallness of the axial-vector decay constant of the $^{1}P_{1}$ axial-vector meson can be tested by measuring various ${b}_{1}\ensuremath{\rho}$ modes to see if $\ensuremath{\Gamma}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{\ensuremath{-}}{\ensuremath{\rho}}^{+})\ensuremath{\ll}\ensuremath{\Gamma}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{+}{\ensuremath{\rho}}^{\ensuremath{-}})$ and $\ensuremath{\Gamma}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{b}_{1}^{\ensuremath{-}}{\ensuremath{\rho}}^{0})\ensuremath{\ll}\ensuremath{\Gamma}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{b}_{1}^{0}{\ensuremath{\rho}}^{\ensuremath{-}})$. (v) For the penguin-dominated modes ${a}_{1}{K}^{*}$ and ${b}_{1}{K}^{*}$, it is found that the former are dominated by transverse polarization amplitudes, whereas the latter are governed by longitudinal polarization states. (vi) The rates of $B\ensuremath{\rightarrow}{K}_{1}(1270){K}^{*}$ and ${K}_{1}(1400){K}^{*}$ are generally very small. The decay modes ${K}_{1}^{\ensuremath{-}}{K}^{*+}$ and ${K}_{1}^{+}{K}^{*\ensuremath{-}}$ are of particular interest as they are the only $AV$ modes which receive contributions solely from weak annihilation. (vii) For tree-dominated $B\ensuremath{\rightarrow}AA$ decays, the ${a}_{1}^{+}{a}_{1}^{\ensuremath{-}}$, ${a}_{1}^{\ensuremath{-}}{a}_{1}^{0}$, ${a}_{1}^{\ensuremath{-}}{b}_{1}^{+}$, ${a}_{1}^{\ensuremath{-}}{b}_{1}^{0}$, ${b}_{1}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${b}_{1}^{0}{\ensuremath{\rho}}^{\ensuremath{-}}$ modes have sizable branching ratios, of order $(20--40)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. (viii) There are many penguin-dominated $B\ensuremath{\rightarrow}AA$ decays within the reach of $B$ factories: ${K}_{1}(1270)({a}_{1},{b}_{1}^{\ifmmode\pm\else\textpm\fi{}})$, ${K}_{1}(1400)({b}_{1},{a}_{1}^{\ifmmode\pm\else\textpm\fi{}})$, ${K}_{1}(1270)({f}_{1}(1285),{f}_{1}(1420))$ and ${K}_{1}(1400)({f}_{1}(1420),{h}_{1}(1170))$.