Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons

Abstract

The hadronic charmless B decays into a scalar meson and a pseudoscalar meson are studied within the framework of QCD factorization. Although the light scalar mesons $f_0(980)$ and $a_0(980)$ are widely perceived as primarily the four-quark bound states, in practice it is difficult to make quantitative predictions based on the four-quark picture for light scalars. Hence, predictions are made in the 2-quark model for the scalar mesons. Based on the QCD sum rule method, we have derived the leading-twist light-cone distribution amplitudes of scalar mesons and their decay constants. The short-distance approach suffices to explain the observed large rates of $f_0(980)K^{-}$ and $f_0(980){\bar{K}}^0$ that receive major penguin contributions from the $b\to ss\bar{s}$ process. When $f_0(980)$ is assigned as a four-quark bound state, there exist extra diagrams contributing to $B\to f_0(980)K$. Therefore, a priori the $f_0(980)K$ rate is not necessarily suppressed for a four-quark state $f_0(980)$. The calculated ${\bar{B}}^0\to a_0^{+}(980){\pi }^{-}$ and $a_0^{+}(980)K^{-}$ rates exceed slightly the current experimental limits. If the branching ratio of ${\bar{B}}^0\to a_0^{+}(1450){\pi }^{-}$ is measured at the level of $(4\sim 6)\times 10^{-6}$ while $a_0^{+}(980){\pi }^{-}$ is found to be smaller, say, of order $(1\sim 2)\times 10^{-6}$ or even smaller than this, it will be likely to imply a 2-quark nature for $a_0(1450)$ and a four-quark assignment for $a_0(980)$. The penguin-dominated modes $a_0(980)K$ and $a_0(1450)K$ receive dominant weak annihilation contributions.

Comments: 42 pages and 5 figures. Form factors for B to excited scalar mesons are calculated, signs are flipped for the decay constants of excited states (Appendix B), Tables 5 to 9 are revised. Version to appear in PRD