Abstract
We present an analysis of two isovector scalar resonant contributions to the $B$ decays into charmonia plus $K\bar K$ or $\pi\eta$ pair in the perturbative QCD approach. The Flatt\'{e} model for the $a_0(980)$ resonance and the Breit Wigner formula for the $a_0(1450)$ resonance are adopted to parametrize the timelike form factors in the dimeson distribution amplitudes, which capture the important final state interactions in these processes. The predicted distribution in the $K^+K^-$ invariant mass as well as its integrated branching ratio for the $a_0(980)$ resonance in the $B^0\rightarrow J/\psi K^+K^-$ mode agree well with the current available experimental data. The obtained branching ratio of the quasi-two-body decay $B^0\rightarrow J/\psi a_0(980)(\rightarrow \pi^0\eta)$ can reach the order of $10^{-6}$, letting the corresponding measurement appear feasible. For the $a_0(1450)$ component, our results could be tested by further experiments in the LHCb and Belle II. We also discuss some theoretical uncertainties in detail in our calculation.
Highlights
Many scalar mesons with quantum numbers JP 1⁄4 0þ have been well established in the experiment [1]
We mainly focus on the isovector scalar resonances a0ð980Þ and a0ð1450Þ in the B → ψðKK ; πηÞ decays with charmonia ψ 1⁄4 J=ψ; ψð2SÞ, while the corresponding Bs decay modes are forbidden because the sspair that has I 1⁄4 0 and does not allow the isovector resonance production upon hadronization
The resulting decay amplitudes A are equivalent to previous calculations in Ref. [39] by replacing the S-wave ππ form factor with the corresponding KKðπηÞ one in Eq (12)
Summary
Many scalar mesons with quantum numbers JP 1⁄4 0þ have been well established in the experiment [1]. Two important low-lying scalar resonances, namely, isoscalar f0ð980Þ and isovector a0ð980Þ, are of special interest Their almost degenerate masses would lead to a mixing with each other through isospin violating effects [2,3,4,5]. Several B decays involving scalar mesons have been observed, either with an f0ð980Þ [6,7] or a0ð980Þ [8] in the final state. More general review about the use of the chiral unitary approach to study the final-state strong interactions in weak decays, one refer to [25] for details It is found both f0ð980Þ and a0ð980Þ resonances contribute to the B0 → J=ψ KþK−, while only the f0ð980Þ [a0ð980Þ] resonance influences the distribution in Bs → J=ψKþK− (B0 → J=ψπ0η).
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