$a_0(1450)$-state twist-2 light-cone distribution amplitude moments within QCD sum rules and its implication in $\bar B^0\to a_0(1450)^+\ell^-\bar\nu_\ell$ decays

Abstract

Based on longstanding puzzle for the structure of light scalar meson, it is meaningful to make a deep research for its property in different decay processes especially in the bottom meson semileptonic decays. The current experimental and theoretical predictions are inclined to the quark-antiquark state in $B$-decays, which is also the basic starting point of this work. Firstly, the first five-order $a_0(1450)$-state leading-twist distribution amplitude $\xi$-moments are calculated by using the QCD sum rule within background field theory, which all the gluon-condensate and quark-condensate are calculated up to full dimension-six accuracy. We present the their values up to nineth-order at initial scale. Then we construct $a_0(1450)$-state twist-2 LCDA with light-cone harmonic oscillator models as the scenario 1 (S1), where the model parameters are determined by fitting the first five odd $\xi$-moments using the least squares method. On the other hand, the truncated form of Gegenbauer polynomials expansion up to second-order is also considered as the scenario 2 (S2) to make a comparison, where the relationship between Gegenbauer moments and LCDA moments are considered. Subsequently, we calculated the $\bar{B}^0 \to a_0(1450)^+$ transition form factors (TFFs) by using the light-cone sum rules approach, incorporating contributions from both twist-2 and twist-3 LCDAs. By extrapolating TFFs to the entire physical $q^2$-region with simplified series expansion, the differential decay width and branching ratios for the $\bar B^0\to a_0(1450)^+\ell^-\bar\nu_\ell$ semileptonic decay are obtained. Finally, we present three angular observables including forward-backward asymmetry, lepton polarization asymmetry and $q^2$-differential flat term.