What can we learn from $B\to a_1(1260)(b_1(1235))\ddot{I}€(K)$ decays?

Abstract

We investigate the $B\to a_1(1260)(b_1(1235))\ddot{I}€(K)$ decays under the factorization scheme and find many discrepancies between theoretical predictions and the experimental data. In the tree dominated processes, large contributions from color-suppressed tree diagrams are required in order to accommodate with the large decay rates of $B^{-}\to a_1^0\ddot{I}{€}^{-}$ and $B^{-}\to a_1^{-}\ddot{I}{€}^0$. For ${\bar{B}}^0\to (a_1^{+},b_1^{+})K^{-}$ decays which are both induced by $b\to s$ transition, theoretical predictions on their decay rates are larger than the data by a factor of 2.8 and 5.5, respectively. Large electro-weak penguins or some new mechanism are expected to explain the branching ratios of $B^{-}\to b_1^0{K}^{-}$ and $B^{-}\to a_1^{-}{\bar{K}}^0$. The soft-collinear-effective-theory has the potential to explain large decay rates of $B^{-}\to a_1^0\ddot{I}{€}^{-}$ and $B^{-}\to a_1^{-}\ddot{I}{€}^0$ via a large hard-scattering form factor $\hat{I}{\P }_J^{B\to a_1}$. We will also show that, with proper charming penguins, predictions on the branching ratios of ${\bar{B}}^0\to (a_1^{+},b_1^{+})K^{-}$ can also be consistent with the data.

16 pages, no figure