Abstract
In the article, we assume the two scalar nonet mesons below and above 1 GeV are all $\bar{q}q$ states, in case I, the scalar mesons below 1 GeV are the ground states, in case II, the scalar mesons above 1 GeV are the ground states. We calculate the $B-S$ form-factors by taking into account the perturbative ${\mathcal{O}}(\alpha_s)$ corrections to the twist-2 terms using the light-cone QCD sum rules and fit the numerical values of the form-factors into the single-pole forms, which have many phenomenological applications.
Highlights
The underlying structures of the scalar mesons are not well established theoretically, there are many candidates with the quantum numbers J PC = 0++ below 2 GeV, which cannot be accommodated in one qq nonet
We assume that the scalar mesons are all qq states, in case I, the scalar mesons below 1 GeV are the ground states, in case II, the scalar mesons above 1 GeV are the ground states; and study the B − S transition form-factors with the light-cone QCD sum rules (LCSR) [3,4,5]
From the Table, we can see that the perturbative O(αs) corrections are about (15–35) % and (5– 20) % for the B − S form-factors with the scalar mesons bellow and above 1 GeV, respectively, we should take them into account consistently
Summary
The underlying structures of the scalar mesons are not well established theoretically, there are many candidates with the quantum numbers J PC = 0++ below 2 GeV, which cannot be accommodated in one qq nonet Speaking, they can be calcified into two nonets, the nonet { f0(600), a0(980), κ(800), f0(980)} below 1 GeV and the nonet { f0(1370), a0(1450), K. The transition form-factors in the semi-leptonic decays depend on the dynamics of strong interactions among the quarks in the initial and final mesons, and depend on the structures of the involved mesons. The B − S transition form-factors have been calculated with the LCSR [9,10,11,12], the three-point QCD sum rules [13,14,15], the perturbative QCD [16], the light front quark model
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