Revisiting charmless hadronic B decays to scalar mesons

Hadronic charmless B decays to scalar mesons are studied within the framework of QCD factorization (QCDF). Considering two different scenarios for scalar mesons above 1 GeV, we find that the data favor the scenario in which the scalars $a_0(1450)$ and $K_0^*(1430)$ are the lowest lying $q\bar q$ bound states. This in turn implies a preferred four-quark nature for light scalars below 1 GeV. Assuming $K_0^*(1430)$ being a lowest lying $q\bar s$ state, we show that the data of $B\to K_0^*(1430)η^{(')}$ and $B\to K_0^*(1430)(ρ,ω,ϕ)$ can be accommodated in QCDF without introducing power corrections induced from penguin annihilation, while the predicted $B^-\to \ov K_0^{*0}(1430)π^-$ and $\ov B^0\to K_0^{*-}(1430)π^+$ are too small compared to experiment. In principle, the data of $K_0^*(1430)π$ modes can be explained if penguin-annihilation induced power corrections are taken into account. However, this will destroy the agreement between theory and experiment for $B\to K_0^*(1430)(η^{(')},ρ,ω,ϕ)$. Contrary to the pseudoscalar meson sector where $B\to Kη'$ has the largest rate in 2-body decays of the $B$ meson, we show that $Br(B\to K_0^*η')<\B(B\to K_0^*η)$. The decay $\ov B^0\to a_0(980)^+K^-$ is found to have a rate much smaller than that of $\ov B^0\to a_0(980)^+π^-$ in QCDF, while it is the other way around in pQCD. Experimental measurements of these two modes will help discriminate between these two different approaches. Assuming 2-quark bound states for $f_0(980)$ and $f_0(500)$, the observed large rates of $f_0(980)K$ and $f_0(980)K^*$ modes can be explained in QCDF with the $f_0(980)\!-\!f_0(500)$ mixing angle $θ$ in the vicinity of $20^\circ$.

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