Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the $B \rightarrow S$ transition form factors

Abstract

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons a0, K * 0 and f0 within the QCD sum rules. The QCD sum rules are improved by a consistent treatment of the sizable s-quark mass effects within the framework of the background field approach. Adopting the valence quark component (q1q2) as the dominant structure of the scalar mesons, our estimation for their masses are close to the measured a0(1450), K * 0 (1430) and f0 (1710). From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs φ s,σ a 0 : ξ

$$B-S$$ B - S transition form-factors with the light-cone QCD sum rules

“…In Tables 4, 5, 6, 7, we present the B − S transition formfactors from the LCSR [9][10][11][12], the three-point QCD sum rules [13][14][15], and also the results without perturbative O(α s ) corrections in the LCSR. From the Table, we can see that the perturbative O(α s ) 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.…”

“…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 [17], etc. In Refs.…”

“…In Refs. [9][10][11][12], the B − S form-factors are calculated with the LCSR in the leading order approximation, the perturbative O(α s ) corrections are neglected. Due to the lengthy calculations, only perturbative O(α s ) corrections to the twist-2 and twist-3 terms in the LCSR for the B − P, V form-factors [18][19][20][21][22][23][24][25][26] and perturbative O(α 2 s ) corrections to the twist-2 terms in the LCSR for the B − π form-factor [27] are studied up to now, where the P and V denote the light pseudoscalar and vector mesons, respectively.…”

Revisiting the pion leading-twist distribution amplitude within the QCD background field theory

“…The present results for µ = 1 GeV are obtained by first get the DA behavior with the help of the moments at µ = M and apply the pion DA running equation [3] to run the DA from µ = M to µ = 1 GeV, and then get the moments at µ = 1 GeV. Using those moments (36,37,38), together with the formulas (27,28,29), we can obtain the Gegenbauer moments a (1 GeV) = 0.24 ± 0.14 ± 0.08 [22] and 0.20 ± 0.03 [23]. A LCSR analysis on the pion transition form factor gives a π 2 (1 GeV) = 0.24 ± 0.14 ± 0.08 [22], 0.19 ± 0.05 [18], 0.32 [19], 0.44 [20] and 0.27 [21].…”

“…The QCD sum rules within the background field theory has already been adopted to study the meson properties, cf.Refs. [33][34][35][36][37][38].…”