Large non-factorizable contributions in $B\to a_0{a}_0$ decays

Abstract

We investigate three tree-dominated $B\to a_0{a}_0$ decays for the first time in the perturbative QCD(pQCD) approach at leading order in the standard model, with $a_0$ standing for the light scalar $a_0(980)$ state, which is assumed as a meson based on the model of conventional two-quark$(q\bar{q})$ structure. All the topologies of the Feynman diagrams such as the non-factorizable spectator ones and the annihilation ones are calculated in the pQCD approach. It is of great interest to find that, contrary to the known $B\to \pi \pi$ decays, the $B\to a_0{a}_0$ decays are governed by the large non-factorizable contributions, which give rise to the large $B\to a_0{a}_0$ decay rates in the order of $10^{-6}\sim 10^{-5}$, although the $a_0$ meson has an extremely small vector decay constant $f_{a_0}$. Also observed are large direct CP-violating asymmetries around $15\%$ and $30\%$ for the $B^0\to a_0^0{a}_0^0$ and $a_0^{+}{a}_0^{-}$ modes. These sizable predictions could be easily examined at the running Large Hadron Collider and the near future Super-B/Belle-II experiments. The future precision measurements combined with these pQCD predictions might be helpful to explore the complicated QCD dynamics and the inner structure of the light scalar $a_0$, as well as to complementarily constrain the unitary angle $\alpha$.

Comments: 17 pages, 3 figures, and 2 tables; references added, contents improved, to appear in JPG, matching the published version